Adding and subtracting fractions using a picture
When we add fractions, a picture helps us see how many equal parts make up the whole. The denominator tells us into how many equal parts the whole is divided. The numerator tells us how many of these parts we have.
When fractions have the same denominator, we only add the numerators. When fractions have different denominators, we first need to rewrite them so that they use equal-sized parts.
Fractions with the same denominator
Let us look at the example:
$1/10 + 3/10 = 4/10$
The whole is divided into 10 equal parts. First, we have 1/10, which means one square. Then we add 3/10, which means three more squares. Altogether, we have 4/10.
Orange shows the first fraction, and green shows the second fraction.
Because both fractions are divided into tenths, we can add them directly:
$1 + 3 = 4$, so $1/10 + 3/10 = 4/10$
Fractions with different denominators
Now let us try this example:
$1/3 + 2/9$
Here we cannot add the fractions right away, because they do not have the same denominators. The first fraction is written in thirds, and the second one in ninths.
But we can draw it if we use 9 squares. Then one third is equal to 3 squares (the first orange row). We add two ninths in green. The whole square is divided into 9 equal parts. Altogether, we get 5/9.
With pictures like these, always imagine that you are adding the shaded squares together. The picture shows you how many equal parts you already have and how many you will have altogether after adding more.
Subtracting fractions
We can also use a picture when we subtract fractions. For example:
$7/9 - 2/9 = 5/9$
The whole is divided into 9 equal parts. First, we shade 7 parts. Then we take away 2 parts. There are 5 parts left, so the answer is 5/9.
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When fractions have the same denominator, we subtract the numerators:
$7 - 2 = 5$, so $7/9 - 2/9 = 5/9$
