Solving Equations by Multiplying or Dividing 1 1

Solving Equations by Multiplying or Dividing 1 -1 and Expressions 1 -4 Variables Chapter 1 Algebra Toolbox 1 -4 Solving Equations by Multiplying or Dividing Objective: solve equations using multiplication or division Pre-Algebra

Solving Equations by Multiplying or Dividing 1 -1 and Expressions 1 -4 Variables Agenda Warm Up Problem of the Day Lesson Presentation Practice Activity Quiz Pre-Algebra

Solving Equations by Multiplying or Dividing 1 -1 and Expressions 1 -4 Variables Warm Up Solve. 1. x 3 = 9 x = 12 2. 16 = n + 9 n = 7 k=1 3. 5 + k = 6 4. 47 = t 19 t = 66 5. 15 = x + 2 x = 13 Pre-Algebra

Solving Equations by Multiplying or Dividing 1 -1 and Expressions 1 -4 Variables Problem of the Day Jackie went shopping for a new wardrobe. She bought seven new shirts and four new pairs of pants. She made sure that they can all be worn together in combinations. How many outfits can she put together? 28 Pre-Algebra

Solving Equations by Multiplying or Dividing 1 -1 and Expressions 1 -4 Variables Learn to solve equations using multiplication and division. Pre-Algebra

Solving Equations by Multiplying or Dividing 1 -1 and Expressions 1 -4 Variables Vocabulary Division Property of Equality Multiplication Property of Equality Pre-Algebra

Solving Equations by Multiplying or Dividing 1 -1 and Expressions 1 -4 Variables 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 2 2 12 = 6 2 x=y z z Pre-Algebra

Solving Equations by Multiplying or Dividing 1 -1 and Expressions 1 -4 Variables Example 1: Solving Equations Using Division Solve 8 x = 32 8 8 1 x = 4 x=4 Divide both sides by 8. 1 • x=x Check 8 x = 32 ? 32 8(4) = Substitute 4 for x. ? 32 32 = Pre-Algebra

Solving Equations by Multiplying or Dividing 1 -1 and Expressions 1 -4 Variables Try This: Example 1 Solve 9 x = 36 9 9 1 x = 4 x=4 Divide both sides by 9. 1 • x=x Check 9 x = 36 ? 36 9(4) = Substitute 4 for x. ? 36 36 = Pre-Algebra

Solving Equations by Multiplying or Dividing 1 -1 and Expressions 1 -4 Variables You can solve a division equation using the Multiplication Property of Equality. MULTIPLICATION PROPERTY OF EQUALITY Words You can multiply both sides of an equation by the same number, and the statement will still be true. Pre-Algebra Numbers 2 • 3=6 4 • 2 • 3=4 • 6 8 • 3 = 24 Algebra x=y z x = zy

Solving Equations by Multiplying or Dividing 1 -1 and Expressions 1 -4 Variables Example 2: Solving Equations Using Multiplication Solve n = 7. 7 n = 7 • 7 Multiply both sides by 7. n = 49 Check n =7 7 ? 49 = 7 7 ? 7 7= Pre-Algebra Substitute 49 for n.

Solving Equations by Multiplying or Dividing 1 -1 and Expressions 1 -4 Variables Try This: Example 2 Solve n = 16 4 n = 4 • 16 4 • 4 Multiply both sides by 4. n = 64 Check n = 16 4 64 =? 16 4 ? 16 16 = Pre-Algebra Substitute 64 for n.

Solving Equations by Multiplying or Dividing 1 -1 and Expressions 1 -4 Variables 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 Pre-Algebra Cups of Flour 1. 5 Bread pudding 4 Cookies (1 doz. ) 2 Pumpkin pie 1 Sheet cake 8 Tiramisu 3

Solving Equations by Multiplying or Dividing 1 -1 and Expressions 1 -4 Variables Example 3 Continued cups of flour for 1 dozen cookies 2 number of dozen cookies • 2 c = 8 2 2 c =4 c = cups of flour in 1 cake = 8 Write the equation. Divide both sides by 2. Joe can make 4 dozen cookies with the same amount of flour that he would need for 1 sheet cake. Pre-Algebra

Solving Equations by Multiplying or Dividing 1 -1 and Expressions 1 -4 Variables Try This: Example 3 cups of flour for number of bread pudding desserts = • = 4 4 b = 8 4 4 c =2 b cups of flour in 1 cake 8 Write the equation. Divide both sides by 4. Joe can make 2 bread pudding desserts with the same amount of flour that he would need for 1 sheet cake. Pre-Algebra

Solving Equations by Multiplying or Dividing 1 -1 and Expressions 1 -4 Variables Example 4: Money Application 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 1 4 total amount needed = amount raised so far • x = 50 1 x = 50 4 4 • 1 x = 4 • 50 4 x = 200 Meg needs $200 total. Pre-Algebra Write the equation. Multiply both sides by 4.

Solving Equations by Multiplying or Dividing 1 -1 and Expressions 1 -4 Variables Try This: Example 4 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? fraction of total amount raised so far total amount needed 1 8 • x = = amount raised so far 750 1 x = 750 Write the equation. 8 8 • 1 x = 8 • 750 Multiply both sides by 8. 8 x = 6000 The library needs to raise a total of $6000. Pre-Algebra

Solving Equations by Multiplying or Dividing 1 -1 and Expressions 1 -4 Variables Sometimes it is necessary to solve equations by using two inverse operations. For instance, the equation 6 x 2 = 10 has multiplication and subtraction. Variable term Multiplication 6 x 2 = 10 Subtraction To solve this equation, add to isolate the term with the variable in it. Then divide to solve. Pre-Algebra

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

Solving Equations by Multiplying or Dividing 1 -1 and Expressions 1 -4 Variables Try This: Example 5 Solve 4 y + 5 = 29. Step 1: 4 y + 5 = 29 Subtract 5 from both sides to – 5 isolate the term with y in it. 4 y Step 2: Pre-Algebra = 24 4 y = 24 Divide both sides by 4. 4 4 y=6

Solving Equations by Multiplying or Dividing 1 -1 and Expressions 1 -4 Variables Lesson Quiz Solve. 1. k = 3 k = 18 6 2. 16 t = 112 t = 7 b = 14 b = 126 9 4. 3 n + 17 = 29 n = 4 3. 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. 3 x = 63; 21 pages Pre-Algebra

Solving Equations by Multiplying or Dividing 1 -1 and Expressions 1 -4 Variables Let’s try some! Pre-Algebra