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Solving Equations by by Solving Equations 1-3 1-3 Multiplying or Dividing Multiplying or Dividing Warm Up Lesson Presentation Lesson Quiz Holt McDougal Algebra 1 Algebra 1 Solving Equations by 1-3 Multiplying or Dividing Warm Up 9/1 Turn these into YOUR tray when finished! Evaluate each expression. 1. (–7)(2.8) 2. 0.96 ÷ 6 3. (–9)(–9) Holt McDougal Algebra 1 Solving Equations by 1-3 Multiplying or Dividing Objective Solve one-step equations in one variable by using multiplication or division. Holt McDougal Algebra 1 Solving Equations by 1-3 Multiplying or Dividing 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. Inverse Operations Operation Multiplication Division Holt McDougal Algebra 1 Inverse Operation Division Multiplication Solving Equations by 1-3 Multiplying or Dividing Properties of Equality WORDS Subtraction Property of Equality You can subtract the same number from both sides of an equation, and the statement will still be true. NUMBERS ALGEBRA Holt McDougal Algebra 1 7=7 7–5=7–5 2=2 a=b a–c=b–c Solving Equations by 1-3 Multiplying or Dividing Properties of Equality WORDS Addition Property of Equality You can add the same number to both sides of an equation, and the statement will still be true. NUMBERS ALGEBRA Holt McDougal Algebra 1 3=3 3+2=3+2 5=5 a=b a+c=b+c Solving Equations by 1-3 Multiplying or Dividing Properties of Equality WORDS Multiplication Property of Equality You can multiply both sides of an equation by the same number, and the statement will still be true. NUMBERS ALGEBRA Holt McDougal Algebra 1 6=6 6(3) = 6(3) 18 = 18 a=b ac = bc Solving Equations by 1-3 Multiplying or Dividing Properties of Equality 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 8 8 = 4 4 2 =2 ALGEBRA a=b (c ≠ 0) a = a c c Holt McDougal Algebra 1 Solving Equations by 1-3 Multiplying or Dividing 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 Check 16 = 4c 16 16 Holt McDougal Algebra 1 4(4) 16 To check your solution, substitute 4 for c in the original equation. Solving Equations by 1-3 Multiplying or Dividing Example 1A: Solving Equations by Using Multiplication Solve the equation. j –8 = 3 Since j is divided by 3, multiply both sides by 3 to undo the division. –24 = j Check j –8 = 3 –24 –8 3 –8 –8 Holt McDougal Algebra 1 To check your solution, substitute –24 for j in the original equation. Solving Equations by 1-3 Multiplying or Dividing Example 2A: Solving Equations by Using Division Solve the equation. Check your answer. 9y = 108 y = 12 Check Since y is multiplied by 9, divide both sides by 9 to undo the multiplication. 9y = 108 9(12) 108 Holt McDougal Algebra 1 108 To check your solution, substitute 12 for y in the 108 original equation. Solving Equations by 1-3 Multiplying or Dividing Example 1B: Solving Equations by Using Multiplication Solve the equation. n = 2.8 6 Since n is divided by 6, multiply both sides by 6 to undo the division. n = 16.8 n = 2.8 Check 6 To check your solution, 16.8 2.8 substitute 16.8 for n in the 6 2.8 2.8 original equation. Holt McDougal Algebra 1 Solving Equations by 1-3 Multiplying or Dividing Scavenger Hunt! Directions: 1. Find someone with the same card as you (Jack, Queen, King, Ace) 2. When you have found a partner, both of you need to come up and pick a piece of paper from my hand. 3. Around the room, there are different equations with numbers (solutions) in the top left corner. YOU WILL START AT THE POSTER THAT HAS YOUR NUMBER FROM THE PIECE OF PAPER IN THE TOP LEFT CORNER. 4. Start at number 1 on your sheet wherever you start. Once you solve an equation, find the next problem sheet that has that solution in the top left corner and that will go in slot number 2, etc. Continue until finished. Winners get a prize! Holt McDougal Algebra 1 Solving Equations by 1-3 Multiplying or Dividing Warm-Up 9/6 MAKE A NEW WARM-UP SHEET 1. Solve the equation AND CHECK YOUR ANSWER –4.8 = –6v 2. Solve the equation AND CHECK YOUR ANSWER y –13 = 3 Holt McDougal Algebra 1 Solving Equations by 1-3 Multiplying or Dividing Warm-Up 9/7 1. What does the word ‘reciprocal’ mean? 2. Why do we check our work on homework, tests, quizzes, etc.? Holt McDougal Algebra 1 Solving Equations by 1-3 Multiplying or Dividing VOCABULARY Reciprocal Holt McDougal Algebra 1 Solving Equations by 1-3 Multiplying or Dividing Check It Out! Example 1c Solve the equation. Check your answer. c =7 8 Since c is divided by 8, multiply both sides by 8 to undo the division. c = 56 Check c =7 8 56 7 8 7 7 Holt McDougal Algebra 1 To check your solution, substitute 56 for c in the original equation. Solving Equations by 1-3 Multiplying or Dividing Check It Out! Example 1a Solve the equation. Check your answer. p = 10 5 Since p is divided by 5, multiply both sides by 5 to undo the division. p = 50 Check p = 10 5 To check your solution, 50 10 substitute 50 for p in the 5 10 10 original equation. Holt McDougal Algebra 1 Solving Equations by 1-3 Multiplying or Dividing Check It Out! Example 2b Solve the equation. Check your answer. 0.5y = –10 y = –20 Since y is multiplied by 0.5, divide both sides by 0.5 to undo the multiplication. Check 0.5y = –10 To check your solution, 0.5(–20) –10 –10 –10 substitute –20 for y in the original equation. Holt McDougal Algebra 1 Solving Equations by 1-3 Multiplying or Dividing Remember that dividing a fraction by a fraction is the same as multiplying by the reciprocal. What is a reciprocal? Holt McDougal Algebra 1 Solving Equations by 1-3 Multiplying or Dividing Example 3A: Solving Equations That Contain Fractions Solve the equation. 5 w = 20 6 The reciprocal of 5 is 6 . Since w is 6 5 5 multiplied by , multiply both sides 6 6 by . 5 w = 24 Check 5 w = 20 6 20 20 20 Holt McDougal Algebra 1 To check your solution, substitute 24 for w in the original equation. Solving Equations by 1-3 Multiplying or Dividing Warm-Up 9/12 Use the same warm up sheet you were using last week. 1) When our operation is multiplication or division, what do we want our coefficient (the number in front of our variable), to be? (0, 3, 1, 620,000,021,023??) 2) Why in world do we even care about solving one-step equations? How does it apply to you? Holt McDougal Algebra 1 Solving Equations by 1-3 Multiplying or Dividing Example 3B: Solving Equations That Contain Fractions Solve the equation. 3 = 1 z 16 8 The reciprocal of 1 is 8. Since z is 8 1 multiplied by , multiply both sides 8 by 8. 3=z 2 3 =1z Check 16 8 To check your solution, substitute 3 for z in the 2 original equation. 3 3 16 16 Holt McDougal Algebra 1 Solving Equations by 1-3 Multiplying or Dividing In groups of four… In groups of four, you are going to work together to solve the next few problems. Each of you will be assigned one step of the problem. 1 whiteboard, 1 marker, 1 eraser PER GROUP Step 1: The oldest person will complete step one of the problem. Step 2: The next oldest person will complete step 2 of the problem. Step 3: The third oldest person will complete step 3 of the problem. Step 4: The youngest person will complete step 4 of the problem. ALL TOGETHER, COME UP WITH YOUR ANSWER ON ONE WHITE BOARD! Holt McDougal Algebra 1 Solving Equations by 1-3 Multiplying or Dividing Check It Out! Example 3b Solve the equation. 4j = 2 3 6 j=1 Holt McDougal Algebra 1 4j is the same as 4 j. 6 6 The reciprocal of 4 is 6 . Since j is 6 4 4 multiplied by , multiply both sides 6 6 by . 4 Solving Equations by 1-3 Multiplying or Dividing Check It Out! Example 3b Continued Solve the equation. 4j = 2 3 6 Check 4j = 2 6 3 To check your solution, substitute 1 for j in the original equation. Holt McDougal Algebra 1 Solving Equations by 1-3 Multiplying or Dividing Check It Out! Example 3c Solve the equation. 1 w = 102 6 The reciprocal of 1 is 6. Since w is 6 multiplied by 1 , multiply both sides 6 by 6 . w = 712 Check 1 w = 102 6 102 102 102 Holt McDougal Algebra 1 To check your solution, substitute 712 for w in the original equation. Solving Equations by 1-3 Multiplying or Dividing Check It Out! Example 3a Solve the equation. Check your answer. 1 – 1 = b 5 4 5=b –4 Check The reciprocal of 1 is 5. Since b is 5 1 multiplied by , multiply both sides 5 by 5. 1b 1 = – 4 5 Holt McDougal Algebra 1 To check your solution, substitute – 5 for b in the 4 original equation. Solving Equations by 1-3 Multiplying or Dividing Example 4: Application Ciro puts 1 4 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. 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. m = $1140 Holt McDougal Algebra 1 Ciro earned $1140 mowing lawns. Solving Equations by 1-3 Multiplying or Dividing 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. Holt McDougal Algebra 1 Solving Equations by 1-3 Multiplying or Dividing Exit Ticket Using a sticky note, write your initials then put it in the area how you are feeling right now 1)I have no idea what is going on 1)I kind of understand this but need more help 2)I GOT THIS! Holt McDougal Algebra 1