Help with Mixed Fractions: Division and Measurements

Mixed Fractions

A mixed fraction combines a whole number, like one, three or eight, with a fraction, like 1/2, 2/3 or 7/8. You might use a fraction to show that your family drank 2 1/2 (two and one half) gallons of milk this week, or you ran 1 3/4 (one and three-quarters) of a mile.

Measurement

Mixed fractions are commonly used for measurements that contain a number of whole units, as well as a fractional unit. For instance, you might measure a piece of paper that's between five and six inches long. On a ruler, the space between five and six inches will be divided into fractions: 1/8, 1/4, 3/8, 1/2 and so on. You'll express the paper's length as the lower whole number (five) and the nearest fraction, such as 5 3/8 or 5 3/4.

Division

Improper Fractions

Dividing mixed fractions is only possible if you turn the mixed fraction into an improper fraction. This is simply a fraction with a numerator that's larger than the denominator. To make this conversion, follow these steps:

1. Multiply the mixed fraction's denominator by the whole number. For instance, if the mixed fraction is 4 3/7, multiply 7 x 4.

2. Add that product to the mixed fraction's numerator. The result becomes the numerator of the answer. For example, 7 x 4 = 28, and 28 + 3 = 31, so 31 is the answer's numerator.

3. Write the new numerator over the denominator from the mixed fraction. For example, 4 3/7 = 31/7.

Multiplying Reciprocals

Now that you can change mixed fractions into improper fractions, the next step is to divide them. Dividing any fraction, including an improper fraction, involves multiplying one fraction by the reciprocal of the other one. To get the reciprocal, just reverse the numerator and the denominator. For instance, 3/4 becomes 4/3.

To solve your division problem, convert the mixed fraction to an improper fraction first. For instance, 4 1/2 becomes 9/2. Then, if you're dividing by a fraction, like 1/3, find its reciprocal (3/1). Last, you'll just multiply those two fractions together to get 27/2. Here's the step-by-step process:

4 1/2 ÷ 1/3

= 9/2 ÷ 1/3

= 9/2 x 3/1

= 27/2