3. Adding familiar fractions — Learner Route

Fractions · Step 3

Adding familiar fractions

Put fraction pieces together. Start when the pieces are already the same size, then make one simple change when they are not.

Look first

Two sevenths and three sevenths

The pieces are already the same size. Put them together and count them.

2/7
+
3/7
Notice

What stays the same?

2/7 + 3/7 = 5/7
The denominator
The denominator tells us the size of each piece. We are still using sevenths, so it stays 7.
The numerator
The numerator tells us how many pieces we have. We count 2 + 3 = 5 pieces.
Now the pieces differ

One half plus one quarter

A half and a quarter are different-sized pieces. Before we can count them together, make the half out of quarters.

1/2
+
1/4
One more familiar refinement

One third plus one sixth

Each third can be split into two sixths.

1/3 = 2/6

Tap the button to see a different representation of the same fraction.

1/3
+
1/6
2/6 + 1/6 = 3/6 = 1/2
3/6
3/6=1/2
Interactive lab

Choose the sum

Look at the pieces, then choose the fraction they make altogether.

Choose an answer.
Method Trainer

Add familiar fractions

Try five new examples. Your answers feed into your Practice Lab log on this device.

Question 1 of 5 · 0 answered

Type the sum as a fraction, whole number or decimal. Equivalent fractions are accepted.

You have learned

When fraction pieces are the same size, keep that piece size and count how many pieces you have.

If one familiar piece can be split simply to match the other — such as halves into quarters — do that first. A general method for any two fractions comes later.

1 · Picture it2 · Equivalent3 · Add4 · Subtract5 · Mixed numbers6 · Whole × fraction7 · Fraction × fraction8 · Add any two9 · Divide10 · Simplify