Cancelling FractionsDate: 05/06/2002 at 09:28:32 From: Stuart Subject: Cancelling fractions I am having a little trouble doing the extension task of my maths homework, cancelling fractions. Please could you give me some advice? I have to fill in the missing numbers : 1. 2/? x 6/7 x ?/12 = 2/3 2. ?/2 x 2/3 x ?/7 = 2/7 3. 1/4 x 4/? x ?/5 = 2/5 4.?/6 x ?/3 x 1/5 =2/3 5. 7/8 x 16/12 x ?/? = 2 I think that there must be a formula for doing this but can not see it. I have tried for the last 24 hours. Thank you for your help. Stuart Teare Date: 05/06/2002 at 10:40:15 From: Doctor Ian Subject: Re: Cancelling fractions Hi Stuart, There isn't a 'formula' so much as a 'process'. Let's look at the first one: 2 6 ? 2 - * - * -- = - ? 7 12 3 Because multiplication is commutative, i.e., a *b = b * a we can rewrite the equation this way: 2 * 6 * ? 2 ---------- = - (This is how you multiply fractions.) ? * 7 * 12 3 ? * 2 * 6 2 ---------- = - (Multiplication is commutative.) ? * 7 * 12 3 ? 2 * 6 2 - * ------ = - (This is how you un-multiply fractions!) ? 7 * 12 3 ? 1 2 - * - = - (Simplify the second fraction.) ? 7 3 Note that if we multiply both sides of the equation by 7/1, we get ? 1 7 2 7 - * - * - = - * - ? 7 1 3 1 ? 14 - = -- ? 3 We can check that by substituting back into the original equation: 2 6 14 2 - * - * -- = - 3 7 12 3 / / 2 6 14 2 - * - * -- = - Cancel 3 7 12 3 / / 14 2 ----- = - Cancel 3 * 7 3 / 2 2 - = - True. 3 3 Once you get some practice with this, you can start doing the cancellations beforehand: / 1 4 ? 2 - * - + - = - Cancel 4 ? 5 5 / 1 * ? 2 ----- = - ? * 5 5 That can cut down the amount of writing that you have to do, and sometimes lets you see the answer right away. I hope this helps. Write back if you'd like to talk more about this, or anything else. - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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