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**Solving Equations by**Multiplying or Dividing 2-2 Warm Up Lesson Presentation Lesson Quiz Holt Algebra 1 Holt McDougal Algebra 1**2**3 Warm Up Evaluate each expression. 1. (–7)(2.8) 2. 0.96 ÷ 6 3. (–9)(–9) 4. 5. 6. 19.6 0.16 81 1 1.8**Objective**Solve one-step equations in one variable by using multiplication or division.**Solving an equation that contains multiplication or division**is similar to solving an equation that contains addition or subtraction. Use inverse operations to undo the operations on the variable. Multiplication Division Division Multiplication**j**–8 = 3 –24 3 j –8 = Check 3 –8 Example 1A: Solving Equations by Using Multiplication Solve the equation. Since j is divided by 3, multiply both sides by 3 to undo the division. –24 = j To check your solution, substitute –24 for j in the original equation. –8 –8 **n**= 2.8 6 n = 2.8 Check 6 16.8 2.8 6 Example 1B: Solving Equations by Using Multiplication Solve the equation. Since n is divided by 6, multiply both sides by 6 to undo the division. n = 16.8 To check your solution, substitute 16.8 for n in the original equation. 2.8 2.8 **p**= 10 5 p = 10 Check 5 50 10 5 Check It Out! Example 1a Solve the equation. Check your answer. Since p is divided by 5, multiply both sides by 5 to undo the division. p = 50 To check your solution, substitute 50 for p in the original equation. 10 10 **y**–13 = 3 –39 3 y –13 = Check 3 –13 Check It Out! Example 1b Solve the equation. Check your answer. Since y is divided by 3, multiply both sides by 3 to undo the division. –39 = y To check your solution, substitute –39 for y in the original equation. –13 –13 **c**= 7 8 c = 7 Check 8 56 7 8 Check It Out! Example 1c Solve the equation. Check your answer. Since c is divided by 8, multiply both sides by 8 to undo the division. c = 56 To check your solution, substitute 56 for c in the original equation. 7 7 **Check 9y = 108**Example 2A: Solving Equations by Using Division Solve the equation. Check your answer. 9y = 108 Since y is multiplied by 9, divide both sides by 9 to undo the multiplication. y = 12 To check your solution, substitute 12 for y in the original equation. 9(12) 108 108 108 **Check –4.8 = –6v**Example 2B: Solving Equations by Using Division Solve the equation. Check your answer. –4.8 = –6v Since v is multiplied by –6, divide both sides by –6 to undo the multiplication. 0.8 = v –4.8 –6(0.8) To check your solution, substitute 0.8 for v in the original equation. –4.8 –4.8 **Check 16 = 4c**Check It Out! Example 2a Solve the equation. Check your answer. 16 = 4c Since c is multiplied by 4, divide both sides by 4 to undo the multiplication. 4 = c To check your solution, substitute 4 for c in the original equation. 16 4(4) 16 16 **Check 0.5y = –10**Check It Out! Example 2b Solve the equation. Check your answer. 0.5y = –10 Since y is multiplied by 0.5, divide both sides by 0.5 to undo the multiplication. y = –20 To check your solution, substitute –20 for y in the original equation. 0.5(–20) –10 –10 –10 **Check 15k = 75**Check It Out! Example 2c Solve the equation. Check your answer. 15k = 75 Since k is multiplied by 15, divide both sides by 15 to undo the multiplication. k = 5 To check your solution, substitute 5 for k in the original equation. 15(5) 75 75 75 **Remember that dividing is the same as multiplying by the**reciprocal. When solving equations, you will sometimes find it easier to multiply by a reciprocal instead of dividing. This is often true when an equation contains fractions.**6**5 6 5 6 5 6 5 The reciprocal of is . Since w is multiplied by , multiply both sides by . 5 w = 20 Check 6 20 Example 3A: Solving Equations That Contain Fractions Solve the equation. 5 w= 20 6 w = 24 To check your solution, substitute 24 for w in the original equation. 2020 **3**2 1 3 3 8 1 1 3 16 16 8 8 2 The reciprocal of is 8. Since z is multiplied by , multiply both sides by 8. = z 3 16 1 Check = z To check your solution, substitute for z in the original equation. 8 Example 3B: Solving Equations That Contain Fractions Solve the equation. 3 = z 16 **1**5 4 4 1 5 1 1 5 5 4 5 The reciprocal of is 5. Since b is multiplied by , multiply both sides by 5. – = b 1 1 = b – Check 4 5 To check your solution, substitute – for b in the original equation. Check It Out! Example 3a Solve the equation. Check your answer. –= b **4j**6 Solve the equation. 2 4j is the same as j. = 3 6 6 4 6 4 4 6 4 6 4 6 The reciprocal of is . Since j is multiplied by , multiply both sides by . Check It Out! Example 3b j = 1**Solve the equation.**2 4j = 3 6 4j = Check 6 2 3 Check It Out! Example 3b Continued To check your solution, substitute 1 for j in the original equation. **1**1 6 6 The reciprocal of is 6. Since w is multiplied by , multiply both sides by 6 . 1 Check w = 102 6 102 Check It Out! Example 3c Solve the equation. 1 w= 102 6 w = 712 To check your solution, substitute 712 for w in the original equation. 102102 **1**Ciro puts of the money he earns from mowing lawns into a college education fund. This year Ciro added $285 to his college education fund. Write and solve an equation to find how much money Ciro earned mowing lawns this year. 4 Example 4: Application one-fourth times earnings equals college fund Write an equation to represent the relationship. Substitute 285 for c. Since m is divided by 4, multiply both sides by 4 to undo the division. Ciro earned $1140 mowing lawns. m = $1140**Check it Out! Example 4**The distance in miles from the airport that a plane should begin descending, divided by 3, equals the plane's height above the ground in thousands of feet. A plane began descending 45 miles from the airport. Use the equation to find how high the plane was flying when the descent began. Distance divided by 3 equals height in thousands of feet Write an equation to represent the relationship. Substitute 45 for d. 15 = h The plane was flying at 15,000 ft when the descent began.**8**8 = a a 4 4 = c c WORDS Division Property of Equality You can divide both sides of an equation by the same nonzero number, and the statement will still be true. NUMBERS 8 = 8 2 = 2 ALGEBRA a = b (c ≠ 0) Properties of Equality**Lesson Quiz: Part 1**Solve each equation. 1. 2. 3. 8y = 4 4. 126 = 9q 5. 6. 21 2.8 –14 40**7. A person's weight on Venus is about his or her**weight on Earth. Write and solve an equation to find how much a person weighs on Earth if he or she weighs 108 pounds on Venus. 9 10 Lesson Quiz: Part 2