Learn to solve equations using multiplication and division.

Vocabulary Division Property of Equality Multiplication Property of Equality

DIVISION PROPERTY OF EQUALITY You can solve a multiplication equation using the Division Property of Equality. DIVISION PROPERTY OF EQUALITY Words Numbers Algebra You can divide both sides of an equation by the same nonzero number, and the equation will still be true. 4 • 3 = 12 x = y 4 • 3 = 12 x = y 2 2 z z 12 = 6 2

Additional Example 1: Solving Equations Using Division Solve 8x = 32. 8x = 32 8x = 32 Divide both sides by 8. 8 8 1x = 4 1 • x = x x = 4 Check 8x = 32 8(4) = 32 ? Substitute 4 for x. 32 = 32 ? 

MULTIPLICATION PROPERTY OF EQUALITY You can solve a division equation using the Multiplication Property of Equality. MULTIPLICATION PROPERTY OF EQUALITY Words Numbers Algebra You can multiply both sides of an equation by the same number, and the statement will still be true. 2 • 3 = 6 x = y 4 • 2 • 3 = 6 z x = y 8 • 3 = 24

Additional Example 2: Solving Equations Using Multiplication 7 Solve = 7. n 7 = 7 7 • 7 • Multiply both sides by 7. n = 49 Check n 7 = 7 49 7 = 7 ? Substitute 49 for n. 7 = 7 ? 

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

= =  • Additional Example 3 Continued cups of flour for 1 dozen cookies number of dozen cookies cups of flour in 1 cake  = • = 2 c 8 2c = 8 Write the equation. 2c = 8 Divide both sides by 2. 2 2 c = 4 Joe can make 4 dozen cookies with the same amount of flour that he would need for 1 sheet cake.

= =  • Additional Example 4: Money Application 1 4 x 50 x = 50 1 4 Meg has saved $50, which is one-fourth of the amount she needs for a school trip. What is the total amount she needs? fraction of amount raised so far  total amount needed = amount raised so far 1 4 • = x 50 x = 50 1 4 Write the equation. x = 50 1 4 Multiply both sides by 4. 4 • 4 • x = 200 Meg needs $200 total.

Sometimes it is necessary to solve equations by using two inverse operations. For instance, the equation 6x  2 = 10 has multiplication and subtraction. Variable term 6x  2 = 10 Multiplication Subtraction To solve this equation, add to isolate the term with the variable in it. Then divide to solve.

Additional Example 5: Solving a Simple Two-Step Equation Solve 3y – 7 = 20. Step 1: 3y – 7 = 20 Add 7 to both sides to isolate the term with y in it. + 7 + 7 3y = 27 Step 2: 3y = 27 Divide both sides by 3. 3 3 y = 9

Lesson Quiz Solve. 1. = 3 2. 16t = 112 k k = 18 3. = 14 6 1. = 3 2. 16t = 112 3. = 14 4. 3n + 17 = 29 5. Joan is making a scrapbook of her pictures. She wants to put three pictures on each page. She has 63 photos. Write and solve an equation to find how many pages she will need for all of the photos. k 6 k = 18 t = 7 b 9 b = 126 n = 4 3x = 63; 21 pages