2.2 Solve Equations using the Division and Multiplication Properties of Equality
Learning objectives.
By the end of this section, you will be able to:
 Solve equations using the Division and Multiplication Properties of Equality
 Solve equations that require simplification
 Translate to an equation and solve
 Translate and solve applications
Be Prepared 2.5
Before you get started, take this readiness quiz.
Simplify: −7 ( 1 −7 ) . −7 ( 1 −7 ) . If you missed this problem, review Example 1.68 .
Be Prepared 2.6
Evaluate 9 x + 2 9 x + 2 when x = −3 x = −3 . If you missed this problem, review Example 1.57 .
Solve Equations Using the Division and Multiplication Properties of Equality
You may have noticed that all of the equations we have solved so far have been of the form x + a = b x + a = b or x − a = b x − a = b . We were able to isolate the variable by adding or subtracting the constant term on the side of the equation with the variable. Now we will see how to solve equations that have a variable multiplied by a constant and so will require division to isolate the variable.
Let’s look at our puzzle again with the envelopes and counters in Figure 2.5 .
In the illustration there are two identical envelopes that contain the same number of counters. Remember, the left side of the workspace must equal the right side, but the counters on the left side are “hidden” in the envelopes. So how many counters are in each envelope?
How do we determine the number? We have to separate the counters on the right side into two groups of the same size to correspond with the two envelopes on the left side. The 6 counters divided into 2 equal groups gives 3 counters in each group (since 6 ÷ 2 = 3 6 ÷ 2 = 3 ).
What equation models the situation shown in Figure 2.6 ? There are two envelopes, and each contains x x counters. Together, the two envelopes must contain a total of 6 counters.
If we divide both sides of the equation by 2, as we did with the envelopes and counters,  
we get: 
We found that each envelope contains 3 counters. Does this check? We know 2 · 3 = 6 2 · 3 = 6 , so it works! Three counters in each of two envelopes does equal six!
This example leads to the Division Property of Equality .
The Division Property of Equality
For any numbers a , b , and c , and c ≠ 0 c ≠ 0 ,
When you divide both sides of an equation by any nonzero number, you still have equality.
Manipulative Mathematics
The goal in solving an equation is to ‘undo’ the operation on the variable. In the next example, the variable is multiplied by 5, so we will divide both sides by 5 to ‘undo’ the multiplication.
Example 2.13
Solve: 5 x = −27 . 5 x = −27 .
To isolate , “undo” the multiplication by 5.  
Divide to ‘undo’ the multiplication.  
Simplify.  
Check:  
Substitute for  
Since this is a true statement, is the solution to . 
Try It 2.25
Solve: 3 y = −41 . 3 y = −41 .
Try It 2.26
Solve: 4 z = −55 . 4 z = −55 .
Consider the equation x 4 = 3 x 4 = 3 . We want to know what number divided by 4 gives 3. So to “undo” the division, we will need to multiply by 4. The Multiplication Property of Equality will allow us to do this. This property says that if we start with two equal quantities and multiply both by the same number, the results are equal.
The Multiplication Property of Equality
For any numbers a , b , and c ,
If you multiply both sides of an equation by the same number, you still have equality.
Example 2.14
Solve: y −7 = −14 . y −7 = −14 .
Here y y is divided by −7 −7 . We must multiply by −7 −7 to isolate y y .
Multiply both sides by .  
Multiply.  
Simplify.  
Check:  
Substitute .  
Divide. 
Try It 2.27
Solve: a −7 = −42 . a −7 = −42 .
Try It 2.28
Solve: b −6 = −24 . b −6 = −24 .
Example 2.15
Solve: − n = 9 . − n = 9 .
Remember is equivalent to .  
Divide both sides by .  
Divide.  
Notice that there are two other ways to solve . We can also solve this equation by multiplying both sides by and also by taking the opposite of both sides.  
Check:  
Substitute .  
Simplify. 
Try It 2.29
Solve: − k = 8 . − k = 8 .
Try It 2.30
Solve: − g = 3 . − g = 3 .
Example 2.16
Solve: 3 4 x = 12 . 3 4 x = 12 .
Since the product of a number and its reciprocal is 1, our strategy will be to isolate x x by multiplying by the reciprocal of 3 4 3 4 .
Multiply by the reciprocal of .  
Reciprocals multiply to 1.  
Multiply.  
Notice that we could have divided both sides of the equation by to isolate . While this would work, most people would find multiplying by the reciprocal easier.  
Check:  
Substitute .  
Try It 2.31
Solve: 2 5 n = 14 . 2 5 n = 14 .
Try It 2.32
Solve: 5 6 y = 15 . 5 6 y = 15 .
In the next example, all the variable terms are on the right side of the equation. As always, our goal in solving the equation is to isolate the variable.
Example 2.17
Solve: 8 15 = − 4 5 x . 8 15 = − 4 5 x .
Multiply by the reciprocal of .  
Reciprocals multiply to 1.  
Multiply.  
Check:  
Let .  
Try It 2.33
Solve: 9 25 = − 4 5 z . 9 25 = − 4 5 z .
Try It 2.34
Solve: 5 6 = − 8 3 r . 5 6 = − 8 3 r .
Solve Equations That Require Simplification
Many equations start out more complicated than the ones we have been working with.
With these more complicated equations the first step is to simplify both sides of the equation as much as possible. This usually involves combining like terms or using the distributive property.
Example 2.18
Solve: 14 − 23 = 12 y − 4 y − 5 y . 14 − 23 = 12 y − 4 y − 5 y .
Begin by simplifying each side of the equation.
Simplify each side.  
Divide both sides by .  
Check:  
Substitute .  
Try It 2.35
Solve: 18 − 27 = 15 c − 9 c − 3 c . 18 − 27 = 15 c − 9 c − 3 c .
Try It 2.36
Solve: 18 − 22 = 12 x − x − 4 x . 18 − 22 = 12 x − x − 4 x .
Example 2.19
Solve: −4 ( a − 3 ) − 7 = 25 . −4 ( a − 3 ) − 7 = 25 .
Here we will simplify each side of the equation by using the distributive property first.
Distribute.  
Simplify.  
Simplify.  
Divide both sides by to isolate .  
Divide.  
Check:  
Substitute .  
Try It 2.37
Solve: −4 ( q − 2 ) − 8 = 24 . −4 ( q − 2 ) − 8 = 24 .
Try It 2.38
Solve: −6 ( r − 2 ) − 12 = 30 . −6 ( r − 2 ) − 12 = 30 .
Now we have covered all four properties of equality—subtraction, addition, division, and multiplication. We’ll list them all together here for easy reference.
Properties of Equality
When you add, subtract, multiply, or divide the same quantity from both sides of an equation, you still have equality.
Translate to an Equation and Solve
In the next few examples, we will translate sentences into equations and then solve the equations. You might want to review the translation table in the previous chapter.
Example 2.20
Translate and solve: The number 143 is the product of −11 −11 and y .
Begin by translating the sentence into an equation.
Translate.  
Divide by .  
Simplify.  
Check: 
Try It 2.39
Translate and solve: The number 132 is the product of −12 and y .
Try It 2.40
Translate and solve: The number 117 is the product of −13 and z .
Example 2.21
Translate and solve: n n divided by 8 is −32 −32 .
Begin by translating the sentence into an equation. Translate.  
Multiple both sides by 8.  
Simplify.  
Check:  Is divided by 8 equal to −32?  
Let .  Is divided by equal to ?  
Translate.  
Simplify. 
Try It 2.41
Translate and solve: n n divided by 7 is equal to −21 −21 .
Try It 2.42
Translate and solve: n n divided by 8 is equal to −56 −56 .
Example 2.22
Translate and solve: The quotient of y y and −4 −4 is 68 68 .
Translate.  
Multiply both sides by .  
Simplify.  
Check:  Is the quotient of and equal to ?  
Let .  Is the quotient of and equal to ?  
Translate.  
Simplify. 
Try It 2.43
Translate and solve: The quotient of q q and −8 −8 is 72.
Try It 2.44
Translate and solve: The quotient of p p and −9 −9 is 81.
Example 2.23
Translate and solve: Threefourths of p p is 18.
Begin by translating the sentence into an equation. Remember, “of” translates into multiplication.
Translate.  
Multiply both sides by  
Simplify.  
Check:  Is threefourths of equal to 18?  
Let  Is threefourths of 24 equal to 18?  
Translate.  
Simplify. 
Try It 2.45
Translate and solve: Twofifths of f f is 16.
Try It 2.46
Translate and solve: Threefourths of f f is 21.
Example 2.24
Translate and solve: The sum of threeeighths and x x is onehalf.
Translate.  
Subtract from each side.  
Simplify and rewrite fractions with common denominators.  
Simplify.  
Check:  Is the sum of threeeighths and equal to onehalf?  
Is the sum of threeeighths and oneeighth equal to onehalf?  
Translate.  
Simplify.  
Simplify. 
Try It 2.47
Translate and solve: The sum of fiveeighths and x is onefourth.
Try It 2.48
Translate and solve: The sum of threefourths and x is fivesixths.
Translate and Solve Applications
To solve applications using the Division and Multiplication Properties of Equality, we will follow the same steps we used in the last section. We will restate the problem in just one sentence, assign a variable, and then translate the sentence into an equation to solve.
Example 2.25
Denae bought 6 pounds of grapes for $10.74. What was the cost of one pound of grapes?
What are you asked to find?  The cost of 1 pound of grapes 
Assign a variable.  Let = the cost of one pound. 
Write a sentence that gives the information to find it.  The cost of 6 pounds is $10.74. 
Translate into an equation.  
Solve.  
The grapes cost $1.79 per pound.  
Check: If one pound costs $1.79, do 6 pounds cost #10.74? 
Try It 2.49
Translate and solve:
Arianna bought a 24pack of water bottles for $9.36. What was the cost of one water bottle?
Try It 2.50
At JB’s Bowling Alley, 6 people can play on one lane for $34.98. What is the cost for each person?
Example 2.26
Andreas bought a used car for $12,000. Because the car was 4years old, its price was 3 4 3 4 of the original price, when the car was new. What was the original price of the car?
What are you asked to find?  The original price of the car 
Assign a variable.  Let = the original price. 
Write a sentence that gives the information to find it.  $12,000 is of the original price. 
Translate into an equation.  
Solve.  
The original cost of the car was $16,000.  
Check: Is of $16,000 equal to $12,000? 
Try It 2.51
The annual property tax on the Mehta’s house is $1,800, calculated as 15 1,000 15 1,000 of the assessed value of the house. What is the assessed value of the Mehta’s house?
Try It 2.52
Stella planted 14 flats of flowers in 2 3 2 3 of her garden. How many flats of flowers would she need to fill the whole garden?
Section 2.2 Exercises
Practice makes perfect.
In the following exercises, solve each equation using the Division and Multiplication Properties of Equality and check the solution.
8 x = 56 8 x = 56
7 p = 63 7 p = 63
−5 c = 55 −5 c = 55
−9 x = −27 −9 x = −27
−809 = 15 y −809 = 15 y
−731 = 19 y −731 = 19 y
−37 p = −541 −37 p = −541
−19 m = −586 −19 m = −586
0.25 z = 3.25 0.25 z = 3.25
0.75 a = 11.25 0.75 a = 11.25
−13 x = 0 −13 x = 0
24 x = 0 24 x = 0
x 4 = 35 x 4 = 35
z 2 = 54 z 2 = 54
−20 = q −5 −20 = q −5
c −3 = −12 c −3 = −12
y 9 = −16 y 9 = −16
q 6 = −38 q 6 = −38
m −12 = 45 m −12 = 45
−24 = p −20 −24 = p −20
− y = 6 − y = 6
− u = 15 − u = 15
− v = −72 − v = −72
− x = −39 − x = −39
2 3 y = 48 2 3 y = 48
3 5 r = 75 3 5 r = 75
− 5 8 w = 40 − 5 8 w = 40
24 = − 3 4 x 24 = − 3 4 x
− 2 5 = 1 10 a − 2 5 = 1 10 a
− 1 3 q = − 5 6 − 1 3 q = − 5 6
− 7 10 x = − 14 3 − 7 10 x = − 14 3
3 8 y = − 1 4 3 8 y = − 1 4
7 12 = − 3 4 p 7 12 = − 3 4 p
11 18 = − 5 6 q 11 18 = − 5 6 q
− 5 18 = − 10 9 u − 5 18 = − 10 9 u
− 7 20 = − 7 4 v − 7 20 = − 7 4 v
In the following exercises, solve each equation requiring simplification.
100 − 16 = 4 p − 10 p − p 100 − 16 = 4 p − 10 p − p
−18 − 7 = 5 t − 9 t − 6 t −18 − 7 = 5 t − 9 t − 6 t
7 8 n − 3 4 n = 9 + 2 7 8 n − 3 4 n = 9 + 2
5 12 q + 1 2 q = 25 − 3 5 12 q + 1 2 q = 25 − 3
0.25 d + 0.10 d = 6 − 0.75 0.25 d + 0.10 d = 6 − 0.75
0.05 p − 0.01 p = 2 + 0.24 0.05 p − 0.01 p = 2 + 0.24
−10 ( q − 4 ) − 57 = 93 −10 ( q − 4 ) − 57 = 93
−12 ( d − 5 ) − 29 = 43 −12 ( d − 5 ) − 29 = 43
−10 ( x + 4 ) − 19 = 85 −10 ( x + 4 ) − 19 = 85
−15 ( z + 9 ) − 11 = 75 −15 ( z + 9 ) − 11 = 75
Mixed Practice
In the following exercises, solve each equation.
9 10 x = 90 9 10 x = 90
5 12 y = 60 5 12 y = 60
y + 46 = 55 y + 46 = 55
x + 33 = 41 x + 33 = 41
w −2 = 99 w −2 = 99
s −3 = −60 s −3 = −60
27 = 6 a 27 = 6 a
− a = 7 − a = 7
− x = 2 − x = 2
z − 16 = −59 z − 16 = −59
m − 41 = −14 m − 41 = −14
0.04 r = 52.60 0.04 r = 52.60
63.90 = 0.03 p 63.90 = 0.03 p
−15 x = −120 −15 x = −120
84 = −12 z 84 = −12 z
19.36 = x − 0.2 x 19.36 = x − 0.2 x
c − 0.3 c = 35.70 c − 0.3 c = 35.70
− y = −9 − y = −9
− x = −8 − x = −8
In the following exercises, translate to an equation and then solve.
187 is the product of −17 −17 and m .
133 is the product of −19 −19 and n .
−184 −184 is the product of 23 and p .
−152 −152 is the product of 8 and q .
u divided by 7 is equal to −49 −49 .
r divided by 12 is equal to −48 −48 .
h divided by −13 −13 is equal to −65 −65 .
j divided by −20 −20 is equal to −80 −80 .
The quotient c c and −19 −19 is 38.
The quotient of b b and −6 −6 is 18.
The quotient of h h and 26 is −52 −52 .
The quotient k k and 22 is −66 −66 .
Fivesixths of y is 15.
Threetenths of x is 15.
Fourthirds of w is 36.
Fivehalves of v is 50.
The sum of ninetenths and g is twothirds.
The sum of twofifths and f is onehalf.
The difference of p and onesixth is twothirds.
The difference of q and oneeighth is threefourths.
In the following exercises, translate into an equation and solve.
Kindergarten Connie’s kindergarten class has 24 children. She wants them to get into 4 equal groups. How many children will she put in each group?
Balloons Ramona bought 18 balloons for a party. She wants to make 3 equal bunches. How many balloons did she use in each bunch?
Tickets Mollie paid $36.25 for 5 movie tickets. What was the price of each ticket?
Shopping Serena paid $12.96 for a pack of 12 pairs of sport socks. What was the price of pair of sport socks?
Sewing Nancy used 14 yards of fabric to make flags for onethird of the drill team. How much fabric, would Nancy need to make flags for the whole team?
MPG John’s SUV gets 18 miles per gallon (mpg). This is half as many mpg as his wife’s hybrid car. How many miles per gallon does the hybrid car get?
Height Aiden is 27 inches tall. He is 3 8 3 8 as tall as his father. How tall is his father?
Real estate Bea earned $11,700 commission for selling a house, calculated as 6 100 6 100 of the selling price. What was the selling price of the house?
Everyday Math
Commission Every week Perry gets paid $150 plus 12% of his total sales amount over $1,250. Solve the equation 840 = 150 + 0.12 ( a − 1250 ) 840 = 150 + 0.12 ( a − 1250 ) for a , to find the total amount Perry must sell in order to be paid $840 one week.
Stamps Travis bought $9.45 worth of 49cent stamps and 21cent stamps. The number of 21cent stamps was 5 less than the number of 49cent stamps. Solve the equation 0.49 s + 0.21 ( s − 5 ) = 9.45 0.49 s + 0.21 ( s − 5 ) = 9.45 for s , to find the number of 49cent stamps Travis bought.
Writing Exercises
Frida started to solve the equation −3 x = 36 −3 x = 36 by adding 3 to both sides. Explain why Frida’s method will not solve the equation.
Emiliano thinks x = 40 x = 40 is the solution to the equation 1 2 x = 80 1 2 x = 80 . Explain why he is wrong.
ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.
ⓑ What does this checklist tell you about your mastery of this section? What steps will you take to improve?
This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission.
Want to cite, share, or modify this book? This book uses the Creative Commons Attribution License and you must attribute OpenStax.
Access for free at https://openstax.org/books/elementaryalgebra2e/pages/1introduction
 Authors: Lynn Marecek, MaryAnne AnthonySmith, Andrea Honeycutt Mathis
 Publisher/website: OpenStax
 Book title: Elementary Algebra 2e
 Publication date: Apr 22, 2020
 Location: Houston, Texas
 Book URL: https://openstax.org/books/elementaryalgebra2e/pages/1introduction
 Section URL: https://openstax.org/books/elementaryalgebra2e/pages/22solveequationsusingthedivisionandmultiplicationpropertiesofequality
© Jul 24, 2024 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.
Solving Equations by Multiplication and Division
Andymath.com features free videos, notes, and practice problems with answers! Printable pages make math easy. Are you ready to be a mathmagician?
Solve for x.
\(\textbf{1)}\) \( 4x=16 \) show answer the answer is \( x=4 \), \(\textbf{2)}\) \( 8x=48 \) show answer the answer is \( x=6 \), \(\textbf{3)}\) \( \frac{x}{4}=8 \) show answer the answer is \( x=32 \), \(\textbf{4)}\) \( \frac{x}{3}=14 \) show answer the answer is \( x=42 \), \(\textbf{5)}\) \( \frac{x}{2}=3 \) show answer the answer is \( x=6 \), \(\textbf{6)}\) \( 9x=3 \) show answer the answer is \( x=\frac{1}{3} \), see related pages\(\), \(\bullet\text{ equation calculator }\) \(\,\,\,\,\,\,\,\,\text{(symbolab.com)}\), \(\bullet\text{ solving equations by addition and subtraction}\) \(\,\,\,\,\,\,\,\,x+3=4…\), \(\bullet\text{ solving equations by multiplication and division}\) \(\,\,\,\,\,\,\,\,8x=48…\), \(\bullet\text{ solving multistep equations}\) \(\,\,\,\,\,\,\,\,3x+2=14…\), \(\bullet\text{ solving equations with variables on both sides}\) \(\,\,\,\,\,\,\,\,3x+5=7x3…\), \(\bullet\text{ solving equations with decimals}\) \(\,\,\,\,\,\,\,\,43.5+0.2x=51.1…\), \(\bullet\text{ solving equations with fractions}\) \(\,\,\,\,\,\,\,\,\frac{2}{5}x+\frac{2}{3}=\frac{8}{3}…\), solving equations by multiplication and division is a common technique used in algebra to find the value of an unknown variable. the definition of solving equations by multiplication and division is the process of isolating the variable by using the inverse operations of multiplication and division. this means that if the variable is being multiplied by a number, we can divide both sides of the equation by that number to solve for the variable. similarly, if the variable is being divided by a number, we can multiply both sides of the equation by that number to solve for the variable. we learn about solving equations by multiplication and division in math class because it is a fundamental skill that is necessary for solving more complex equations and problems in higher level math courses. it also helps us understand the concept of solving equations in general, which is a key skill in many realworld situations. solving equations by multiplication and division is typically taught in middle or high school algebra classes. one common mistake when solving equations by multiplication and division is forgetting to distribute the inverse operation to all of the terms on the side of the equation that you are working on. for example, if you are solving for x in the equation "2x = 6", and you divide both sides by 2, you must remember to divide the 2 in front of the x as well as the 6 on the right side of the equation. a fun fact about solving equations by multiplication and division is that this technique has been used for centuries to solve mathematical problems. in fact, ancient civilizations like the greeks and romans used similar methods to solve equations in their own ways. it is not clear who specifically discovered the technique of solving equations by multiplication and division, as this method has been used and developed over time by many mathematicians. however, the concept of solving equations can be traced back to ancient civilizations like the egyptians and babylonians. some related topics to solving equations by multiplication and division include algebraic expressions, linear equations, and inverse operations. understanding these concepts can help you become more proficient at solving equations by multiplication and division. 5 real world examples of solving equations by multiplication and division a recipe calls for 2 cups of flour to make a certain number of cookies. you want to make a batch that is three times as large, so you need 32= >6 cups of flour. a car gets an average of 25 miles per gallon of gas. you have a 15gallon tank and want to know how far you can drive on a full tank. you can drive 2515= >375 miles on a full tank. a store is offering a 20% discount on all clothing. if a shirt normally costs $50, how much will it cost with the discount the discounted price is 50*(1.2)= >40 dollars. you have a rectangular garden that is 30 feet long and 20 feet wide. you want to divide it into four equal sections with a pathway running down the middle. the width of the pathway is x. the total width of the four sections is 302x, and each section must be 20/4=5 feet wide. setting the two expressions equal, we have 302x=5, so x= >12.5 feet. a bag contains x red marbles and y blue marbles. the total number of marbles is 15, and the ratio of red marbles to blue marbles is 3:2. we can set up the equation 3x/(3+2)=15/(3+2), which simplifies to 3x=15 and x= >5. we can then solve for y by substituting this value back into the equation y=155= >10. there are 5 red marbles and 10 blue marbles in the bag. 5 other math topics that use solving equations by multiplication and division solving systems of equations: a system of equations is a set of two or more equations that are solved simultaneously. one common method for solving systems of equations is to use the elimination method, which involves multiplying or dividing one or both of the equations by a constant and then adding or subtracting the resulting equations to eliminate one of the variables. rational expressions: a rational expression is an expression that is the ratio of two polynomials. solving equations involving rational expressions often requires the use of the principle of crossmultiplication, which involves multiplying both sides of the equation by the denominator of the rational expression in order to clear the fraction. quadratic equations: a quadratic equation is an equation of the form ax^2 + bx + c = 0, where a, b, and c are constants. one common method for solving quadratic equations is the quadratic formula, which involves using the values of a, b, and c to calculate the two possible solutions for x. inequalities: an inequality is an expression that represents a relationship between two values that is not equal. solving inequalities often involves using the same techniques as those used to solve equations, such as multiplying or dividing both sides of the inequality by a constant or using the principle of crossmultiplication. proportions: a proportion is an equation that states that two ratios are equal. solving proportions often involves setting up a crossmultiplication equation and then solving for the unknown value., about andymath.com, andymath.com is a free math website with the mission of helping students, teachers and tutors find helpful notes, useful sample problems with answers including step by step solutions, and other related materials to supplement classroom learning. if you have any requests for additional content, please contact andy at [email protected] . he will promptly add the content. topics cover elementary math , middle school , algebra , geometry , algebra 2/precalculus/trig , calculus and probability/statistics . in the future, i hope to add physics and linear algebra content. visit me on youtube , tiktok , instagram and facebook . andymath content has a unique approach to presenting mathematics. the clear explanations, strong visuals mixed with dry humor regularly get millions of views. we are open to collaborations of all types, please contact andy at [email protected] for all enquiries. to offer financial support, visit my patreon page. let’s help students understand the math way of thinking thank you for visiting. how exciting.
 Skip to main content
 Skip to primary sidebar
 Skip to footer
Additional menu
Khan Academy Blog
Free Math Worksheets — Over 100k free practice problems on Khan Academy
Looking for free math worksheets.
You’ve found something even better!
That’s because Khan Academy has over 100,000 free practice questions. And they’re even better than traditional math worksheets – more instantaneous, more interactive, and more fun!
Just choose your grade level or topic to get access to 100% free practice questions:
Kindergarten, basic geometry, prealgebra, algebra basics, high school geometry.
 Trigonometry
Statistics and probability
High school statistics, ap®︎/college statistics, precalculus, differential calculus, integral calculus, ap®︎/college calculus ab, ap®︎/college calculus bc, multivariable calculus, differential equations, linear algebra.
 Addition and subtraction
 Place value (tens and hundreds)
 Addition and subtraction within 20
 Addition and subtraction within 100
 Addition and subtraction within 1000
 Measurement and data
 Counting and place value
 Measurement and geometry
 Place value
 Measurement, data, and geometry
 Add and subtract within 20
 Add and subtract within 100
 Add and subtract within 1,000
 Money and time
 Measurement
 Intro to multiplication
 1digit multiplication
 Addition, subtraction, and estimation
 Intro to division
 Understand fractions
 Equivalent fractions and comparing fractions
 More with multiplication and division
 Arithmetic patterns and problem solving
 Quadrilaterals
 Represent and interpret data
 Multiply by 1digit numbers
 Multiply by 2digit numbers
 Factors, multiples and patterns
 Add and subtract fractions
 Multiply fractions
 Understand decimals
 Plane figures
 Measuring angles
 Area and perimeter
 Units of measurement
 Decimal place value
 Add decimals
 Subtract decimals
 Multidigit multiplication and division
 Divide fractions
 Multiply decimals
 Divide decimals
 Powers of ten
 Coordinate plane
 Algebraic thinking
 Converting units of measure
 Properties of shapes
 Ratios, rates, & percentages
 Arithmetic operations
 Negative numbers
 Properties of numbers
 Variables & expressions
 Equations & inequalities introduction
 Data and statistics
 Negative numbers: addition and subtraction
 Negative numbers: multiplication and division
 Fractions, decimals, & percentages
 Rates & proportional relationships
 Expressions, equations, & inequalities
 Numbers and operations
 Solving equations with one unknown
 Linear equations and functions
 Systems of equations
 Geometric transformations
 Data and modeling
 Volume and surface area
 Pythagorean theorem
 Transformations, congruence, and similarity
 Arithmetic properties
 Factors and multiples
 Reading and interpreting data
 Negative numbers and coordinate plane
 Ratios, rates, proportions
 Equations, expressions, and inequalities
 Exponents, radicals, and scientific notation
 Foundations
 Algebraic expressions
 Linear equations and inequalities
 Graphing lines and slope
 Expressions with exponents
 Quadratics and polynomials
 Equations and geometry
 Algebra foundations
 Solving equations & inequalities
 Working with units
 Linear equations & graphs
 Forms of linear equations
 Inequalities (systems & graphs)
 Absolute value & piecewise functions
 Exponents & radicals
 Exponential growth & decay
 Quadratics: Multiplying & factoring
 Quadratic functions & equations
 Irrational numbers
 Performing transformations
 Transformation properties and proofs
 Right triangles & trigonometry
 Nonright triangles & trigonometry (Advanced)
 Analytic geometry
 Conic sections
 Solid geometry
 Polynomial arithmetic
 Complex numbers
 Polynomial factorization
 Polynomial division
 Polynomial graphs
 Rational exponents and radicals
 Exponential models
 Transformations of functions
 Rational functions
 Trigonometric functions
 Nonright triangles & trigonometry
 Trigonometric equations and identities
 Analyzing categorical data
 Displaying and comparing quantitative data
 Summarizing quantitative data
 Modeling data distributions
 Exploring bivariate numerical data
 Study design
 Probability
 Counting, permutations, and combinations
 Random variables
 Sampling distributions
 Confidence intervals
 Significance tests (hypothesis testing)
 Twosample inference for the difference between groups
 Inference for categorical data (chisquare tests)
 Advanced regression (inference and transforming)
 Analysis of variance (ANOVA)
 Scatterplots
 Data distributions
 Twoway tables
 Binomial probability
 Normal distributions
 Displaying and describing quantitative data
 Inference comparing two groups or populations
 Chisquare tests for categorical data
 More on regression
 Prepare for the 2020 AP®︎ Statistics Exam
 AP®︎ Statistics Standards mappings
 Polynomials
 Composite functions
 Probability and combinatorics
 Limits and continuity
 Derivatives: definition and basic rules
 Derivatives: chain rule and other advanced topics
 Applications of derivatives
 Analyzing functions
 Parametric equations, polar coordinates, and vectorvalued functions
 Applications of integrals
 Differentiation: definition and basic derivative rules
 Differentiation: composite, implicit, and inverse functions
 Contextual applications of differentiation
 Applying derivatives to analyze functions
 Integration and accumulation of change
 Applications of integration
 AP Calculus AB solved free response questions from past exams
 AP®︎ Calculus AB Standards mappings
 Infinite sequences and series
 AP Calculus BC solved exams
 AP®︎ Calculus BC Standards mappings
 Integrals review
 Integration techniques
 Thinking about multivariable functions
 Derivatives of multivariable functions
 Applications of multivariable derivatives
 Integrating multivariable functions
 Green’s, Stokes’, and the divergence theorems
 First order differential equations
 Second order linear equations
 Laplace transform
 Vectors and spaces
 Matrix transformations
 Alternate coordinate systems (bases)
Frequently Asked Questions about Khan Academy and Math Worksheets
Why is khan academy even better than traditional math worksheets.
Khan Academy’s 100,000+ free practice questions give instant feedback, don’t need to be graded, and don’t require a printer.
Math Worksheets  Khan Academy 

Math worksheets take forever to hunt down across the internet  Khan Academy is your onestopshop for practice from arithmetic to calculus 
Math worksheets can vary in quality from site to site  Every Khan Academy question was written by a math expert with a strong education background 
Math worksheets can have ads or cost money  Khan Academy is a nonprofit whose resources are always free to teachers and learners – no ads, no subscriptions 
Printing math worksheets use up a significant amount of paper and are hard to distribute during virtual learning  Khan Academy practice requires no paper and can be distributed whether your students are inperson or online 
Math worksheets can lead to cheating or a lack of differentiation since every student works on the same questions  Khan Academy has a full question bank to draw from, ensuring that each student works on different questions – and at their perfect skill level 
Math worksheets can slow down student learning since they need to wait for feedback  Khan Academy gives instant feedback after every answer – including hints and video support if students are stuck 
Math worksheets take up time to collect and take up valuable planning time to grade  Khan Academy questions are graded instantly and automatically for you 
What do Khan Academy’s interactive math worksheets look like?
Here’s an example:
What are teachers saying about Khan Academy’s interactive math worksheets?
“My students love Khan Academy because they can immediately learn from their mistakes, unlike traditional worksheets.”
Is Khan Academy free?
Khan Academy’s practice questions are 100% free—with no ads or subscriptions.
What do Khan Academy’s interactive math worksheets cover?
Our 100,000+ practice questions cover every math topic from arithmetic to calculus, as well as ELA, Science, Social Studies, and more.
Is Khan Academy a company?
Khan Academy is a nonprofit with a mission to provide a free, worldclass education to anyone, anywhere.
Want to get even more out of Khan Academy?
Then be sure to check out our teacher tools . They’ll help you assign the perfect practice for each student from our full math curriculum and track your students’ progress across the year. Plus, they’re also 100% free — with no subscriptions and no ads.
Get Khanmigo
The best way to learn and teach with AI is here. Ace the school year with our AIpowered guide, Khanmigo.
For learners For teachers For parents
Child Login
 Kindergarten
 Number charts
 Skip Counting
 Place Value
 Number Lines
 Subtraction
 Multiplication
 Word Problems
 Comparing Numbers
 Ordering Numbers
 Odd and Even
 Prime and Composite
 Roman Numerals
 Ordinal Numbers
 In and Out Boxes
 Number System Conversions
 More Number Sense Worksheets
 Size Comparison
 Measuring Length
 Metric Unit Conversion
 Customary Unit Conversion
 Temperature
 More Measurement Worksheets
 Writing Checks
 Profit and Loss
 Simple Interest
 Compound Interest
 Tally Marks
 Mean, Median, Mode, Range
 Mean Absolute Deviation
 Stemandleaf Plot
 Boxandwhisker Plot
 Permutation and Combination
 Probability
 Venn Diagram
 More Statistics Worksheets
 Shapes  2D
 Shapes  3D
 Lines, Rays and Line Segments
 Points, Lines and Planes
 Transformation
 Quadrilateral
 Ordered Pairs
 Midpoint Formula
 Distance Formula
 Parallel, Perpendicular and Intersecting Lines
 Scale Factor
 Surface Area
 Pythagorean Theorem
 More Geometry Worksheets
 Converting between Fractions and Decimals
 Significant Figures
 Convert between Fractions, Decimals, and Percents
 Proportions
 Direct and Inverse Variation
 Order of Operations
 Squaring Numbers
 Square Roots
 Scientific Notations
 Speed, Distance, and Time
 Absolute Value
 More PreAlgebra Worksheets
 Translating Algebraic Phrases
 Evaluating Algebraic Expressions
 Simplifying Algebraic Expressions
 Algebraic Identities
 Quadratic Equations
 Systems of Equations
 Polynomials
 Inequalities
 Sequence and Series
 Complex Numbers
 More Algebra Worksheets
 Trigonometry
 Math Workbooks
 English Language Arts
 Summer Review Packets
 Social Studies
 Holidays and Events
 Worksheets >
 Algebra >
 Equations >
 OneStep >
 Multiplication / Division
OneStep Equation: Multiplication and Division Worksheets
These printable onestep equation worksheets involve the multiplication and division operation to solve them. Given below are separate exercises for equations which involve integers, fractions and decimals coefficients. The pdf worksheets are meticulously designed for 6th grade, 7th grade, and 8th grade students. You can access some of them for free.
Integers: Level 1
Solve the onestep equations by performing multiplication and division operation. 'Level 1' has simple equations for the beginners.
 Download the set
Integers: Level 2
In 'Level 2' the complexity of the problems increases. Solve each onestep equation by multiplying and dividing them. Each worksheet has 10 problems for practice.
Fractions: Level 1
These printable worksheets have proper and improper fractions in their coefficients, serving well in examining the skills of grade 6, grade 7, and grade 8 students.
Fractions: Level 2
In 'Level 2' fraction worksheets, mixed numbers become the coefficients of the given equations. Perform the multiplication and division operation to solve them.
Decimals: Multiplication and Division
Multiply and divide to solve each onestep equation. The terms used here are combinations of decimals and integers. Download these pdf worksheets to give ample practice to students.
OneStep Equations: Integers, Fractions and Decimals
A mix of integers, fractions and decimals are used to form equations in these worksheets. These worksheets are mixed review pages for children.
One Step Equation Word Problems Worksheets
Solve this extensive collection of onestep equation word problems that involves integers, fractions, and decimals. These worksheets are tailormade for middle school students.
(15 Worksheets)
Related Worksheets
» TwoStep Equation
» MultiStep Equation
» Equation Word Problems
» Translating Phrases
Become a Member
Membership Information
Printing Help
How to Use Online Worksheets
How to Use Printable Worksheets
Privacy Policy
Terms of Use
Copyright © 2024  Math Worksheets 4 Kids
This is a membersonly feature!
Core Math Worksheets
Addition worksheets, subtraction worksheets, multiplication worksheets, division worksheets, fact family worksheets, long division worksheets, negative numbers, exponents worksheets, order of operations worksheets, fraction worksheets, fractions worksheets, graphic fractions, equivalent fractions, reducing fractions, comparing fractions, adding fractions, subtracting fractions, multiplying fractions, dividing fractions, fractions as decimals, fraction decimal percent, word problems, prealgebra word problems, money word problems, combining like terms, properties of multiplication, exponent rules, linear equations, one step equations, two step equations, factoring polynomials, quadratic equations, other worksheets, place value, percentages, rounding numbers, ordering numbers, standard, expanded, word form, mean median mode range, ratio worksheets, probability worksheets, roman numerals, factorization, gcd, lcm, prime and composite numbers, prealgebra, geometry worksheets, blank clocks, telling analog time, analog elapsed time, greater than and less than, arithmetic sequences, geometric sequences, venn diagram, graph worksheets, measurement & conversions, inches measurement, metric measurement, metric si unit conversions, customary unit conversions, customary and metric, patterns and puzzles, number patterns, patterns with negatives, missing operations, magic square, number grid puzzles, word search puzzles, color by number, addition color by number, subtraction color by number, multiplication color by number, division color by number, color by number, holiday & seasonal, valentine's day, st. patrick's day, thanksgiving, early learning, base ten blocks, printable flash cards, number matching, number tracing, missing numbers, picture math addition, picture math subtraction, picture math multiplication, picture math division, multiplication chart, multiplication table, prime numbers chart, hundreds chart, place value chart, roman numerals chart, handwriting paper, graph paper, coordinate plane, spaceship math checkoff, square root chart, fraction chart, probability chart, measurement chart, number line, comic strip template, calculators, age calculator, factoring calculator, fraction calculator, slope calculator, degrees to radians, percentage calculator, prime factorization calculator, roman numeral converter, long division calculator, multiplication calculator, math worksheets by grade, preschool math worksheets, kindergarten math worksheets, 1st grade math worksheets, 2nd grade math worksheets, 3rd grade math worksheets, 4th grade math worksheets, 5th grade math worksheets, 6th grade math worksheets, worksheet news, word problems: mixed multiplication and division word problems.
This worksheets combine basic multiplication and division word problems. The division problems do not include remainders. These worksheets require the students to differentiate between the phrasing of a story problem that requires multiplication versus one that requires division to reach the answer.
Mixed Multiplication and Division Word Problems 1
Mixed Multiplication and Division Word Problems 2
Practicing the operations separately is a good start for each operation, but an important word problem skill is also figuring out which math operation is needed to solve a specific question. The worksheets in this section combine both multiplication word problems and division word problems on the same worksheet, so students not only need to solve the problem but they need to figure out how to do it.
By moving into these worksheets quickly, it avoids the crutch where students learn that they always need to add or always need to subtract the two values in a problem to get the answer. This forces students to really understand the intent of the problem, not just scan the text looking for numbers.
Copyright 20082024 DadsWorksheets, LLC
High Impact Tutoring Built By Math Experts
Personalized standardsaligned oneonone math tutoring for schools and districts
In order to access this I need to be confident with:
Multiplication and division
Here you will learn about multiplication and division, including strategies on how to multiply and divide various types of rational numbers.
Students first learn about multiplication and division in the 3 rd grade and 4 th grade with their work with operations and algebraic thinking, as well as number and operations base ten and fractions.
What is multiplication and division?
Multiplication and division are two of the four basic operations. Multiplication is finding the product of two or more numbers, and division is finding the quotient of two numbers.
Multiplication is basically the repeated addition of equal groups.
For example, 4 equal groups of 3 :
In a multiplication equation, the answer to multiplying one number by another is called the product. The multiplicand is the quantity to be multiplied by the multiplier, which will give you a product.
The product will be 0 if either the multiplicand or multiplier is 0 .
Arrays are visual models that represent multiplication.
For example, this array shows 3 rows of 6 which is the same as 3 \times 6 .
3 \times 6=18
Step by step guide: Understanding Multiplication
Multiplication is commutative. The order in which the calculation is performed does not matter.
For example,
3\times{4}=4\times{3}=12
Multiplying multidigit numbers
To multiply multidigit numbers, you can use the algorithm or the area model.
The area model is a rectangular model where the product represents finding the area of the rectangle.
For example, multiply 42 \times 62 using an area model.
2400+120+80+4=2604
42 \times 62=2604
Stepbystep guide: Multiplying multidigit numbers
Multiplicative comparisons
You can use multiplication to make comparisons between quantities. Multiplicative comparisons compare two quantities by showing that one quantity is how many times larger or smaller than another quantity.
Mike has 3 lollipops. Michelle has 4 times as many lollipops as Mike. How many lollipops does Michelle have?
Michelle has 4\times 3=12 lollipops.
Jillian has 24 inches of hair ribbon. Suzanne has half that amount. How long is Suzanne’s hair ribbon?
Suzanne’s ribbon is \cfrac{1}{2} \times 24=12 \text { inches }
Step by step guide: Multiplicative comparisons
[FREE] Multiplication And Division Worksheet (Grade 3 to 7)
Use this worksheet to check your grade 3 to 7 students’ understanding of multiplication and division. 15 questions with answers to identify areas of strength and support!
Multiplying rational numbers
You can multiply rational numbers. Rational numbers include multidigit numbers, integers, fractions, and decimals. When multiplying positive and negative numbers, the following rules apply:
For example, (3) \times(5)=15
Step by step guide: Multiplying and dividing integers
Division shares or breaks a number into equal sized groups.
For example, the number 12 can be divided into 4 equal groups of 3 .
In a division equation, the answer you get when you divide one number by another is called the quotient.
The word quotient comes from Latin and means ‘how many times.’ When dividing, you are finding out ‘how many times’ a number goes into another number.
The quotient will only be 0 if the dividend is 0 but the divisor is not.
8 \div 0=\text {Does not exist }
Step by step guide: Understanding division
Unlike multiplication, division is not commutative. If the order of the numbers within the calculation changes, the result will change.
12 \div 4 ≠ 4 \div 12
To solve division problems with larger numbers, you can use long division.
For example, 452.1 \div 3
Stepbystep guide: Long division
Step by step guide: Dividing multidigit numbers
Division can also be done with positive and negative integers, fractions, and decimals. When dividing positive and negative numbers, the following rules apply:
For example, (20) \div (5)=4
Step by step guide: Multiplying and dividing rational numbers
Common Core State Standards
How does this relate to 4 th – 7 th grade math?
 Grade 3: Operations and Algebraic Thinking ( 3.OA.A.1) Interpret products of whole numbers, for example, interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each.
 Grade 3: Operations and Algebraic Thinking (3.OA.A.2) Interpret wholenumber quotients of whole numbers, for example, interpret 56 \div 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each.
 Grade 3: Operations and Algebraic Thinking (3.OA.C.7) Fluently multiply and divide within 100 , using strategies such as the relationship between multiplication and division.
 Grade 4: Operations and Algebraic Thinking (4.OA.2) Multiply or divide to solve word problems involving multiplicative comparison, for example, by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.
 Grade 4: Number and Operations – Fractions (4.NF.B.4) Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
 Grade 5: Number and Operations Base Ten (5.NBT.B.5) Fluently multiply multidigit whole numbers using the standard algorithm.
 Grade 5: Number and Operations – Fractions (5.NF.B.7) Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.
 Grade 6: Number System (6.NS.C.6) Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.
 Grade 7: Number System (7.NS.A.2) Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
How to do multiplication and division
There are several strategies to multiply and divide numbers. For more specific stepbystep guides, check out the individual pages linked in the “What is multiplication and division?” section above or read through the examples below.
In order to multiply using a visual model:
Draw the array.
 Count the objects in each row.
 Find the total .
In order to divide using a visual model:
Count the objects in each group.
 Write the answer .
In order to multiply and divide multidigit numbers:
Perform the multiplication or division algorithm.
Write the answer.
In order to find multiplicative comparisons:
Draw a model.
Write an equation.
Solve the equation and label the answer.
Multiplication and division examples
Example 1: multiply using a model.
Use a visual model to multiply 5 \times 3.
5 x 3 is 5 rows of 3.
2 Count the objects in each row.
3 Find the total .
There are 3 chips in each row, 3+3+3+3+3=15
3 \times 5=15
Example 2: multiply using algorithm
Multiply 99 \times 7.
Using the algorithm,
99 \times 7=693
Example 3: multiply and divide rational numbers
Multiply 1.23 \times 3.2.
1.23 \times 3.2=3.936
Example 4: divide using a visual model
Divide: 9 \div 3
Example 5: dividing rational numbers
Divide: 15.4 \div 2
15.4 \div 2=7.7
Example 6: multiplicative comparison
Bobby has 3 baseball cards. Joey has five times as many cards as Bobby. How many cards does Joey have?
3 \times 5= \, ?
Joey has 15 baseball cards.
Teaching tips for multiplication and division
 Use manipulatives to reinforce the conceptual understanding of multiplication and division.
 Include real world scenarios so that students can connect the mathematical concepts to the world around them.
 Reinforce to students that the concept of multiplication and division is the same regardless if the numbers are whole numbers or rational numbers.
 Using the area model for multiplication and division can be a fun way for students to understand multiplication and division while also reinforcing math facts.
 To practice multiplication facts, consider using digital and nondigital games instead of flashcards. Game playing is a fun way for students to remember the times tables.
Easy mistakes to make
 Confusing the rules for multiplying and dividing positive and negative numbers For example, multiplying (4)\times (8) and getting a product of 32 instead of 32 .
 Misinterpreting the meaning of key words in word problems resulting in using the incorrect operation For example, thinking that the word “of” means to divide instead of multiply.
Practice multiplication and division questions
1) Which multiplication expression represents this array?
Count the number of objects in each row.
There are 5 objects in each row which is 5+5.
5+5 is the same as 2 \times 5.
So, 2 \times 5 is the correct expression.
2) Multiply 104 \times 3.
Use the algorithm for multiplying multidigit numbers, regrouping when necessary.
104 \times 3=312
3) Multiply 53 \times 32.
You can use the area model to multiply 53 \times 32.
Add the products together: 1500+100+90+6=1696
53 \times 32=1696
4) Use the array to find the quotient of 16 \div 4 .
Divide the array into 4 equal groups and then count how many objects are in each group.
16 \div 4 = 4
5) Divide 128 \div 4.
Divide the numbers using the algorithm for long division.
128 \div 4= 32
6) Chris has 3 pencils. Pam has four times as many pencils as Chris. How many pencils does Pam have?
Draw a picture.
4 \times 3=12
Pam has 12 pencils.
Multiplication and division FAQs
Yes, the rules for multiplying and dividing positive and negative numbers hold true regardless if the numbers are whole numbers or rational numbers. Stepbystep guide : Negative numbers
Knowing your multiplication facts and division facts helps when solving problems.
Repeated subtraction is a way for students to begin to develop an understanding of division.
There is not one best strategy to use when multiplying multidigit numbers. Some strategies, can be quicker than others, but not better.
Knowing your multiplication tables helps to answer questions faster than when you do not know them.
The commutative property of multiplication is: 5 \times 3=3 \times 5 , the order of the numbers does not matter.
The next lessons are
 Types of numbers
 Rounding numbers
 Factors and multiples
Still stuck?
At Third Space Learning, we specialize in helping teachers and school leaders to provide personalized math support for more of their students through highquality, online oneonone math tutoring delivered by subject experts.
Each week, our tutors support thousands of students who are at risk of not meeting their gradelevel expectations, and help accelerate their progress and boost their confidence.
Find out how we can help your students achieve success with our math tutoring programs .
[FREE] Common Core Practice Tests (3rd to 8th Grade)
Prepare for math tests in your state with these 3rd Grade to 8th Grade practice assessments for Common Core and state equivalents.
Get your 6 multiple choice practice tests with detailed answers to support test prep, created by US math teachers for US math teachers!
Privacy Overview
 > >

Chapter 2, Lesson 3: Solving Equations by Using Multiplication and Division
 Extra Examples
 Personal Tutor
 SelfCheck Quizzes
The resource you requested requires you to enter a username and password below:
Password:  
Please read our Terms of Use and Privacy Notice before you explore our Web site. To report a technical problem with this Web site, please contact the site producer .
IMAGES
VIDEO
COMMENTS
Lesson 2 Homework Practice Multiplication and Division Equations Solve each equation. Check your solution. 1. −−−k 11 = 3 2. 16b = 32 3. 72 = 12x 4. 42 = 14y 5. −−−x 16 = 1 6. 12k = 60 7. −−a 13 = 0 8. 99 = 99y 9. −−h 8 = 2 10. 15 = − y 5 11. −−h 3 = 7 12. 1 = −−x 6 13. 9 = −−m 2 14. 5b = 55 15.
Lesson/Title Page 11 A Plan for Problem Solving .....1 12 Variables, Expressions, and Properties ... 110 Solving Multiplication and Division Equations .....10 21 Rational Numbers ... Practice A Plan for Problem Solving Toppings Price 1 $12.99 2 $13.79 3 $14.59 4 $15.39
Section 7.3 Solving Equations Using Multiplication or Division 311 Division Property of Equality Words When you divide each side of an equation by the same nonzero number, the two sides remain equal. Numbers 8 ⋅ 4 = 32 Algebra 4x = 32 8 ⋅ 4 ÷ 4 = 32 ÷ 4 4x 4 = 32 — 4 8 = 8 x = 8 EXAMPLE 2 Solving an Equation Using Division Solve 5b = 65. 5b = 65 Write the equation.
Math fact fluency should not be based on the ability to perform a memorized series of steps. It is so much more than that. Throughout your math fact instruction and practice this year, try to keep three main words in mind when it comes to how your students are solving a problem or equation: EFFECTIVE, EFFICIENT, FLEXIBLE.
134 Chapter 4 Equations and Inequalities 4.2 Lesson Multiplication Property of Equality Words Multiplying each side of an equation by the same number produces an equivalent equation. Algebra If a = b, then a ⋅ c = b ⋅ c. Division Property of Equality Words Dividing each side of an equation by the same number produces an equivalent equation.
Problem Solving Handbook CrossCurricular Projects Other Calculator Keystrokes Meet the Authors About the Cover Scavenger Hunt Recording Sheet Vocabulary Puzzlemaker Custom Chapter Resources Chapter Readiness Quiz Chapter Test Concepts in Motion RealWorld Careers Standardized Test Practice Vocabulary Review Lesson Resources Extra Examples ...
Learn how to use the Division and Multiplication Properties of Equality to solve equations with integers, fractions, and decimals. See examples, exercises, and definitions with stepbystep solutions.
in the everyday world.The materials are organized by chapter and lesson, with one Word Problem Practiceworksheet for every lesson in Glencoe Math Connects, Course 3. Always keep your workbook handy. Along with your textbook, daily homework, and class notes, the completed Word Problem Practice Workbookcan help you review for quizzes and tests.
Solve Equations Using the Division and Multiplication Properties of Equality. You may have noticed that all of the equations we have solved so far have been of the form x + a = b x + a = b or x − a = b x − a = b. We were able to isolate the variable by adding or subtracting the constant term on the side of the equation with the variable.
27 Solving Division Equations LESSON Solve each equation. Check your answers. 1.! 6 s!! 7 2.! 5 v!! 9 3. 12 !! q 7! 4.! m 2 ... Practice C 27 Solving Division Equations LESSON Solve each equation. Check your answers. 1.! 1 s 8!! 16 2.! 2 v 4!! 32 3.! q 9 ... Solving Division Equations You can use multiplication and division to write related ...
Andymath.com is a free math website with the mission of helping students, teachers and tutors find helpful notes, useful sample problems with answers including step by step solutions, and other related materials to supplement classroom learning.
Find over 100,000 free practice questions on various math topics, from early math to calculus. Choose your grade level or topic and get instant feedback and interactive exercises.
This web page offers printable worksheets for onestep equations involving multiplication and division. It does not provide the direct answer for 13.40 divided by 4, but it may help students learn how to solve similar problems.
In this math lesson, we learn to solve equations with x divided by a number, like x/3 = 14. To find x, we isolate it by multiplying both sides of the equation by the divisor (3). This gives us x = 42. Finally, we check our answer by substituting x back into the original equation to make sure it's correct.
Multiplication and Division as Inverse Operations. Two extremely important observations: The inverse of multiplication is division. If we start with a number x and multiply by a number a, then dividing the result by the number a returns us to the original number x. In symbols, \[ \frac{a \cdot x}{a} = x.\nonumber \]
Lesson Resources Extra Examples Personal Tutor SelfCheck Quizzes. Hotmath Homework Help Math Review ... Mathematics. Home > Chapter 6 > Lesson 2. California Algebra 1: Concepts, Skills, and Problem Solving. Chapter 6, Lesson 2: Solving Inequalities by Multiplication and Division. Extra Examples; Personal Tutor; SelfCheck Quizzes; Log In.
This worksheets combine basic multiplication and division word problems. The division problems do not include remainders. These worksheets require the students to differentiate between the phrasing of a story problem that requires multiplication versus one that requires division to reach the answer.
Practice Makes Perfect. Solve Equations Using the Division and Multiplication Properties of Equality. In the following exercises, solve each equation for the variable using the Division Property of Equality and check the solution.
Learn how to multiply and divide various types of rational numbers, including multidigit numbers, integers, fractions, and decimals. Find definitions, rules, strategies, worksheets, and Common Core standards for grades 3 to 7.
The lesson will focus on solving division problems using multiplication and on the relationship between multiplication and division. H: Remind students of the prizebag scenario from the previous lesson and solve the problem again as a group. Correlate the problem with the number sentences that represent it. E: Have students use the Match Them ...
Problem Solving Handbook CrossCurricular Projects ... Chapter Test Concepts in Motion RealWorld Careers Standardized Test Practice Vocabulary Review Lesson Resources Extra Examples Personal Tutor SelfCheck Quizzes ... Algebra 1. Chapter 2, Lesson 3: Solving Equations by Using Multiplication and Division. Extra Examples; Personal Tutor; Self ...
PreK through grade 2 (Khan Kids) Early math review; 2nd grade; 3rd grade; 4th grade; 5th grade; 6th grade; 7th grade; 8th grade; Illustrative math 3rd grade; Illustrative math 4th grade; ... Differential equations; Linear algebra; See all Math; Test prep; Digital SAT. NEW. LSAT; MCAT; Science; Middle school biology;
Lesson Resources Extra Examples Personal Tutor SelfCheck Quizzes. Hotmath Homework Help ... Mathematics. Home > Chapter 2 > Lesson 3. California Algebra 1: Concepts, Skills, and Problem Solving. Chapter 2, Lesson 3: Solving Equations by Using Multiplication and Division. Extra Examples; Personal Tutor; SelfCheck Quizzes; Log In.