# Year 5 Maths

# Putting Fractions in their Lowest Terms

A fraction is in its lowest terms when its numerator and denominator have no common factor greater than 1; in other words, when no number larger than 1 can divide into both the numerator and denominator without a remainder. So, to put a fraction in its lowest terms, divide the numerator and denominator by common factors, until there is no common factor left greater than one.

Here is an example. Put ^{3}/_{9} in its lowest terms. You can divide both 3 and 9 by 3. They have 3 as a common factor.

1 and 3 have no common factor greater than 1. Therefore, ^{1}/_{3} is in its lowest terms.
Now try putting ^{12}/_{18} in its lowest terms. You can divide both 12 and 18 by 2.

But you can go further. You can divide both 6 and 9 by 3.

There are no more common factors greater than 1.

^{2}/_{3} is the only one of these equivalent fractions that is written in its lowest terms. You could have done this problem in one step by noticing that 12 and 18 have 6 as a common factor. 6 is the greatest common factor of 12 and 18.

When you divide the numerator and denominator by their greatest common factor, you put a fraction into its lowest terms in one step.

This activity is adapted from pages 239-240 of What Your Year 5 Child Needs to Know, which can be purchased here.