BUILDING FRACTIONS: Problem 1

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 1:: Create a fraction equivalent to that has a denominator of 35.
Answer:: The answer is the fraction .
Solution:: 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 35.
Since 5 7 = 35, use the fraction as 1. Now can be written as .
The product is . We have created a fraction with a denominator equal to 35 that is equivalent to the fraction .
Check:: Now prove to yourself with your calculator that your answer is correct. Calculate 2 divided by 5 and calculate 14 divided by 35; both should yield the same answer. If you are correct, the answers are the same (equivalent) and you have successfully built a fraction.