## GMAT Quantitative Review

## 3.0 Math Review

### 3.1 Arithmetic

### 2. Fractions

In a fraction , *n* is the *numerator* and *d* is the *denominator*. The denominator of a fraction can never be 0, because division by 0 is not defined.

Two fractions are said to be *equivalent* if they represent the same number. For example, and are equivalent since they both represent the number . In each case, the fraction is reduced to lowest terms by dividing both numerator and denominator by their*greatest common divisor* (gcd). The gcd of 8 and 36 is 4 and the gcd of 14 and 63 is 7.

**Addition and subtraction of fractions.**

Two fractions with the same denominator can be added or subtracted by performing the required operation with the numerators, leaving the denominators the same. For example, and . If two fractions do not have the same denominator, express them as equivalent fractions with the same denominator. For example, to add and , multiply the numerator and denominator of the first fraction by 7 and the numerator and denominator of the second fraction by 5, obtaining and , respectively; .

For the new denominator, choosing the *least common multiple* (lcm) of the denominators usually lessens the work. For , the lcm of 3 and 6 is 6 (not ), so .

**Multiplication and division of fractions.**

To multiply two fractions, simply multiply the two numerators and multiply the two denominators.

For example, .

To divide by a fraction, invert the divisor (that is, find its *reciprocal*) and multiply. For example, .

In the problem above, the reciprocal of is . In general, the reciprocal of a fraction is , where *n* and *d* are not zero.

**Mixed numbers.**

A number that consists of a whole number and a fraction, for example, , is a mixed number:

means .

To change a mixed number into a fraction, multiply the whole number by the denominator of the fraction and add this number to the numerator of the fraction; then put the result over the denominator of the fraction. For example, .