1-4 solving multiplication and division equations pre-algebra learn to solve equations using...
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1-4 Solving Multiplication and Division Equations
Pre-Algebra
Learn to solve equations using multiplication and division.
1-4 Solving Multiplication and Division Equations
Pre-Algebra
Vocabulary
Division Property of EqualityMultiplication Property of Equality
1-4 Solving Multiplication and Division Equations
Pre-Algebra
You can solve a multiplication equation using the Division Property of Equality.
You can divide both sides of an equation by the same nonzero number, and the equation will still be true.
4 • 3 = 122 2
x = yx = y
DIVISION PROPERTY OF EQUALITY
Words Numbers Algebra
z
4 • 3 = 12
12 = 62
z
1-4 Solving Multiplication and Division Equations
Pre-Algebra
Solve 8x = 32.
Additional Example 1: Solving Equations Using Division
8x = 32
1x = 4
Divide both sides by 8.
Check
8x = 328 8
x = 4
8x = 328(4) = 32?
32 = 32? Substitute 4 for x.
1 • x = x
1-4 Solving Multiplication and Division Equations
Pre-Algebra
Solve 9x = 36.
Try This: Example 1
9x = 36
1x = 4
Divide both sides by 9.
Check
9x = 369 9
x = 4
9x = 369(4) = 36?
36 = 36? Substitute 4 for x.
1 • x = x
1-4 Solving Multiplication and Division Equations
Pre-Algebra
You can multiply both sides of an equation by the same number, and the statement will still be true.
2 • 3 = 6x = yx = yz z
MULTIPLICATION PROPERTY OF EQUALITY
Words Numbers Algebra
2 • 3 = 6 4 • 4 •
8 • 3 = 24
You can solve a division equation using the Multiplication Property of Equality.
1-4 Solving Multiplication and Division Equations
Pre-Algebra
Solve = 7.
Additional Example 2: Solving Equations Using Multiplication
n7n7 = 77 • 7 • Multiply both sides by 7.
n = 49
Checkn7 = 7
Substitute 49 for n.497 = 7
?
7 = 7?
1-4 Solving Multiplication and Division Equations
Pre-Algebra
Solve = 16
Try This: Example 2
n4n4 = 164 • 4 • Multiply both sides by 4.
n = 64
Checkn4 = 16
Substitute 64 for n.644 = 16
?
16 = 16?
1-4 Solving Multiplication and Division Equations
Pre-Algebra
Additional Example 3: Food Application
Joe has enough flour to bake one sheet cake but would rather make cookies. How many dozen cookies can he make?
Dessert
Apple crisp
Bread pudding
Cookies (1 doz.)
Pumpkin pie
Sheet cake
Tiramisu
Cups of Flour
1.5
4
2
1
8
3
1-4 Solving Multiplication and Division Equations
Pre-Algebra
Additional Example 3 Continued
cups of flour for 1 dozen cookies
cups of flour in 1 cake =
number of dozen cookies
2 • =c 8
2c = 82 2c = 4
Joe can make 4 dozen cookies with the same amount of flour that he would need for 1 sheet cake.
Write the equation.
Divide both sides by 2.
2c = 8
1-4 Solving Multiplication and Division Equations
Pre-Algebra
Try This: Example 3
cups of flour for bread pudding
cups of flour in 1 cake
= number of bread pudding desserts
4 • =b 8
4b = 84 4c = 2
Joe can make 2 bread pudding desserts with the same amount of flour that he would need for 1 sheet cake.
Write the equation.
Divide both sides by 4.
4b = 8
1-4 Solving Multiplication and Division Equations
Pre-Algebra
Additional Example 4: Money Application
fraction of amount raised so far
amount raised so far =
• =x 50
4 •
x = 200
Meg has saved $50, which is one-fourth of the amount she needs for a school trip. What is the total amount she needs?
Write the equation.
Multiply both sides by 4.
total amount needed
14
x = 5014
4 • x = 5014
Meg needs $200 total.
1-4 Solving Multiplication and Division Equations
Pre-Algebra
Try This: Example 4
amount raised so far =
• =x 750
8 •
x = 6000
The school library needs money to complete a new collection. So far, the library has raised $750, which is only one-eighth of what they need. What is the total amount needed?
Write the equation.
Multiply both sides by 8.
total amount needed
18
x = 75018
8 • x = 75018
The library needs to raise a total of $6000.
fraction of total amount raised so far
1-4 Solving Multiplication and Division Equations
Pre-Algebra
Sometimes it is necessary to solve equations by using two inverse operations. For instance,
the equation 6x 2 = 10 has multiplication and subtraction.
6x 2 = 10
Variable term
Subtraction
Multiplication
To solve this equation, add to isolate the term with the variable in it. Then divide to solve.
1-4 Solving Multiplication and Division Equations
Pre-Algebra
Solve 3y – 7 = 20.
Additional Example 5: Solving a Simple Two-Step Equation
3y – 7 = 20Step 1: Add 7 to both sides to isolate the term with y in it.+ 7 + 7
3y = 27
Step 2: 3y = 273 3 y = 9
Divide both sides by 3.
1-4 Solving Multiplication and Division Equations
Pre-Algebra
Solve 4y + 5 = 29.
Try This: Example 5
4y + 5 = 29Step 1: Subtract 5 from both sides to isolate the term with y in it.– 5 – 5
4y = 24
Step 2: 4y = 244 4 y = 6
Divide both sides by 4.