Transcript 1-9
Solving Equations by 1-9 Multiplying or Dividing Warm Up Problem of the Day Lesson Presentation Lesson Quizzes Solving Equations by 1-9 Multiplying or Dividing Warm Up Write an algebraic expression for each word phrase. 1. A number x decreased by 9 x–9 2. 5 times the sum of p and 6 5(p + 6) 3. 2 plus the product of 8 and n 2 + 8n 4 4. the quotient of 4 and a number c __ c Solving Equations by 1-9 Multiplying or Dividing Problem of the Day How many pieces do you have if you cut a log into six pieces and then cut each piece into 4 pieces? 24 Solving Equations by 1-9 Multiplying or Dividing Learn to solve equations using multiplication and division. Solving Equations by 1-9 Multiplying or Dividing You can solve a multiplication equation using the Division Property of Equality. Solving Equations by 1-9 Multiplying or Dividing Additional Example 1A: Solving Equations Using Division Solve 6x = 48. 6x = 48 6x = 48 6 6 1x = 8 x=8 Use the Division Property of Equality: Divide both sides by 6. 1•x=x Check 6x = 48 ? 6(8) = 48 Substitute 8 for x. ? 48 = 48 Solving Equations by 1-9 Multiplying or Dividing Additional Example 1B: Solving Equations Using Division Solve –9y = 45. –9y –9y –9 1y y = 45 = 45 –9 = –5 = –5 Use the Division Property of Equality: Divide both sides by –9. 1•y=y Check –9y = 45 ? –9(–5) = 45 Substitute –5 for y. ? 45 = 45 Solving Equations by 1-9 Multiplying or Dividing Check It Out: Example 1A Solve 9x = 36. 9x = 36 9x = 36 9 9 1x = 4 x=4 Use the Division Property of Equality: Divide both sides by 9. 1•x=x Check 9x = 36 ? 9(4) = 36 Substitute 4 for x. ? 36 = 36 Solving Equations by 1-9 Multiplying or Dividing Check It Out: Example 1B Solve –3y = 36. –3y –3y –3 1y y = 36 = 36 Use the Division Property of Equality: Divide both sides by –3. –3 = –12 1 • y = y = –12 Check –3y = 36 ? –3(–12) = 36 Substitute –12 for y. ? 36 = 36 Solving Equations by 1-9 Multiplying or Dividing You can solve a division equation using the Multiplication Property of Equality. Solving Equations by 1-9 Multiplying or Dividing Additional Example 2: Solving Equations Using Multiplication b = 5. –4 b = –4 • 5 –4 • –4 b = –20 Solve Check b =5 –4 –20 =? 5 –4 ? 5 = 5 Use the Multiplication Property of Equality: Multiply both sides by –4. Substitute –20 for b. Solving Equations by 1-9 Multiplying or Dividing Check It Out: Example 2 c = 5. –3 c = –3 • 5 –3 • –3 c = –15 Solve Check c =5 –3 –15 =? 5 –3 ? 5 = 5 Use the Multiplication Property of Equality: Multiply both sides by –3. Substitute –15 for c. Solving Equations by 1-9 Multiplying or Dividing Additional Example 3: Money Application To go on a school trip, Helene has raised $670, which is one-fourth of the amount she needs. What is the total amount needed? fraction of amount raised so far 1 4 total amount needed = amount raised so far • x = 670 1 x = 670 Write the equation. 4 4 • 1 x = 4 • 670 Multiply both sides by 4. 4 Helene needs $2680 total. x = 2680 Check: The amount raised so far is about $700. She needs about 4 times this amount, or $2800. The answer is reasonable. Solving Equations by 1-9 Multiplying or Dividing Check It Out: Example 3 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 8. 8 x = 6000 The library needs $6000 total. Check: The amount raised so far is about $800. She needs about 8 times this amount, or $6400. The answer is reasonable. Solving Equations by 1-9 Multiplying or Dividing 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. Solving Equations by 1-9 Multiplying or Dividing Additional Example 4: Solving a Two-Step Equation Solve 3x + 2 = 14. Step 1: 3x + 2 = 14 Subtract 2 to both sides to – 2 – 2 isolate the term with x in it. 3x = 12 Step 2: 3x = 12 Divide both sides by 3. 3 3 x=4 Solving Equations by 1-9 Multiplying or Dividing Check It Out: Example 4 Solve 4y + 5 = 29. Step 1: Step 2: 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 Equations by 1-9 Multiplying or Dividing Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems Solving Equations by 1-9 Multiplying or Dividing Lesson Quiz Solve. 1. 3t = 9 t=3 2. –15 = 3b b = –5 x 3. –4 = –7 x = 28 4. z ÷ 4 = 22 z = 88 5. A roller coaster descends a hill at a rate of 80 feet per second. The bottom of the hill is 400 feet from the top. How long will it take the coaster rides to reach the bottom? 5 seconds Solving Equations by 1-9 Multiplying or Dividing Lesson Quiz for Student Response Systems 1. Solve the equation. 7e = 28 A. e = 1 B. e = 2 C. e = 3 D. e = 4 Solving Equations by 1-9 Multiplying or Dividing Lesson Quiz for Student Response Systems 2. Solve the equation. –72 = 4g A. g = –18 B. g = –17 C. g = –16 D. g = –15 Solving Equations by 1-9 Multiplying or Dividing Lesson Quiz for Student Response Systems 3. Solve the equation. i = –12 –6 A. i = –72 B. i = –18 C. i = 72 D. i = 80 Solving Equations by 1-9 Multiplying or Dividing Lesson Quiz for Student Response Systems 4. Solve the equation. k ÷ 9 = 13 A. k = 104 B. k = 117 C. k = 118 D. k = 123 Solving Equations by 1-9 Multiplying or Dividing Lesson Quiz for Student Response Systems 5. A surf boat descends a stream running downhill at a rate of 15 ft/minute. The bottom of the hill is at 90 ft from the top. How long will it take the surf boat to reach the bottom? A. 3 min B. 4 min C. 5 min D. 6 min