Thank you for the opportunity to help you with your question!
You may want to follow along on my picture as you read.
To do any of these questions all you need to do is set up ratios for what you know and do not know. The problem gives you three pieces of information you know that Amy clips 1. 25 paws 2. in 3 hours and you know 3. 1 hour is what the other ratio will be expressed in.
Set up your ratio using the same labels on the numerator and denominator on both sides. I put paws on top and hours on bottom. For the first fraction I have 25 paws / 3.5 (or 3 1/2 hours). Labeling your units on the fraction makes this much much easier. Set this equal to your other fraction. Your first fraction was set up with paws in the numerator and hours in the denominator so do the same here. You want to know an unknown number (x) of paws in 1 hour so set up the fraction x paws / 1 hour
Whenever you have two fractions equal to one another you can cross multiply. Multiply x paws times 3.5 hours to get 3.5x. On the other side of the equal sign multiply 25 paws times 1 hour to get 25. You should have the equation
3.5x = 25
Now all you have to do is cancel out the 3.5 by dividing it from both sides of the equation. It will cancel on the left side of the equation and on the right side you will have 25 / 3.5 which equals 7.14 paws. Amy's cutting rate is 7.14 paws per hour. Expressed in a fraction this is 50/7 or 7 1/7
Thanks for letting me help. Please feel free to ask any follow ups for clarification on this question.
Sep 9th, 2015
I don't think the picture showed up in the original. The bottom cut off and it should have said 5 / .25 = 20 paws for Penny
Sep 9th, 2015
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