Add any two fractions
You already know the key idea: fractions can only be counted together when the pieces are the same size. So before adding unlike fractions, rewrite both using equal-sized pieces.
13 + 15
In words: One third plus one fifth.
Put the pieces together
Start with one third of a circle and one fifth of an equally sized circle. We can put the two pieces together—but they are different sizes.
One third + one fifth. How can we name their total as a single fraction?
One size that works for both fractions
If one whole is split into thirds, and each third is split into 5 equal parts, we get 15 pieces. The same happens if we start with fifths and split each fifth into 3.
Whatever happens underneath must happen on top
To change thirds into fifteenths, multiply the denominator by 5 and the numerator by 5. To change fifths into fifteenths, multiply both by 3. The fraction’s value stays the same.
23 + 35
The same process works. Rewrite both fractions in fifteenths, then add.
Make equal pieces, then add
Rewrite using equal-sized pieces
Choose the pair of equivalent fractions that are ready to add.
Follow the arrows, then add
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You have learned
Unlike fractions must first be rewritten using equal-sized pieces.
A reliable common denominator is the product of the two denominators. Rewrite each fraction equivalently, then add the numerators.