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# Adding, Subtracting, Multiplying, and Dividing Fractions Study Guide: GED Math (page 4)

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Updated on Mar 23, 2011

### Mixed Numbers

Many improper fractions are equal to whole numbers. For example, = 2 and = 5. But some improper fractions are not equal to a whole number. They represent a whole number plus a proper fraction. A whole number plus a proper fraction is called a mixed number. Examples of mixed numbers are and so on.

When working with mixed numbers, it is usually easiest to change the mixed number to an improper fraction and then perform the given operations. To convert a mixed number to an improper fraction, multiply the whole number part by the denominator. Add this product to the numerator. This sum is the numerator of the improper fraction. The denominator stays the same.

Example

Convert to an improper fraction.

Multiply the whole number part by the denominator: 5 × 3 = 15.

Add this product to the numerator: 15 + 2 = 17.

The improper fraction is .

To convert an improper fraction to a mixed number, divide the numerator by the denominator. Find the whole number part, and the remainder becomes the numerator of the fractional part of the mixed number. The denominator stays the same.

Example

Convert to a mixed number. Find how many times 8 divides into 62:

Find the whole number part: 7.

Find the remainder: 6.

The mixed number is .

To perform mixed-number operations, convert to improper fractions.

Example

Change to improper fractions: .

Find the common denominator: .

Perform the subtraction: .

Change the improper fraction to a mixed number (if needed): .

Practice problems for these concepts can be found at:

Fractions and Decimals Practice Problems: GED Math