On the GED Math section, Fraction fluency is fundamental! You have to be familiar with the standard operations on fractions (adding, subtracting, multiplying, and dividing). Moreover, it’s important to know what fractions *mean* in the context of a word problem.

## Interpreting Fractions

What is a fraction? The simple answer (probably the same one your teacher gave you in first grade) is that a fraction measures a part of the whole. But what does that really mean?

If you shot a basketball 20 times during a game, but only made 15 of the shots into the basket, then you could say that 15/20 (*fifteen-twentieths*) of your shots were on target.

You might also say that you were successful 75% of the time. That’s because when you divide, 15/20 = 15 ÷ 20, you get 0.75, which is the decimal equivalent for 75%.

Furthermore, you could say that you made 3 out of every 4 shots, or 3/4 of your total shots were good. This is because 15/20 and 3/4 are **equivalent fractions**. Multiplying or dividing both the **numerator** (top number) and the **denominator** (bottom number) by the same amount gives you a fraction with the same value as the original. In this case, 15 ÷ 5 = 3, and 20 ÷ 5 = 4 implies that 15/20 = 3/4.

### Improper Fractions and Mixed Numbers

Sometimes a fraction has a larger numerator than denominator. In that case we say that the fraction is **improper.** It’s harder to think of an imporper fraction as a “part out of the whole.” Instead, just interpret the fraction as a division.

For example, 10/4 is improper. But 10/4 = 10 ÷ 4 = 2.5.

**Mixed numbers** combine whole numbers and fractions together. For example, 10/4 = 2.5 = 2 ½. (You can also do long division to find the quotient and remainder. The quotient would be the whole number part, and the remainder is the numerator of the fractional part.)

## Fraction Arithmetic

Believe it or not, it’s much easier to multiply fractions than to add or subtract them! But let’s go in the usual order and talk about addition first.

### Adding and Subtracting

Adding two fractions requires a **common denominator**. First check to see whether the two fractions have the same denominator — if they do, then you can just add the numerators together. But if the denominators are *different*, you have to find the least common denominator and re-express each fraction.

Let’s see how it works by example. Notice that 36 is the least common denominator for 12 and 9, since it’s the first multiple of both numbers. Check out GED Math: Factors, Multiples, and Primes for more info!

Subtracting works exactly the same way, except that the numerators will be subtracted instead. Here’s an example.

### Multiplying and Dividing

To multiply two fractions, simply multiply the numerators and multiply the denominators. Check for cancellation (common factors) before multiplying to save some time.

Dividing is just as easy. You just have to convert the problem into multiplication! The rule is

- When dividing by a fraction, multiply by its reciprocal instead.

In other words,

Here’s an example of the division rule in practice.

#### Example

How many 3/4 foot long pieces can be cut from a 9 foot board, assuming no waste due to cutting?

#### Solution

We are asking how many times one quantity (3/4) will go into another (9). This calls for division. Remember that any whole number can be made into a fraction by dividing by 1.

## Conclusion

Interpreting fractions and knowing how to add, subtract, multiply, and divide them are important skills to master for the GED Mathematics section. With these fundamentals in place, you build up to more advanced topics. Good luck!

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