Home Worksheets Lessons Online games and tutorials Curriculum guide My books Reviews

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.

# Dividing Mixed NumbersFree fraction lesson plan from HomeschoolMath.net

### To solve division, multiply by the reciprocal of the divisor.

This shortcut always works, even when the dividend
or divisor or both are mixed numbers.

Since we need to use the reciprocal of the divisor, and in the end
also multiply fractions, first change the mixed numbers
into fractions.
Then divide using the shortcut you have learned.

In the example on the right, we first change mixed numbers to
fractions. Then, division by 8/3 is changed into multiplication by its
reciprocal, 3/8. Before multiplying, the fractions are simplified.

 1 5 7 ÷  2 2 3 = 12 7 ÷ 8 3 3 ↓ ↓ 12 7 × 3 8 = 9 14 2
The hardest part of dividing mixed numbers is to REMEMBER first to change them into fractions.

1. Divide.

 a.   2 7 8 ÷ 2 5

[available in the book]
 f.   2 4 11 ÷ 4 1 5

2. Now you get to be a “detective” like teachers often need to be, and find out what the kids did wrong.
In each case,  a. explain the mistake made, and  b. solve the problem the right way.

a. Jenny: “I got this:”

 1 8 ÷ 2 5 = 2 40 = 1 20

Jenny's mistake:

Correct calculation:

 1 8 ÷ 2 5 =

b. Mark: “My calculation gives:”

 3 5 ÷ 1 1 4 = 3 5 × 4 1 = 12 5 =  2 2 5

Mark's mistake:

Correct calculation:

 3 5 ÷ 1 1 4 =

[available in the book]
[available in the book]

Another method for dividing fractions

1) Change both fractions to equivalent fractions
that have a common denominator.

2) Divide the numerators only!

This method is not necessarily less work, but it may
make more sense intuitively.

In the example on the right, we can ask:
how many times does 6/20 go into 10/20 ?

Well, that is the same as asking how many times 6 goes to 10?
The answer is: 1 2/3 times.

Example:

 1 2 ÷ 3 10 ↓ ↓ 10 20 ÷ 6 20 ↓ ↓ 10 ÷ 6 = 10 6 = 1 4 6 = 1 2 3

3. Solve using any method.

 a. 5 7 ÷ 9

[available in the book]

 f. 7 1 12 ÷ 6

4. Can you divide by half? Remember to think how many times does one-half go into the dividend.

 a.   2 ÷ 1 2 =

[available in the book]

 i.   105 ÷ 1 2 =

5. a. [available in the book]

b. [available in the book]

c. [available in the book]

d. [available in the book]

6. How many of the same kind of erasers fit into a box with
dimensions 12 in x 10 in x 8 in (length-width-height)?

7. [available in the book]

8. [available in the book]

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.

 Search my math websites: