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Math for Kids/8th grade Ratio Strategies


I have searched the internet and can not find a site that can help. I need to explain how to work out a ratio using a strategy which can be applied to any ratio. The question asked is-If it takes 10 balls of wool to make 15 hats how many beanies will it take to make 4 hats? I can answer this question by converting the ratio into a fraction but need to learn how to do it using a different strategy. Please remember that I need to learn a strategy to work out any ratio not just the answer to this question. Thank-you for your help.

Apologies for the lateness of this reply - I have changed my email address and allexperts hasn't updated it.

You need to work out how many balls 1 hat requires - this is called the unitary method.

Think of it this way...

15 hats = 10 balls

to get 1 hat, you need to reduce 15 hats to 1 hat, so divide by 15.
What you do for 1 side, you do for the other, so divide the number of balls by 15 as well.

So 1 hat = 10/15 - 2/3rds of a ball of wool.

So, 4 hats is 4 times this - 4 x 2/3 = 8/3rds or 2 balls and 2/3 of a ball of wool.

I hope this helps

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Wayne Chadburn


I teach mathematics in a UK secondary school from ages 11 to 18. I can answer most mathematics questions at Key stage 3 level, GCSE and I have taught 'A' level mathematics up to further mathematics level (Modules C1-4, FP1 FP2, S1 S2, M1 M2, D1).


13 years teaching experience, 10 at 'A' level. Past exam marker for the AQA exam board.

First class BSc(Hons) degree in Mathematics and Physics (don't ask me any Physics questions!!! Unless it relates to Mechanics!!) and a PGCE in mathematics education.

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