The Math News

Fractions and Fraction Models

Fractions are a way to show that something is less than a whole. For example, if you ate three pieces of a pizza that had eight pieces in total, then that means that you ate 3/8 of a whole pizza. Fraction models are visual ways to show fractions. Above is a picture of a fraction model.

Multiplication and Division Relationships

There is a relationship between multiplying fractions and dividing them. The relationship is that you have to use multiplication to divide fractions. (See "Dividing Fractions" for more info about this.)

To add and subtract fractions, the denominators need to be equal. To make them equal, you need to find the least common multiple. To do this, multiply both denominators by what you multiply to make them that least common multiple, then multiply the numerator by the same number you multiplied the denominator by. Then, you just add or subtract the fractions that you get as a result, then simplify and/or convert it to a mixed fraction if needed. (Remember, only add the numerators and leave the denominators the same.) For example:

2/3+3/4 LCM: 12 3x4=12 2x4=8= 8/12 4x3=12 3x3=9=9/12 8/12+9/12= 17/12= 1 5/12

Multiplying Fractions

Multiplying fractions is relatively simple. What you do is you just multiply the numerator by the numerator and the denominator by the denominator. Then, same as with adding and subtracting, you simplify it or convert it to a mixed fraction if you need to. Here's an example:

5/7 x 4/6 5x4=20 7x6=42= 20/42= 10/21

Dividing Fractions

In this section, I will tell you how to divide fractions. To divide two fractions, the first thing you need to do is find the reciprocal of the second fraction. To find the reciprocal, just switch around the numerator and the denominator. Then, you need to change the division sign into a multiplication sign. Now, all you need to do is multiply the first fraction by the reciprocal of the second fraction. Here's and example if your still confused:

(2/3) / (4/9) = 2/3x9/4= 18/12= 1 6/12= 1 1/2