Fractions Multiplication: Mixed and Improper Fractions

Here's what we do if to multiply mixed fractions such as 2 1/4 × 1 2/3:

1) Change any mixed fraction to an improper fraction.

2) Multiply the numerators and multiply the denominators.

3) Simplify the answer.

1) 2 × 4 = 8. 8 + 1 = 9. So, 2 1/4 = 9/4.

Also, 1 × 3 = 3. 3 + 2 = 5. So, 1 2/3 = 5/3.

If you don't understand this then please review Fractions Introduction.

2) We rewrite 2 1/4 × 1 2/3 as 9/4 × 5/3.

Multiply the numerators: 9 × 5 = 45.

Multiply the denominators: 4 × 3 = 12.

Our answer is 45/12.

3) 45/12 is simplified to 3 9/45: 12 goes into 45 3 times with a remainder of 9. In turn, 3 9/45 is simplified to 3 1/5:

Factors of 45: 1, 5, 9, 45

Factors of 9: 1, 3, 9

9 ÷ 9 = 1

45 ÷ 9 = 5

If you don't understand this then please review Fractions Introduction.

Here's another example: 4 1/5 × 3 1/2:

Once again, we:

1) Change any mixed fraction to an improper fraction.

2) Multiply the numerators and multiply the denominators.

3) Simplify the answer.

1) 4 × 5 = 20. 20 + 1 = 21. So, 4 1/5 = 21/5.

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

If you don't understand this then please review Fractions Introduction.

2) We rewrite 4 1/5 × 3 1/2 as 21/5 × 7/2.

Multiply the numerators: 21 × 7 = 147.

Multiply the denominators: 5 × 2 = 10.

Our answer is 147/10.

3) 147/10 is simplified to 14 7/10: 10 goes into 147 10 times with a remainder of 7. If you don't understand this then please review Fractions Introduction.

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

Rewrite 3 × 2/7 as 3/1 × 2/7.

Multiply the numerators: 3 × 2 = 6.

Multiply the denominators: 1 × 7 = 7

Our answer it 6/7.

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