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.

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.

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.

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.