Adding Fractions

Add fractions by expressing them in equal-sized parts, combining the numerators, and simplifying.

Equal-sized parts make fraction operations and equivalence visible. Partitioned unit bars keep the whole fixed while shaded pieces show the selected amount. The labels state the exact fractions represented, so equivalence or an operation can be checked against the picture.

Fractions can be added when they describe pieces of the same size.

The central idea

In $3/4$, the denominator $4$ says the whole is divided into four equal parts. The numerator $3$ says three of those parts are selected.

If two fractions already have the same denominator, their pieces match:

\frac14+\frac24=\frac34.

$One quarter plus two quarters represented with fraction bars, producing three quarters.$

Like denominators

For a common denominator $d$,

\frac ad+\frac bd=\frac{a+b}{d}.

A reliable method

Check whether the denominators match.
If not, choose a common denominator—preferably the least common multiple.
Rewrite each fraction as an equivalent fraction.
Add the numerators and keep the common denominator.
Simplify the result.

Example with simplification

Common mistakes

Self-check

Are the pieces the same size before I add?
Did I create equivalent fractions correctly?
Did I add only the numerators?
Can the final fraction be simplified?
Is the size of the answer reasonable?