The Math Helper Book

Perfecting Fractions

Hello everyone, and welcome back! Today's lesson is on the fantastic concept of fractions.

If you ever see a number written like this: 1/2
Or this:
3
5
Or even this:
5
8
7
They're all fractions.

The thing that distinguishes a fraction is the straight line between the numerator (number on top or to the left of the line) and the denominator (number on bottom or to the right of the line).

Numerator/Denominator
Or
Numerator
Denominator

The basic meaning of this line is dividing. A fraction is just a way of writing the numerator divided by the denominator. For example, 1÷2 is written as
1
2

I believe there are two reasons why using fractions is beneficial in some cases.
1. Help you divide/write unevenly divided numbers.
2. Give a perspective to a problem that's not given by any other number form.

Reason #1

Remember from our last lesson that there are some numbers that don't divide evenly into others? For example, 2 can't go into 1 a whole number of times. This may seem troublesome, but with fractions it's incredibly easy to write the answer.

The problem is 1÷2. Remember that the straight line in fractions means division. So ÷ is the same as / .

Write the problem as a fraction: 1/2. It still means the same thing--1 divided by 2. And now that it's written as a fraction, you have an acceptable answer! The answer to 1÷2 is simply 1/2.

Important note: If you are asked to write the answer as a decimal, the fraction answer doesn't work.

Okay, so 1 and 2 are easy numbers. But fractions also help with more complicated divisions. What about 224÷56?

When you set it up as a fraction, it still doesn't look too easy.
224
40

Fractions have specific properties that can make this simpler. The most important one in this case is this: