# A Guide to the GRE/Fractions

## Fractions

To add or subtract fractions, first adjust them so that they have a common denominator. This can be achieved by “cross-multiplying”, or multiplying each by the other's denominator.

Fractions can be adjusted by multiplying the numerator (top) and denominator (bottom) by the same value.has the same value as

The value of + isn't but rather,

```+  Take the original fraction.
```
```   Cross multiply.
```
```+  Work out the parentheses.
```
```           Add accordingly.
```

To multiply fractions, multiply numerators by numerators and denominators by denominators.

```multiplied byis
```

To divide fractions, invert one of the fractions, then multiply them.

divided by= multiplied by=

It doesn't matter which fraction is inverted.

Always reduce fractions which aren't in their lowest terms

```is equal toTo reduce a fraction, divide both the numerator and the denominator by a common factor.  For example, both 3 and 6 are divisible by 3; thus, equals
```

An “improper fraction” is a fraction suchas in which the numerator exceeds the denominator.is the same asor 1.5.

### Practice

Solve for the value of each of the

following.

1. +

```2. ()
```
```3. ÷
```

### Answers to Practice Questions

1.

```+                  Take the initial equation.
```
```+          “Cross multiply.”  Multiply each fraction by the                                        other's         denominator.
```
```+          Work out the parentheses.
```
```+= Add the numerators - leave the denominators be.
```
```=  Reduce the final fraction by dividing both the                                  numerator and denominator by 2, 3, or another                                   common factor.
```
```2.
```

To multiply fractions, multiply numerators by numerators and denominators by denominators - 2(1) over 9(3).

```3.
```

To divide fractions, invert and multiply. This yields a result of 5(1) over 2(1).