Skip to 0 minutes and 8 seconds You need to decide which of these numbers is the smallest, which is the next smallest, which is the next smallest, and which is the largest. This is difficult, because all the numerators are different, which makes it difficult to compare the fractions. If you express the fractions as equivalent fractions with the same denominator, you can then compare the numerators to see which are the smallest, and so on.

Skip to 0 minutes and 36 seconds The best numerator to choose is the lowest common multiple of the numerators. In this case, the lowest common multiple of 4, 6, 7, and 8 is 168. This means that 168 is the smallest number which 4, 6, 7, and 8 all divided into, giving a whole number result.

Skip to 1 minute and 3 seconds To convert 7/8 to an equivalent fraction with a denominator of 168, you multiply the numerator and denominator by 21. This gives 147 over 168. To convert 6/7 to an equivalent fraction with a denominator of 168, you multiply the numerator and denominator by 24. This means that 6/7 is the same as 144 over 168. To convert 3/4 to an equivalent fraction with a denominator of 168, you multiply numerator and denominator by 42. This means that 3/4 is 126 divided by 168. To convert 5/6 to an equivalent fraction with a denominator of 168, you multiply the numerator and denominator by 28. This means that 5/6 is 140 divided by 168.

Skip to 2 minutes and 14 seconds So comparing the numerators, 3/4 is fourth, 5/6 is third, 6/7 is second, and 7/8 is the largest.

Skip to 2 minutes and 33 seconds You can always check your answers with a calculator if you have one. Here, all answers are given to three decimal places. 7/8 is 0.875. 6/7 is 0.857. 3/4 is 0.750. And 5/6 is 0.833. So 3/4 is fourth, 5/6 is third, 6/7 is second, 7/8 is largest.

Skip to 3 minutes and 12 seconds To add these four fractions together, you need to express them all as having the same denominator. The denominator of a fraction tells you what type of fraction you have, and you can only add together things that are of the same type. Here, we have 8ths, 7ths, 4ths– or quarters– and 6ths. They’re all different. And so adding them together doesn’t make any sense. However, if we will express them with the same denominator using the method from before, 8/7 is 147 over 168, 6/7 is 144 over 168, 3/4 is is 126 over 168, and 5/6 is 140 over 168. As these equivalent fractions all have the same denominator, you can add them together.

Skip to 4 minutes and 11 seconds This equals 147 plus 144 plus 126 plus 140, all divided by the common denominator of 168. This equals 557 over 168.

# Understanding numbers

This video will give you the answer to the second set of fractions.

Your next task is to put a series of numbers expressed in different forms in order of size, smallest first.

### The numbers are:

^{3}/_{9}

0.3321

^{4}/_{7}

^{7}/_{16}

4.181 x 10^{-1}

^{6}/_{13}

The solution is in the video in the next step.

© University of East Anglia