Video: KS2-M18 • Paper 1 • Question 28

1 1/15 − 2/5 = _.


Video Transcript

One and one fifteenth take away two-fifths equals what?

Here, we start with a mixed number, one and one fifteenth, and we need to subtract a fraction from it. So let’s start by converting our mixed number into a fraction. If we’re talking in terms of fifteenths, one hole is the same as fifteen fifteenths. So one and one fifteenth is the same as fifteen fifteenths add one fifteenth which equals 16 fifteenths. So we could write our calculation as sixteen fifteenths take away two-fifths.

We know that to add or to subtract fractions, they need to have a common denominator. And at the moment, the denominators are different. How can we change the fractions so that they have the same denominator? Well, what if we convert two-fifths into fifteenths. Two-fifths has a denominator of five. To convert fifths into fifteenths, we multiply the denominator by three. So that the fraction still has the same value, we need to do the same to the numerator. Two times three equals six.

Two-fifths is the same as six fifteenths. And so, we can now write our calculation as sixteen fifteenths take away six fifteenths. 16 take away six equals 10. And so six fifteenths take away six fifteenths equals ten fifteenths. We could write the answer as ten fifteenths. This would be completely correct. But we could also simplify the fraction.

What one number can we divide 10 and 15 by to make them smaller? Well, both 10 and 15 are multiples of five. Let’s divide the numerator and the denominator both by five to simplify the fraction. 10 divided by five equals two and 15 divided by five equals three. And so, it’s also possible to give an answer of two-thirds.

We worked through several steps to find the answer. First, we looked at the number one and one fifteenth and we thought to ourselves that this was a mixed number. So we decided to think about how we could write this as a fraction. Once we’d converted it into a fraction, our calculation became a subtraction which involved two fractions now. But we still couldn’t take away the fractions because the two denominators were different. So we converted two-fifths into fifteenths.

And by doing this, both fractions now had common denominators. So we could quickly subtract six fifteenths from sixteen fifteenths to leave us with ten fifteenths. Although we could write ten fifteenths as the answer, we also realize that we could divide the numerator and the denominator by five to simplify it.

One and one fifteenth take away two-fifths equals ten fifteenths or two-thirds.

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