Warm Up Multiply. –2 1. –3 2. –15 – 10 3. 0.05(2.8) 0.14 5 6 1 2 –2 1. –3 2. 2 3 –15 – 10 3. 0.05(2.8) 0.14 4. –0.9(16.1)‏ –14.49

Reciprocal: one of two numbers whose product is 1. *To find the reciprocal of a fraction, flip the fraction.

To divide fractions: Keep Change Flip Multiply by the reciprocal. (Flip the 2nd fraction and multiply.) Multiply the numerators. Multiply the denominators. Simplify. Keep Change Flip

Example 1: Dividing Fractions Divide. Write the answer in simplest form. 5 11 1 2 A. ÷ 5 11 ÷ 1 2 5 11 • 2 1 = Multiply by the reciprocal. 5 11 • 2 1 = No common factors. 10 11 = Simplest form

Example 1: Dividing Fractions Divide. Write the answer in simplest form. 3 8 B. 2 ÷ 2 3 8 ÷ 2 = 19 8 2 1 ÷ Write as an improper fraction. = 19 8 1 2 Multiply by the reciprocal. 19 • 1 8 • 2 = No common factors 19 16 = 3 16 = 1 19 ÷ 16 = 1 R 3

A. ÷ 28 45 Divide. Write the answer in simplest form. 7 15 3 4 7 15 ÷ Check It Out: Example1 Divide. Write the answer in simplest form. 7 15 3 4 A. ÷ 7 15 ÷ 3 4 7 15 • 4 3 = Multiply by the reciprocal. 7 • 4 15 • 3 = No common factors. 28 45 = Simplest form

B. 4 ÷ 3 ÷ ÷ 3 4 1 Divide. Write the answer in simplest form. Check It Out: Example1 Divide. Write the answer in simplest form. 2 5 B. 4 ÷ 3 = 22 5 3 1 ÷ Write as an improper fraction. 2 5 ÷ 3 4 = 22 5 1 3 Multiply by the reciprocal. 22 • 1 5 • 3 = No common factors. 7 15 = or 1 22 15 22 ÷ 15 = 1 R 7

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 1. 1.32 0.4 1.32 0.4 10 13.2 4 = = 1 decimal place 1 zero

Example 2: Dividing Decimals Find 0.384 ÷ 0.24. 0.384 0.24 0.384 ÷ 0.24 = 100 38.4 24 = 38.4 24 = Divide. = 1.6

Check It Out: Example 2 Find 0.585 ÷ 0.25. 0.585 0.25 0.585 ÷ 0.25 = 100 58.5 25 = 58.5 25 = Divide. = 2.34

Example 3: Evaluating Expressions with Fractions and Decimals Evaluate the expression for the given value of the variable. 5.25 for n = 0.15 A. n 100 100 0.15 has 2 decimal places, so use . 5.25 0.15 = 100 525 15 = Divide. = 35 When n = 0.15, = 35. 5.25 n

Example 3: Evaluating Expressions with Fractions and Decimals Evaluate the expression for the given value of the variable. 4 5 k ÷ for k = 5 B. Multiply by the reciprocal. 5 4 = 5 1 • 4 5 5 ÷ 5 • 5 1 • 4 = 25 4 1 4 6 Divide. When k = 5, k ÷ = . 4 5 1 4 6

Check It Out: Example 3 Evaluate the expression for the given value of the variable. 2.55 A. for b = 0.75 b 100 100 0.75 has 2 decimal places, so use . 2.55 0.75 2.55 0.75 = 100 100 255 75 = Divide. = 3.4 When b = 0.75, = 3.4. 2.55 b

u ÷ , for u = 9 9 ÷ = = = 15 No common factors When u = 9, u ÷ = . 15 Check It Out: Example 3 Evaluate the expression for the given value of the variable. 4 7 u ÷ , for u = 9 B. = 9 1 9 ÷ 4 7 7 4 Multiply by the reciprocal. 9 • 7 1 • 4 = No common factors = 3 4 15 When u = 9, u ÷ = . 3 4 15 4 7

Understand the Problem Example 4: Problem Solving Application 1 2 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? 3 4 1 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. 1 2 3 4

Example 4 Continued 2 Make a Plan Set up an equation.

÷ = n • = n , or 1 batches of cookies. Example 4 Continued Solve 3 Let n = number of batches. 1 2 3 4 = n ÷ 3 4 2 1 = n • 6 4 , or 1 batches of cookies. 1 2

Example 4 Continued Look Back 4 One cup of oats would make two batches so 1 is a reasonable answer. 1 2

Lesson Quiz Divide. 5 6 1 2 –1 8 9 1. 2 ÷ –1 2. –14 ÷ 1.25 –11.2 3. 3.9 ÷ 0.65 6 112 x 4. Evaluate for x = 6.3. 17.7 5. A penny weighs 2.5 grams. How many pennies would it take to equal one pound (453.6 grams)?  182