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Dividing fractions by a whole number

The video below shows two kinds of examples of fraction division where we do not have to use the "rule", but instead can use "mental math". The first type is dividing fractions by whole numbers. The second is divisions where the answer is a whole number.

When a fraction is divided by a whole number, think of dividing pie pieces between a certain number of people. You can always check each division by multiplication. Multiply the answer and the divisor, and you should get the original dividend.
4 5   of a pie is divided between two people.       4 5  ÷ 2 =  2 5    Check:   2 5  × 2  =  4 5	6 8   is divided between three people.       6 8  ÷ 3 =  2 8    Check:  2 8  × 3  =  6 8

1.  Color each person's share with a different color, and write a division sentence.

2. Write a division sentence for each problem and solve. 

Sometimes you need to split existing pieces into smaller pieces when you divide pie pieces between a certain number of people.
1/2 of a pie is divided   between three people.   1 2  ÷ 3 =   1 6    Check:  1 6  × 3  =  3 6  =  1 2	1/5 of a pie is divided   between three people.       1 5  ÷ 3 =  1 15     Check:   1 15  × 3  =  3 15   =  1 5

3. The leftover pie is divided equally. How much does each one get? Write a division sentence.

a. Divide between two people.        1 2  ÷ 2 =	b. [available in the book]
d. Divide between two people.
		i. Divide between three people.

Can you notice a shortcut?

 

4. Solve the following problems, based on the shortcut you hopefully noticed in the previous exercise.

5. Solve the opposite problems: if each person got this much pie, how much was there originally?

a.

÷ 3  =  1 4

b.

[available in the book]

d.

÷ 3  =  3 10

This time we will divide several leftover pie pieces between some people.

3/4 is divided between two people. One fourth piece is split into two. Each person gets 1/4 and 1/8.        3 4  ÷ 2 =  1 4  +  1 8  =   3 8 Another way of solving the same problem is to split each fourth piece into 2. This means we change the 3/4 into 6/8.     3 4  ÷ 2   ↓     6 8  ÷ 2  =  3 8

6. The leftover pie is divided equally. How much does each one get? Write a division sentence.

a. Divide 5/6 between two people.     First split each piece into 2 new ones.           5 6  ÷ 2 =	b. [available in the book]
c. [available in the book]	d. [available in the book]
e. [available in the book]	f. Divide 4/5 between three people.     First split each piece into 3.          4 5  ÷ 3 =

The ideas in this fraction lesson are taken from the Math Mammoth Fractions 2 book. Only a few examples of each problem type are shown; you should make more problems of each kind for the student.

Math Mammoth Fractions 2 A self-teaching worktext that teaches fractions using visual models, a sequel to Math Mammoth Fractions 1. The book covers simplifying fractions, multiplication and division of fractions and mixed numbers, converting fractions to decimals, and ratios. Available as an affordable download ($5.00), and also as a printed copy. => Learn more and see the free samples! See more topical Math Mammoth books

Next lesson: Dividing Fractions 2a: How Many Times Does It Fit?