Year 8 Interactive Maths - Second Edition

Fractions

Proper Fraction

If the numerator is smaller than the denominator, then the fraction is said to be a proper fraction.

Note:

Proper fractions are smaller than 1.

Improper Fraction

If the numerator is greater than the denominator, then the fraction is said to be an improper fraction.

Note: 

Improper fractions are greater than 1.

Equivalent Fractions

We notice that:

In general:

The numerator of a fraction and denominator of a fraction can be multiplied by the same number without altering the value of the fraction.

In general:

The numerator of a fraction and denominator of a fraction can be divided by the same number without altering the value of the fraction.

Example 1

Solution:

We find, by trial and error, that 7 divides into both the numerator and denominator.

Setting out:

Usually, we set out the solution as follows:

Note:

Key Terms

fraction, numerator, denominator, proper fraction, improper fraction, equivalent fraction, simplest form, cancelling