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Working with fractions: part 2

Working with fractions: part 2
You need to decide which of these three fractions is the smallest, the middle sized, and the largest.
In order to do this, you will need to express the fractions as equivalent fractions with the same denominator, and then compare the new numerators. The denominator to choose is the lowest common multiple. And the lowest common multiple of 5, 7, and 8 which are the three denominators in the fractions, is 280. This means that 280 is the smallest number that 5, 7, and 8 all divided into, given a whole number solution. To convert 3/5 into an equivalent fraction with a denominator of 280, you multiply the numerator and denominator by 56. This means that 3/5 is the same as 168 divided by 280.
To convert 4/7 to an equivalent fraction with a denominator of 280, you multiply the numerator and denominator by 40. This means that 4/7 is the same as 160 divided by 280. To convert 5/8 to an equivalent fraction with a denominator of 280, you multiply numerator and denominator by 35. This means that 5/8 is 175 divided by 280. Now, looking at these three new fractions you can see that 4/7 is the smallest, 3/5 is the next smallest, and 5/8 is the biggest.
You could always use a calculator to check your answer, if you have one. Here, all answers are given to three decimal places, 3/5 is 0.600. 4/7 is 0.571, and 5/8 is 0.625. So again, 4/7 is the smallest, 3/5 is the next, and 5/8 is the biggest.
In order to add fractions together you need to have fractions with equivalent denominators, or a so-called common denominator. This is because you can only add together things that are the same, and the denominator tells you what type of fraction you have. Here, we have 5ths and 7ths at 8ths. And they’re all different. However, you can use the method from the question before to express them as equivalent fractions with denominators of 180. So 3/5 is 168/280, 4/7 is 160/280, and 5/8 is 175/280. As these three new fractions have the same denominator, you can add them together. This gives 168 plus 160 plus 175 all over the common denominator of 280, which is 503/280.

In this video is the solution to question in the previous step.

Now tackle the second set of fractions which is slightly harder, putting them in order of size and then find the sum of the three fractions. The answer is in the video in the next step. If you struggle, study the video in the next step and the maths tutor will gently take you through the solution.

Set 2)

7/8, 6/7, 3/4, 5/6

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