3 ÷ ¼ = 12 Dividing Fractions Lee made 3 pizzas and cut each into fourths. How many pieces does Lee have to share? 3 ÷ ¼ = 12

Reciprocal The problem on the previous slide showed three pies that were divided into fourths to get 12 slices to share. That is because… 3 ÷ ¼ = 3 x 4.

Reciprocals Whole #s Reciprocal of the Whole #s Fractions Reciprocal of the Fractions Mixed #s Reciprocal of the Mixed #s

2 ÷ ½ = 2 x 2 = 4 Let’s Model it. 2 ÷ ½ = 4 1 2 3 4 Two Bars…Each divided in half. 1 2 3 4 Where’s the reciprocal? So, how many times does ½ go into 2? 2 ÷ ½ = 2 x 2 = 4

4 2 vs. 4 ½

How many wholes? What did each whole get divided into? How many equal parts is the result?

How many wholes? What did each whole get divided into? How many equal parts? 4 thirds 12 equal parts Dividing a number is the same as multiplying its reciprocal 4 ÷ 1/3 = 4 x 3 = 12 1/3 3/1 RECIPROCAL

Use the bars above to help you model 4 ÷ ¼.

Use the bars above to help you model 4 ÷ ¼. 1. Decide on the fractional part to divide the 4 wholes. FOURTHS

Use the bars above to help you model 4 ÷ ¼. Decide on the fractional part to divide the 4 wholes. 2. Divide each whole by that fractional part.

4 ÷ ¼ = 4 x 4 = 16 Use the bars above to help you model 4 ÷ ¼. 2 3 4 5 6 8 9 10 11 7 12 13 14 15 16 Use the bars above to help you model 4 ÷ ¼. Decide on the fractional part to divide the 4 wholes. 2. Divide each whole by that fractional part. 3. Count the parts – Answer… “How many times does ¼ go into 4?” 4 ÷ ¼ = 4 x 4 = 16

Use the bars above to help you model 3 ¾.

Use the bars above to help you model 3 ¾. 1. Decide on the fractional part to divide the 3 wholes. FOURTHS

Use the bars above to help you model 3 ¾. A A A B B B A A A B B B Use the bars above to help you model 3 ¾. 1. Decide on the fractional part to divide the 4 wholes. 2. Divide each whole by that fractional part, AND shade is every three of the four.

3 ¾ = x = = 4 Use the bars above to help you model 3 ¾. A A A B B B A A A B B B Use the bars above to help you model 3 ¾. 1. Decide on the fractional part to divide the 4 wholes. 2. Divide each whole by that fractional part, AND shade is every three of the four. 3. Count your parts… Answer – “How many times does ¾ go into 3?” 3 4 12 3 ¾ = x = = 4 ___ ___ ___ 1 3 3

Use the bars above to help you model 4 ÷ ¾.

Use the bars above to help you model 4 ÷ ¾. 1. Decide on the fractional part to divide the 4 wholes. FOURTHS

Use the bars above to help you model 4 ÷ ¾. A A A B B B A A A B B B A A A Use the bars above to help you model 4 ÷ ¾. Decide on the fractional part to divide the 4 wholes. 2. Divide each whole by that fractional part, AND shade is every three of the four.

Use the bars above to help you model 4 ÷ ¾. A A A B B B A A A B B B A A A Use the bars above to help you model 4 ÷ ¾. Decide on the fractional part to divide the 4 wholes. 2. Divide each whole by that fractional part, AND shade is every three of the four. 3. Count your parts… Answer – “How many times does ¾ go into 4?”

Use the bars above to help you model 4 ÷ ¾. A A A B B B A A A B B B A A A C Use the bars above to help you model 4 ÷ ¾. 13 __ Decide on the fractional part to divide the 4 wholes. 2. Divide each whole by that fractional part, AND shade is every three of the four. Count your parts… Answer – “How many times does ¾ go into 4?” 4. There’s a remainder!

Modeling Fraction by a Whole Number