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Fractions Division: Mixed and Improper Fractions

What we do is to divide mixed fractions such as 3 1/4 ÷ 2 2/3? We do the same steps as we did when we multiplied mixed fractions with the additional step of flipping (turning over) the second fraction (called the multiplier, as you learned in Basic Multiplication, Lesson 13) :

1) Change any mixed fraction to an improper fraction.
2) Flip (turn over) the second fraction. 3) Multiply the numerators and multiply the denominators.
4) Simplify the answer.

1) 3 × 4 = 12. 12 + 1 = 13. So, 3 1/4 = 13/4.
Also, 2 × 3 = 6. 6 + 2 = 8. So, 2 2/3 = 8/3.
If you don't understand this then please review Fractions Introduction.

2) We flip (turn over) 8/3 to get 3/8.

3) We rewrite 3 1/4 ÷ 2 2/3 as 13/4 × 3/8.
Multiply the numerators: 13 × 3 = 39.
Multiply the denominators: 4 × 8 = 32.
Our answer is 45/12.

4) 39/32 is simplified to 1 7/32. If you don't understand this then please review Fractions Introduction.


Here's another example: 6 1/5 ÷ 4 1/2:

Once again, we:
1) Change any mixed fraction to an improper fraction.
2) Flip (turn over) the second fraction. 3) Multiply the numerators and multiply the denominators.
4) Simplify the answer.

1) 6 × 5 = 30. 30 + 1 = 31. So, 6 1/5 = 31/5.
Also, 4 × 2 = 8. 8 + 1 = 9. So, 4 1/2 = 9/2.
If you don't understand this then please review Fractions Introduction.

2) We flip (turn over) 9/2 to get 2/9.

3) We rewrite 6 1/5 ÷ 4 1/2 as 31/5 × 9/2.
Multiply the numerators: 31 × 9 = 279.
Multiply the denominators: 5 × 2 = 10.
Our answer is 279/10.

4) 279/10 is simplified to 27 9/10: 10 goes into 279 27 times with a remainder of 9. If you don't understand this then please review Fractions Introduction.


What if we have a fraction divided by a whole number, such as 3 1/2 ÷ 7? In Basic Division, we learned that any number divided by 1 is itself: for example, 7 ÷ 7 = 1. The FoxyMath way is to convert the whole number to a fraction and rewrite the equation:
Rewrite 3 1/2 ÷ 7 as 3 1/2 ÷ 7/1.

1) 3 × 2 = 6. 6 + 1 = 7. So, 3 1/2 = 7/2.

2) We flip (turn over) 7/1 to get 1/7.

3) We rewrite 3 1/2 ÷ 7 as 7/2 × 1/7.
Multiply the numerators: 7 × 1 = 7.
Multiply the denominators: 2 × 7 = 14.
Our answer is 279/10.

4) 7/14 is simplified to 1/2.

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