#### Fractions - Dividing Fractions Skills Needed:
~Multiplication facts
~Division facts
~Converting improper fractions to mix numbers
~Converting mixed numbers to improper fractions
~Reducing fractions
~Find the reciprocal
To find the reciprocal of a number is to find another number that gives a product of one when multiplied together. For instance 3/5 and 5/3 are reciprocals of one another. Let us prove it by multiplying them. 3/5 X 5/3 = 15/15 = 1.

I. Steps for Dividing Fractions
1) Rewrite as a multiplication problem using the reciprocal of the 2nd number
2) Multiply the numerators
3) Multiply the denominators
4) If necessary, reduce to the lowest terms

Example: 4/8 divided by 2/3

1) Rewrite as a multiplication problem using the reciprocal of the 2nd number
4/8 X 3/2 =

1) Multiply the numerators: 4 X 3 = 12

2) Multiply the denominators: 8 X 2 = 16

3) If necessary, reduce to the lowest terms
12/16 = 3/4
If needed, refer to the article, Reducing Fractions at the end of this article.

In summary, 4/8 divided by 2/3 = 3/4

II. Steps for Dividing Fractions With Mixed Numbers
1) Convert all mixed numbers to improper fractions
2) Rewrite as a multiplication problem using the reciprocal of the 2nd number
3) Multiply numerators
4) Multiply denominators
5) If necessary, reduce to the lowest terms

Example: 6 4/5 divided by 1 2/3
1) Convert mixed numbers to improper fractions
Multiply the whole number and the denominator. Then, add the numerator. The denominator remains the same.

6 4/5 = 6 x 5 + 4 = 34/5

1 2/3 = 1 X 2 + 3 = 5/3

Now, the problem reads: 34/5 divided by 5/3

2) Rewrite as a multiplication problem using the reciprocal of the 2nd number
34/5 divided by 3/5
2) Multiply numerators: 34 X 3 = 102

3) Multiply denominators: 5 X 5 = 25

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.

102/25 =
The line between the 102 and 25 is called the fraction bar. The fraction bar denotes division. So read this number as 102 divided by 25. When you do the division, you get 4 with a remainder of 2. The 2 represents 4 wholes. Let us say 4 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, 102/25 = 4 2/25

In summary,
6 4/5 divided by 1 2/3 =
34/5 divided by 5/3
34/5 X 3/5 = 102/25 = 4 2/5

III. Steps for Dividing Fractions and Whole Numbers
1) Change whole numbers to fractions
2) Rewrite as a multiplication problem using the reciprocal of the 2nd number
3) Multiply numerators
4) Multiply denominators
5) If necessary, simplify to the lowest terms

Example: 8 X 3/7
1) Change whole numbers to fractions: 8 = 8/1
Remember, one is the denominator for all whole numbers

2) Rewrite as a multiplication problem using the reciprocal of the 2nd number
8/1 X 7/3 =

2) Multiply numerators: 8 X 7 = 56

3) Multiply denominators: 1 X 3 = 3

Thus: 8/1 X 7/3 = 56/3

4) If necessary, simplify to the lowest terms

56/ 3 = 18 2/3
The above fraction 56/3 is an improper fraction and it is improper to leave it that way! So, 56 was divided by 3. The result is 18 remainder 2. Eighteen represents the whole number and the remainder is represented as the fraction 2/3.

In summary, 8 divided by 3/7 =
8/1 divided by 3/7
8/1 X 7/3 = 56/3 = 18 2/3.

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