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Math for Kids/8th grade Ratio Strategies

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Question
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.

Answer
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

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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).

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

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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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