by Alison Bazel
Problem
A sugar cookie recipe calls for 4 1/2 cups of sugar. Alison wants to make 2/3 of the normal amount of sugar. How much sugar will Alison use in her recipe?
Solution
To find the amount of sugar Alison will need, you need to multiply.
But first, you convert 4 1/2 cups of sugar to 9/2. You get 9/2 by multiplying the denominator, 2, by the whole number, 4 (which equals 8).
Next you will add the 8 to the numerator, 1. That will give you 9. Lastly, you keep the denominator of the fraction from the mixed number, which is 2. That gives you 9/2.
Now you will multiply 9/2 by 2/3. You can do 9x2 and 2x3, but you can do it with simpler numbers so the multiplication is easier for you.
You can do something called cross simplifying. First, to cross simplify, you will see if the opposite fractions' numerator and denominator go into each other.
For example, the denominator of 2/3, 3, goes into 9 three times. So you can cross out nine and replace it to three. But then you have to do the same with the opposite denominator.
3 goes into 3 once, so you would cross off the three and replace it with one. You can do the same with the other numerator and denominators, too.
Both the numerator and denominator would be simplified to one. Now, all you have to do is multiply 3x1 and 1x1.
Your answer should be 3.
So, Alison will use three cups of sugar instead of 4 1/2.
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Learn how to derive the equation of an ellipse when the center of the ellipse is at the origin.