Math fractions made easy

Updated July 20, 2017

Fractions can be one of the most difficult parts of math, for kids as well as adults. This is unfortunate because fractions are particularly useful in everyday applications. While fractions can be confusing for lots of reasons, that doesn't mean that they have to be difficult. A few tips and guidelines can help you master this important mathematical concept.

The Basics

A fraction is a way to represent parts of a whole. The bottom number of the fraction (called the denominator) tells you how many parts the whole has been divided into. The top number (the numerator) tells you how many of those parts you have. Think of a pie divided into equal pieces. The fraction 5/8 indicates that the pie has been divided into eight equal slices, of which there are still five left.

Manipulating, Adding and Subtracting

Now that you understand what a fraction is, you need to know how you can change, or manipulate, a fraction. If you multiply or divide the top and bottom numbers by the same thing, the amount you have doesn't change. Just like two quarters is the same as one half of a dollar, all fractions can be expressed in more than one way. Thus you can change 1/4 into 2/8 by multiplying both the top and bottom by 2, and also turn 6/9 into 2/3 by dividing the top and bottom both by 3.

This is important because it allows you to add and subtract fractions. In order to add two fractions together, they have to have the same bottom number. To add to fractions that don't already have the same bottom number, you need to change one or both of the fractions. If you want to add 1/3 and 1/4, you need to first change both bottom numbers to the same thing. To do that, multiply the top and bottom of 1/3 by 4, and the top and bottom of 1/4 by 3. Now you have 4/12 + 3/12. Once the bottom numbers match, all you have to do is add the top numbers together, so 1/3 +1/4=4/12 + 3/12 = 7/12.

Knowing what numbers to use to change the fractions can be tricky, but you can always simply multiply both the top and bottom of each fraction by the bottom number of the other fraction.

Multiplying and Dividing.

Interestingly, multiplying and dividing fractions is simpler than adding and subtracting. To multiply two fractions together, all you have to do is multiply the two top numbers together, and the two bottom numbers together. For instance 3/4 x 2/6 = 6/24 because 3 x 2= 6 and 4 x 6 = 24.

For division, you do the same thing, but first you have to flip the top and bottom numbers of the second fraction. As an example: 2/3 ÷ 3/4 = 2/3 x 4/3 = 8/9 because 2 x 4 = 8 and 3 x 3 =9.

Mixed Numbers and Improper Fractions

Now that you can add, subtract, multiply, and divide, there's only one more thing about fractions that you need to know. Sometimes, fractions are used to express numbers that are more than one. To continue our example, this is like having one whole pie and a few pieces of another. There are two ways to express these kinds of fractions. The first is called an improper fraction, which means a fraction that has a bigger top number than bottom number, as in 9/8 or 14/5. You can also write these values as mixed numbers, which means a whole number followed by a fraction such as 1½ or 4¾.

You can switch a mixed number to an improper fraction by multiplying the whole number by the bottom number of the fraction and adding the result to the top number of the fraction, so that 2¾=11/4. To change an improper fraction into a mixed number, divide the top number by the bottom number, leaving a remainder. The answer from your division becomes the whole number, and the remainder becomes the new top number for your fraction: 5/2 = 2½ because 5 ÷ 2= 2 with a remainder of 1.

Now all you need to do to master fractions is to keep these rules in mind--and practice.

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