1. 1-4 Solving Multiplication and Division Equations Pre-Algebra Learn to solve equations using multiplication and division.

2. 1-4 Solving Multiplication and Division Equations Pre-Algebra Addition and subtraction are inverse operations, which means they “undo” each other. To solve an equation, use inverse operations to isolate the variable. This means getting the variable alone on one side of the equal sign.

3. 1-4 Solving Multiplication and Division Equations Pre-Algebra Multiplication and division are inverse operations, which means they “undo” each other. To solve an equation, use inverse operations to isolate the variable. This means getting the variable alone on one side of the equal sign.

4. 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 = 12 22 x = y DIVISION PROPERTY OF EQUALITY WordsNumbersAlgebra z 4 3 = 12 z 6 = 6

5. 1-4 Solving Multiplication and Division Equations Pre-Algebra Solve 8x = 32. Example 1: Solving Equations Using Division 8 x = 32 1 x = 4 Divide both sides by 8. Check 8 x = 32 88 x = 4 8 x = 32 8(4) = 32 ? 32 = 32 ? Substitute 4 for x. 1 x = x

6. 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 = 6 x = y z z MULTIPLICATION PROPERTY OF EQUALITY WordsNumbersAlgebra 2 3 = 6 4 4 8 3 = 24 You can solve a division equation using the Multiplication Property of Equality.

7. 1-4 Solving Multiplication and Division Equations Pre-Algebra Solve = 7. Example 2: Solving Equations Using Multiplication n 7 n 7 = 7 7 7 Multiply both sides by 7. n = 49 Check n 7 = 7 Substitute 49 for n. 49 7 = 7 ? 7 = 7 ?

8. 1-4 Solving Multiplication and Division Equations Pre-Algebra Multiplication and division are inverse operations, which means they “undo” each other. To solve an equation, use inverse operations to isolate the variable. This means getting the variable alone on one side of the equal sign.

9. 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 = 12 22 x = y DIVISION PROPERTY OF EQUALITY WordsNumbersAlgebra z 4 3 = 12 z 6 = 6

10. 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 = 12 22 x = y DIVISION PROPERTY OF EQUALITY WordsNumbersAlgebra z 4 3 = 12 z 6 = 6

11. 1-4 Solving Multiplication and Division Equations Pre-Algebra Solve 9x = 36. Try This: Example 1 9 x = 36 1 x = 4 Divide both sides by 9. Check 9 x = 36 99 x = 4 9 x = 36 9(4) = 36 ? 36 = 36 ? Substitute 4 for x. 1 x = x

12. 1-4 Solving Multiplication and Division Equations Pre-Algebra Solve = 16 Try This: Example 2 n 4 n 4 = 16 4 4 Multiply both sides by 4. n = 64 Check n 4 = 16 Substitute 64 for n. 64 4 = 16 ? 16 = 16 ?

13. 1-4 Solving Multiplication and Division Equations Pre-Algebra Example 3: Food Application Ace 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

14. 1-4 Solving Multiplication and Division Equations Pre-Algebra Example 3 Continued cups of flour for 1 dozen cookies cups of flour in 1 cake  = number of dozen cookies 2 = c 8 2 c = 8 2 2 c = 4 Ace 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. 2 c = 8

15. 1-4 Solving Multiplication and Division Equations Pre-Algebra Example 4: Money Application fraction of amount raised so far amount raised so far  = = x 50 4 x = 200 Faith 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 1 4 x = 50 1 4 4 1 4 Olivia needs $200 total.

16. 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. 6 x − 2 = 10 Variable term Subtraction Multiplication To solve this equation, add to isolate the term with the variable in it. Then divide to solve.

17. 1-4 Solving Multiplication and Division Equations Pre-Algebra Solve 3y – 7 = 20. Example 5: Solving a Simple Two-Step Equation 3 y – 7 = 20 Step 1: Add 7 to both sides to isolate the term with y in it. + 7 3 y = 27 Step 2: 3 y = 27 3 3 y = 9 Divide both sides by 3.

18. 1-4 Solving Multiplication and Division Equations Pre-Algebra Solve 4y + 5 = 29. Example 5: Solving a Simple Two-Step Equation 4y + 5 = 29Step 1: Subtract 5 from both sides to isolate the term with y in it. – 5 4 y = 24 Step 2: 4 y = 24 4 4 y = 6 Divide both sides by 4.

19. 1-4 Solving Multiplication and Division Equations Pre-Algebra Addition and subtraction are inverse operations, which means they “undo” each other. To solve an equation, use inverse operations to isolate the variable. This means getting the variable alone on one side of the equal sign.

20. 1-4 Solving Multiplication and Division Equations Pre-Algebra Multiplication and division are inverse operations, which means they “undo” each other. To solve an equation, use inverse operations to isolate the variable. This means getting the variable alone on one side of the equal sign.

21. 1-4 Solving Multiplication and Division Equations Pre-Algebra Solve 9x = 36. Try This: Example 1 9 x = 36 1 x = 4 Divide both sides by 9. Check 9 x = 36 99 x = 4 9 x = 36 9(4) = 36 ? 36 = 36 ? Substitute 4 for x. 1 x = x

22. 1-4 Solving Multiplication and Division Equations Pre-Algebra Solve = 16 Try This: Example 2 n 4 n 4 = 16 4 4 Multiply both sides by 4. n = 64 Check n 4 = 16 Substitute 64 for n. 64 4 = 16 ? 16 = 16 ?