# BUILDING FRACTIONS: Problem 3

Rule 17:
To build a fraction is the reverse of reducing the fraction. Instead of searching for the 1 in a fraction so that you can reduce, you insert a 1 and build.

Problem 3:
Create a fraction equivalent to that has a denominator of 50.

The answer is the fraction .

Solution:
This problem is a little difficult in that there is no integer you can multiply 20 with and come up with a product of 50. Therefore, let's reduce the fraction first. Reduce .
= .
[You can verify this with your calculator.] Recall that you can multiply any number by 1 without changing the value of the number. (Rule 6). Multiply the fraction by 1. Recall that 1 has many forms, look for the form of 1 that will result in a denominator of 50.
Since 5 10 = 50, use the fraction as 1.
Now can be written as . The product is .
We have created a fraction with a denominator equal to 50 that is equivalent to the fraction .

Check:
Now prove to yourself with your calculator that your answer is correct. Calculate 4 divided by 20 and calculate 10 divided by 50; both should yield the same answer. If you are correct, the answers are the same (equivalent) and you have successfully built a fraction.

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