Lesson 8 Division Equations Home Organization Alyssa is well organized. She wants all of her purses to be lined up on 3 shelves in her closet, with purses on each shelf. Alyssa must have exactly enough purses to organize her closet this way. This means that Alyssa has 12 purses. 12 Purses 3 Shelves Purses on Each Shelf In this problem, Alyssa needed to find out how many purses she could arrange in the way she wanted. This involved filling each position until the purses were organized. 2-93
Lesson 8: Division Equations Reflection How does this relate to a multiplication equation? Objectives for this Lesson In this lesson you will explore the following concepts: Solve a given single-variable division equation with an unknown Solve problems involving one-step equations Division Equations Division equations will look like this: x = 6 y 3 = 12 32 = m 2 The inverse operation of multiplication is division. You used this in solving multiplication equations in Lesson 7. Look at the relationships in these equations: Multiplication Division (12) = 8 8 12 = 3(5) = 15 15 5 = 3 6(7) = 2 2 7 = 6 2-9
Lesson 8: Division Equations The inverse operation of division is multiplication. This property allows you to solve division equations. Modelling Division Equations You can use cups and counters as one way to model a division equation. Example 1 Solve x 6 = 3 using cups and counters. 1. Since the variable is divided by 6, you need 6 cups or counters. 2. The right side is 3 so we need to fill each cup with 3 counters. 2-95
Lesson 8: Division Equations 3. The answer is the total number of counters in the model. The answer is: x = 18 Another way to model an equation is to use an area model. Example 2 Solve c = 5 using a visual model. 1. Draw a picture of the variable as a rectangle. C 2. Since the variable is divided by in the equation, divide the rectangle into equal parts. 3. Now place 5 in each section. 5 5 5 5. How many are in the total? c = 20 2-96
Lesson 8: Division Equations Look at instruction 3 of this example. There are sections of 5 for a total of 20. This means that to solve the equation, you multiplied times 5. The Multiplication Property of Equality The two sides of an equation remain equal if both sides are multiplied by the same number. Remember, the inverse of division is multiplication. You can multiply both sides of the equation by the divisor to get the solution. c = 5 () Y c Y = 5( ) c = 20 Equation Multiply both sides by the divisor. Answer Let s Explore Exploration 1: Division Equations Materials:, Lesson 8, Exploration 1 page from your Workbook, paper, pencil Solve the following division equations using the rectangle provided. Separate the rectangle into the sections needed to model the problem. 2-97
Lesson 8: Division Equations 1. m 2. 3.. 3 = m = 3 m = 3 m 2 6 5 = 5. What is the operation that you would use to find the answer? 6. Can you find the answer using the operation without the model? Why or why not? Solving Division Equations Using the Rule Now try solving one without a model. To check and see if you are correct, put the number back in the equation and divide. If the statement is true, it is correct. Example 3 Solve n 3 = 8 using the rule for division equations and check. 1. Write the equation. n = 8 3 2. Multiply both sides by the divisor 3. n (3) = 8( 3) 3 3. Write the solution. n = 2 2-98
Lesson 8: Division Equations. Check the solution: n 3 = 8 (3) n 3 = 8( 3) 2 3 = 8 n= 2 8= 8 This is what the entire problem will look like on your paper. 5. The answer is: n = 2 Now It s Your Turn Solve and check each equation. a. j 3 = 5 b. h = 2 c. 6 t = 7 Solutions a. j = 15 b. h = 12 c. t = 28 Let s Practice In your Workbook turn to, Lesson 8 and complete 1 to 18. 2-99
Lesson 8: Division Equations Problem Solving with Division Equations Division equations have clue words to let you know that you need to divide. Variable Equal Sign Division a number some number what number is equals gives yields are were will be per a out of ratio of quotient of divided by You can use the clue words to identify the parts of the equation. Division Variable n = 8 3 Equal Sign Here are some sentences that have been written as division equations. Words Equations the quotient of a number and 3 is 5 n 3 = 5 a number divided by equals six y = 6 n = 5 3 y = 6 2-100
Lesson 8: Division Equations Here is an example of how to write a division equation from a sentence: Example Write an equation for the sentence: A number divided by seven equals nine. 1. Circle the operation and equation words. A number divided by seven equals nine. 2. Write the division symbol and equal sign over the clue words. = A number divided by seven equals nine. 3. Underline the words for the numbers and for the variable. = A number divided by seven equals nine.. Write in the variable and numbers. b 7 = 9 A number divided by seven equals nine. 5. Write the equation. b 7 = 9 2-101
Lesson 8: Division Equations Now It s Your Turn Write an equation for each sentence. a. The quotient of a number and eleven is 10. b. A number divided by six equals twelve. c. A number divided by four equals two. Solutions a. n 11 = 10 b. y 6 = 12 c. b = 2 Let s Practice Go online to watch the Notepad Tutor about Division Equations. In your Workbook turn to, Lesson 8 and complete 19 to 2. 2-102