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Skip to 0 minutes and 5 secondsIn order to determine which of these fractions is the smallest and then the next smallest and the next smallest and so on, like before, you need to express them all with the same common denominator and then compare the numerators. Again, the best denominator to choose is the lowest common multiple of the denominators. In this case, the lowest common multiple of 3, 5, 7, and 8 is 840. So 2/3 becomes 560/840. 4/7 is 480/840. 3/5 is 504 divided by 840. And 5/8 is 525 divided by 840. You can see that 4/7 is the smallest. 3/5 is the next. 5/8 is the next. And 2/3 is the largest.

Skip to 1 minute and 4 secondsOf course, you can check your answers on a calculator-- if you have one. Here, answers are given to three decimal places. 2/3 is 0.667. 4/7 is 0.571. 3/5 is 0.600. And 5/8 is 0.625. And so again, 4/7 is the smallest, 3/5 the next, 5/8 the next, and 2/3 the largest.

Skip to 1 minute and 38 secondsYou can only add fractions together which have the same denominator. So you can use your results from the first part of this question to help. 2/3 is 560/840. 4/7 is 480/840. 3/5 is 504/840. And 5/8 is 525/840. All the fractions now have the same denominator. And so you can add them together. This gives 560 plus 480 plus 504 plus 525, all over 840, which equals 2,069/840.

Self assessment: putting numbers in order

Have a go at putting this series of numbers in order, smallest first.

The four numbers are: Avogadro’s number, π, Planck’s constant, e

The answers will be in the video in the next step.

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