Course Dividing Rational Numbers 2-5 Dividing Rational Numbers Course 3 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

Course Dividing Rational Numbers Warm Up Multiply – – –15 – (2.8) 4. –0.9(16.1) –14.49

Course Dividing Rational Numbers Problem of the Day Katie made a bookshelf that is 5 feet long. The first 6 books she put on it took up 8 inches of shelf space. About how many books should fit on the shelf? 45

Course Dividing Rational Numbers Learn to divide fractions and decimals.

Course Dividing Rational Numbers reciprocal Vocabulary

Course Dividing Rational Numbers A number and its reciprocal have a product of 1. To find the reciprocal of a fraction, exchange the numerator and the denominator. Remember that an integer can be written as a fraction with a denominator of 1.

Course Dividing Rational Numbers Multiplication and division are inverse operations. They undo each other. Notice that multiplying by the reciprocal gives the same result as dividing = 2525 = ÷ 1313 = 1313 =

Course Dividing Rational Numbers Additional Example 1A: Dividing Fractions Divide. Write the answer in simplest form. Multiply by the reciprocal ÷ = No common factors ÷ = A. Simplest form =

Course Dividing Rational Numbers Additional Example 1B: Dividing Fractions Divide. Write the answer in simplest form. B ÷ ÷ 22 = ÷ Write as an improper fraction. Multiply by the reciprocal. No common factors = = 3 16 = 1 19 ÷ 16 = 1 R =

Course Dividing Rational Numbers 7 15 ÷ = 7 15 ÷ = Check It Out: Example1A Divide. Write the answer in simplest form. A. Multiply by the reciprocal. No common factors. Simplest form =

Course Dividing Rational Numbers Write as an improper fraction ÷ Multiply by the reciprocal = No common factors. 22 ÷ 15 = 1 R ÷ 3 4 = ÷ B. Divide. Write the answer in simplest form. = = or Check It Out: Example1B

Course Dividing Rational Numbers When dividing a decimal by a decimal, multiply both numbers by a power of 10 so you can divide by a whole number. To decide which power of 10 to multiply by, look at the denominator. The number of decimal places is the number of zeros to write after the = = decimal place1 zero 10

Course Dividing Rational Numbers = = Find ÷ Additional Example 2: Dividing Decimals ÷ 0.24 = 100 Divide =

Course Dividing Rational Numbers = = Find ÷ Check It Out: Example ÷ 0.25 = 100 Divide =

Course Dividing Rational Numbers 5.25 for n = 0.15 n Divide. = 35 Additional Example 3A: Evaluating Expressions with Fractions and Decimals Evaluate the expression for the given value of the variable = has 2 decimal places, so use = When n = 0.15, = n

Course Dividing Rational Numbers k ÷ for k = ÷5 ÷ 5454 = = = = 25 4 Additional Example 3B: Evaluating Expressions with Fractions and Decimals Evaluate the expression for the given value of the variable. Divide. Multiply by the reciprocal. When k = 5, k ÷ =

Course Dividing Rational Numbers 2.55 for b = 0.75 b Divide. = 3.4 Check It Out: Example 3A = = Evaluate the expression for the given value of the variable has 2 decimal places, so use. When b = 0.75, = b

Course Dividing Rational Numbers u ÷, for u = 9 Multiply by the reciprocal = No common factors 4747 = ÷ 4747 = Check It Out: Example 3B Evaluate the expression for the given value of the variable. When u = 9, u ÷ =

Course Dividing Rational Numbers Additional Example 4: Problem Solving Application A cookie recipe calls for cup of oats. You have cup of oats. How many batches of cookies can you bake using all of the oats you have? Understand the Problem The number of batches of cookies you can bake is the number of batches using the oats that you have. List the important information: The amount of oats is cup. One batch of cookies calls for cup of oats

Course Dividing Rational Numbers Course Dividing Rational Numbers Additional Example 4 Continued Set up an equation. 2 Make a Plan

Course Dividing Rational Numbers Course Dividing Rational Numbers Let n = number of batches. Solve = n ÷ , or 1 batches of the cookies Additional Example 4 Continued

Course Dividing Rational Numbers Course Dividing Rational Numbers Look Back4 One cup of oats would make two batches so 1 is a reasonable answer Additional Example 4 Continued

Course Dividing Rational Numbers Check It Out: Example 4 A ship will use of its total fuel load for a typical round trip. If there is of a total fuel load on board now, how many complete trips can be made?

Course Dividing Rational Numbers It takes of the total fuel load for a complete trip. You have of a total fuel load on board right now Understand the Problem The number of complete trips the ship can make is the number of trips that the ship can make with the fuel on board. List the important information: Check It Out: Example 4 Continued

Course Dividing Rational Numbers Set up an equation. 2 Make a Plan Amount of fuel on board Amount of fuel for one trip Number of trips ÷ = Check It Out: Example 4 Continued

Course Dividing Rational Numbers Let t = number of trips. Solve = t ÷ , or 3 round trips, or 3 complete round trips Check It Out: Example 4 Continued

Course Dividing Rational Numbers Look Back4 A full tank will make the round trip 6 times, and is a little more than, so half of 6, or 3, is a reasonable answer Check It Out: Example 4 Continued

Course Dividing Rational Numbers Lesson Quiz Divide –14 ÷ Evaluate for x = x ÷ –11.2 – ÷ A penny weighs 2.5 grams. How many pennies would it take to equal one pound (453.6 grams)? 5. about 181