Fractions guide: understand the whole
A clear introduction to equivalent fractions and adding parts of the same whole.
A little clearer.
Fractions describe equal parts
The denominator tells you how many equal parts make the whole. The numerator tells you how many of those parts are being considered.
The word equal matters. Dividing something into pieces of different sizes does not automatically make each piece the same fraction of the whole.
Different-looking fractions can have the same value
Multiplying or dividing the numerator and denominator by the same non-zero number leaves the value unchanged. You are changing how the same quantity is described, not changing the quantity itself.
Use a common denominator when adding
To add fractions, describe the parts using a common denominator first. Then add the numerators while keeping that denominator.
In the example, one half is rewritten as three sixths and one third as two sixths. The sum is then five sixths.
Ask whether the answer makes sense
A picture or a rough comparison with one whole can help you check a fraction answer. If you add two positive fractions, the result should be larger than either one on its own.
Be careful not to add denominators when adding fractions. The denominator describes the size of the equal parts; it is not another quantity to combine in the same way as the numerator.
