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Solving Multiplication and and Solving Multiplication 1-4 1-4 Division Equations Division Equations Warm Up Problem of the Day Lesson Presentation Pre-Algebra Pre-Algebra Solving Multiplication and 1-4 Division Equations 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 Pre-Algebra x = 13 Solving Multiplication and 1-4 Division Equations 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 Multiplication and 1-4 Division Equations Learn to solve equations using multiplication and division. Pre-Algebra Solving Multiplication and 1-4 Division Equations Vocabulary Division Property of Equality Multiplication Property of Equality Pre-Algebra Solving Multiplication and 1-4 Division Equations You can solve a multiplication equation using the Division Property of Equality. DIVISION PROPERTY OF EQUALITY Words You can divide both sides of an equation by the same nonzero number, and the equation will still be true. Pre-Algebra Numbers Algebra 4 • 3 = 12 4 • 3 = 12 2 2 12 = 6 2 x=y x=y z z Solving Multiplication and 1-4 Division Equations Additional Example 1: Solving Equations Using Division Solve 8x = 32. 8x = 32 8x = 32 8 8 1x = 4 x=4 Divide both sides by 8. 1•x=x Check 8x = 32 ? 32 8(4) = Substitute 4 for x. ? 32 32 = Pre-Algebra Solving Multiplication and 1-4 Division Equations Try This: Example 1 Solve 9x = 36. 9x = 36 9x = 36 9 9 1x = 4 x=4 Divide both sides by 9. 1•x=x Check 9x = 36 ? 36 9(4) = Substitute 4 for x. ? 36 36 = Pre-Algebra Solving Multiplication and 1-4 Division Equations 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 Multiplication and 1-4 Division Equations Additional Example 2: Solving Equations Using Multiplication Solve n = 7. 7 n = 7• 7 7•7 n = 49 Multiply both sides by 7. Check n =7 7 ? 49 = 7 7 ? 7 7= Pre-Algebra Substitute 49 for n. Solving Multiplication and 1-4 Division Equations Try This: Example 2 Solve n = 16 4 n = 4 • 16 4•4 n = 64 Multiply both sides by 4. Check n = 16 4 64 =? 16 4 ? 16 16 = Pre-Algebra Substitute 64 for n. Solving Multiplication and 1-4 Division Equations 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 Pre-Algebra Cups of Flour 1.5 Bread pudding 4 Cookies (1 doz.) 2 Pumpkin pie 1 Sheet cake 8 Tiramisu 3 Solving Multiplication and 1-4 Division Equations Additional Example 3 Continued cups of flour for 1 dozen cookies 2 number of dozen cookies • 2c = 8 2c = 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 Multiplication and 1-4 Division Equations Try This: Example 3 cups of flour for number of bread bread pudding pudding desserts = • = 4 4b = 8 4b = 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 Multiplication and 1-4 Division Equations Additional 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 Multiplication and 1-4 Division Equations 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 1 8 • total amount needed x = = amount raised so far 750 1 x = 750 Write the equation. 8 8 • 1 x = 8 • 750 Multiply both sides by 4. 8 x = 6000 The library needs to raise a total of $6000. Pre-Algebra Solving Multiplication and 1-4 Division Equations 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 Multiplication 6x 2 = 10 Subtraction To solve this equation, add to isolate the term with the variable in it. Then divide to solve. Pre-Algebra Solving Multiplication and 1-4 Division Equations Additional Example 5: Solving a Simple Two-Step Equation Solve 3y – 7 = 20. Step 1: Step 2: Pre-Algebra 3y – 7 = 20 +7 +7 3y = 27 Add 7 to both sides to isolate the term with y in it. 3y = 27 Divide both sides by 3. 3 3 y=9 Solving Multiplication and 1-4 Division Equations Try This: Example 5 Solve 4y + 5 = 29. Step 1: Step 2: Pre-Algebra 4y + 5 = 29 Subtract 5 from both sides to – 5 – 5 isolate the term with y in it. 4y = 24 4y = 24 Divide both sides by 4. 4 4 y=6 Solving Multiplication and 1-4 Division Equations Lesson Quiz Solve. 1. k = 3 k = 18 6 2. 16t = 112 t = 7 3. b = 14 b = 126 9 4. 3n + 17 = 29 n = 4 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. 21 pages Pre-Algebra