Dividing whole numbers and fractions

18 1 3 ÷ 6 How many servings were in 3 packages? Marshall’s mom is buying 3 packages of rolls for Sunday dinner. One serving is of a package. How many servings does she have? 1 6 1 6 3 ÷ To solve, let’s make a model of 3 packages. Divide each package into sixths to represent each serving. How many servings were in 3 packages? 18

20 1 5 ÷ 4 How many pieces would she have? Brandy has 5 yards of ribbon. She wants to divide the ribbon into fourths. How many pieces of ribbon would she have? 1 4 5 ÷ To solve, let’s make a model of 5 yards of ribbon. Divide each yard into fourths to represent each piece. How many pieces would she have? 20

1 2 ÷ 8 16 How many servings would he have? Stephen wants to divide two pies into eighths. How many servings would he have? 1 8 2 ÷ To solve, let’s make a model of 2 pies. Divide each pie into eighths to represent each serving. How many servings would he have? 16

Let’s try to figure out the rule…..

Three packages of rolls divided by 1/6 5 ribbons divided into fourths 2 pies divided into eighths 3 ÷ 1 6 5 ÷ 1 4 = 18 2 ÷ 1 8 = 20 = 16

Reciprocal of a Fraction Switch the Numerator and Denominator

Examples Fraction Reciprocal 1 2 2 1 2 3 3 2 3 4 4 3

Multiply by the Reciprocal Rule : Multiply by the Reciprocal

Let’s try a few problems using the algorithm 6 ÷ 1 7 = 8 ÷ 1 10 = 5 ÷ 2 3 = 7 ÷ 5 6 = 6 x 7 1 = 6 1 x 7 1 = 42 8 x 10 1 = 8 1 x 10 1 = 80 5 x 3 2 = 5 1 x 3 2 = 15 2 = 7 1 2 7 x 6 5 = 7 1 x 6 5 = 42 5 = 8 2 5

Dividing fractions by whole numbers works a little differently. Meghan has 1 3 pan of cornbread left. She wants to divide it into 5 servings to give to her siblings. How much of a serving will each sibling receive? 1 3 ÷ 5 We will draw her pan and shade one third. Each sibling will receive 1 15 Divide that section into five pieces.

1 3 ÷ 5 1 3 x 1 5 = 1 15 We just used a model to solve 1 3 ÷5 = 1 15 . Now let’s solve using the algorithm. 1 3 ÷ 5 1 3 x 1 5 First, we will use the reciprocal of 5 … 1 5 . Then multiply. = 1 15

Divide each section into three pieces. Luke has 1 4 left of a birthday cake. He wants to divide it into 3 servings. How much would be each serving? 1 4 ÷ 3 We will draw the pan and shade one fourth. Divide each section into three pieces. 1 12 Each serving would be

1 4 x 1 3 = 1 12 1 4 ÷ 3 We just used a model to solve 1 4 ÷3 = 1 12 . Now let’s solve using the algorithm. 1 4 ÷ 3 1 4 x 1 3 First, we will use the reciprocal of 3 … 1 3 . Then multiply. = 1 12

Divide each section into two pieces. Gabby has 1 3 left of a cookie cake. She wants to divide it into 2 servings. How much would be each serving? 1 3 ÷ 2 We will draw the pan and shade one third. Divide each section into two pieces. 1 6 Each serving would be

1 3 ÷ 2 1 3 x 1 2 = 1 6 We just used a model to solve 1 3 ÷2 = 1 6 . Now let’s solve using the algorithm. 1 3 ÷ 2 1 3 x 1 2 First, we will use the reciprocal of 2 … 1 2 . Then multiply. = 1 6

Let’s try a few problems using the algorithm. 1 8 ÷ 3 = 1 6 ÷ 9 = 2 3 ÷ 7 = 4 7 ÷ 4 = 1 24 1 54 1 7 2 21