Fractions

• Equivalent fractions: multiply or divide top and bottom by the same number. Simplest form means no common factor is left.
• Convert between mixed numbers and improper (vulgar) fractions.
• Use a common denominator to compare, order, add and subtract fractions.
• Find a fraction of a quantity, and write one number as a fraction of another.
• Convert fractions to decimals and percentages; divide by a fraction by multiplying by its reciprocal.

Cancelling common factors

Multiplying or dividing the numerator and the denominator by the same number gives an equivalent fraction. To write a fraction in its simplest form (lowest terms), divide top and bottom by their highest common factor.

Converting both ways

A vulgar (improper) fraction has a numerator bigger than its denominator, such as 17/5. A mixed number has a whole-number part and a fraction part, such as 3 2/5.

Making fractions comparable

To compare fractions, rewrite them over a common denominator (the lowest common multiple of the denominators is neatest). Then compare the numerators. To find a fraction of a quantity, divide by the denominator and multiply by the numerator.

Part over whole, same units

Write the part on top and the whole underneath, in the same units, then simplify.

Same denominator first

You can only add or subtract fractions with the same denominator. With mixed numbers, the safest method is to convert to improper fractions first; this avoids trouble when the fraction part of the answer would be negative.