Video: KS2-M18 • Paper 1 • Question 35

(4 2/3) − (1 6/7) = _.


Video Transcript

Four and two-thirds take away one and six-sevenths equals what?

In this question, we have to subtract two mixed numbers. We could start by subtracting the whole numbers: four take away one. Now we’re left with three and two-thirds, and we need to subtract six-sevenths. Three and two-thirds is still a mixed number. If we write this as an improper fraction, it will help to make the calculation easier to work with.

We know that one whole is equal to three-thirds. So three wholes is equal to three times that amount, which is nine. So we have nine-thirds and two-thirds, which is eleven-thirds. Three and two-thirds as an improper fraction is eleven-thirds.

Now we have to calculate eleven-thirds take away six-sevenths. These fractions have different denominators. Before we can subtract, we need to find a common denominator. Or, in other words, the denominators need to be the same. So we need to find a common multiple. Which number is a multiple of three and seven?

Three multiplied by seven is 21. Seven multiplied by three is 21. So how many twenty-firsts are equivalent to eleven-thirds? We’ve already multiplied the denominator by seven. We need to do the same to the numerator: 11 multiplied by seven. So eleven-thirds is equal to seventy-seven twenty-firsts. How many twenty-firsts is equal to six-sevenths?

To find the denominator, we multiplied by three. So let’s do the same to the numerator. Six multiplied by three is 18. Now that our fractions have the same denominator, we can subtract: seventy-seven twenty-firsts take away eighteen twenty-firsts. 77 take away 10 is 67, and 67 take away eight is 59. Four and two-thirds take away one and six-sevenths equals fifty-nine twenty-firsts.

To calculate the answer, first we subtracted the whole numbers. Next, we changed three and two-thirds from a mixed number into an improper fraction. Next, we had to find a common denominator, which was 21. So we changed our fractions into twenty-firsts. Finally, we were able to subtract. Four and two-thirds take away one and six-sevenths equals fifty-nine twenty-firsts.

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