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4.NF.B.3

Adding and subtracting fractions

Two amounts are counted in pieces of different sizes. How can they be put together, or one taken from the other, as a single fraction?

Where you are 5 inside

What this area is about

A fraction counts pieces, and its denominator names their size. Counts can be added or subtracted only when they count the same piece, so this whole area rests on one move: rename the fractions in matching pieces, then count. The denominator is never added.

How these fit together

The counting case. Like denominators needs no renaming: for a whole number n \neq 0, \displaystyle \frac{a}{n} + \frac{b}{n} = \frac{a+b}{n}, because both count the same piece \displaystyle \frac{1}{n}.

Renaming first. Tenths and hundredths is the first case with different pieces: each tenth becomes 10 hundredths. Unlike denominators does the same for any two denominators, cutting both into a common piece before counting.

Judging and using it. Estimating rounds each fraction to 0, \displaystyle \frac{1}{2} or 1 to see roughly how big an answer must be. Word problems decide, from a story, whether pieces are being joined or taken away.

A path through it

Like denominators is the plain case, and tenths and hundredths the first renaming. The one fixed step is that unlike denominators comes before the word problems, which use it. Estimating can sit anywhere and is worth doing beside every exact sum.

Next come adding and subtracting mixed numbers, and later operations with rational numbers, where the same renaming works with negative fractions too.

math.wiki · updated 2026-11-08 · CC-BY-SA-4.0