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

Dividing fractions by a whole number
Free fraction lesson plan from HomeschoolMath.net

The video below also shows examplse of dividing fractions by whole numbers:

Division of Fractions Conceptually, part 1

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 =

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

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.