Fractions - Multiplying Fractions

You’ll be glad to know multiplying fractions do not require the same denominators. However, you’ll get the opportunity to practice your knowledge of multiplication facts.

Other Skills Needed:
Converting improper fractions to mix numbers
Converting mixed numbers to improper fractions
Reducing fractions

I. Steps for Multiplying Fractions
1) Multiply the numerators
2) Multiply the denominators
3) If necessary, reduce to the lowest terms

Example: ¾ X 6/8
1) Multiply the numerators: 3 X 6 = 18

2) Multiply the denominators: 4 X 8 = 32

Thus ¾ X 6/8 = 18/32

3) If necessary, reduce to the lowest terms
18/32 = 9/16
If needed, refer to the article, Reducing Fractions.
In summary, ¾ X 6/8 = 18/32 = 9/16


II. Steps for Multiplying Fractions With Mixed Numbers
1) Convert all mixed numbers to improper fractions
2) Multiply numerators
3) Multiply denominators
4) If necessary, reduce to the lowest terms


Example: 2 ¾ X 6/8
1) Convert mixed numbers to improper fractions
Multiply the whole number and the denominator. Then, add the numerator. The denominator remains the same.

2 ¾ = 2 x 4 + 3 = 11/4

Now, the problem reads: 11/4 X 6/8

2) Multiply numerators: 11 X 6 = 66

3) Multiply denominators: 4 X 8 = 32

Thus 11/4 X 6/8 = 66/32
4) If necessary, reduce to the lowest terms
Since, the numerator is larger than the denominator, it is considered an improper fraction. Convert to a mixed number.

66/32 =
The line between the 66 and 32 is called the fraction bar. The fraction bar denotes division. So read this number as 66 divided by 32. When you do the division, you get 2 with a remainder of 2. The 2 represents 2 wholes, let’s say 2 gigantic pizzas. The remainder indicates part of a whole (pizza). So, represent the remainder in fraction form.. Notice that the denominator remains the same.

Thus, 66/32 = 2 2/32 = 2 1/16

Note the fraction 2/32 had common factors and was reduced to 1/16.
In summary,
2 ¾ X 6/8 = 11/4 X 6/8 = 66/32 = 2 2/32 = 2 1/16

III. Steps for Multiplying Fractions and Whole Numbers
1) Change whole numbers to fractions
2) Multiply numerators
3) Multiply denominators
4) If necessary, simplify to the lowest terms

Example: 6/7 X 5
1) Change whole numbers to fractions: 5 = 5/1
Remember, one is the denominator for all whole numbers

2) Multiply numerators: 6 X 5 = 30

3) Multiply denominators: 7 X 1 = 7

Thus: 6/7 X 5 = 30/7

4) If necessary, simplify to the lowest terms

30/ 7 = 4 2/30 = 4 1/15
The above fraction 30/7 is an improper fraction and it is improper to leave it that way! So, 30 was divided by 7. The result is 4 remainder 2. Four represents the whole number and the remainder is represented as the fraction 2/30. …but we’re not finished! The numerator and denominator of 2/30 have factors in common. Therefore, the numerator and denominator were divided by the greatest common factor, 2, in this case, and the final result is 4 1/15.

In summary, 6/7 X 5 = 30/7 = 4 2/30 = 4 1/15.