Video: AQA GCSE Mathematics Higher Tier Pack 5 β€’ Paper 1 β€’ Question 1

π‘˜ : 𝑙 = 5 : 6. Circle the correct statement. [A] 𝑙 is 6/5 of π‘˜ [B] 𝑙 is 5/6 of π‘˜ [C] 𝑙 is 5/11 of π‘˜ [D] 𝑙 is 6/11 of π‘˜.

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Video Transcript

π‘˜ to 𝑙 is equal to five to six. Circle the correct statement. 𝑙 is six-fifths of π‘˜, 𝑙 is five-sixths of π‘˜, 𝑙 is five eleventh of π‘˜, or 𝑙 is six elevenths of π‘˜.

Remember, order matters. So in our fraction, π‘˜ represents five parts whereas 𝑙 represents six parts. We’re going to divide. We want an equation for 𝑙 in terms of π‘˜. So we’re going to divide 𝑙 by π‘˜. In ratio terms, that’s the same as dividing six by five. Since we want an equation for 𝑙 in terms of π‘˜, we’re going to make 𝑙 the subject. To do that, we’re going to do the opposite to dividing by π‘˜. And that’s to multiply both sides of our equation by π‘˜. 𝑙 divided by π‘˜ multiplied by π‘˜ is 𝑙. And six-fifths multiplied by π‘˜ is six-fifths of π‘˜. We can see then that 𝑙 is six-fifths of π‘˜.

Another way to consider this is to think about it in terms of a picture. For every five parts which represent π‘˜, 𝑙 is represented by six parts. This means that one of these little blocks must represent a fifth of π‘˜. Six of those little blocks make up 𝑙. So that means 𝑙 can be made up by six lots of a fifth of π‘˜. To multiply six by one-fifth, we make the denominator of six one. We then multiply the two numerators. Six now multiplied by one is six. And then we multiply the denominators. One multiplied by five is five. Once again, we’ve shown that 𝑙 is six-fifths of π‘˜.

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