1
2
+ 3
5

Simplify all fractions: 3/6 becomes 1/2
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Guide for this category...

Fractions illustrate an important concept, and as such are typically taught fairly early. But the process of actually using them in mathematic operations is relatively difficult. It strikes me as being a little reminiscent of adding numbers from arbitrary bases together.

This section focuses on addition and subtraction. There are two ways of going about performing operations with fractions. The first way, which is taught in school, is to get matching denominators (the number at the bottom of a fraction), multiplying the numerators (the top number) by the opposing denominator. The section below will show this process in detail. The other way is to convert the problems into decimals and figure out how to arrive back at a fraction after the fact. This is how I've often done it, and in fact, how this computer program generates the correct solutions for these problems. First, find a common denominator. This is a number that each number can be multiplied to make. This can always be done by multiplying the two numbers together, but there may be other options that are smaller. In this case, 6 and 8 can both be multiplied to make 24. We multiply 5 by 3, because it takes multiplying 8 by 3 to make 24. A learner might suppose that this process is changing the numbers. They should always remember that a fraction represents the value that is made by division, dividing the top by the bottom . 1 ÷ 2, 3 ÷ 6, and 100 ÷ 200 all equal 0.5. (This is why I feel it is helpful to discuss decimals before fractions.)   