Add and subtract fractions

Addition and subtraction of fractions are understood as combining or comparing quantities expressed in equal-sized parts: equivalent fractions allow unlike denominators to be rewritten with a common denominator, after which numerators are added or subtracted while the denominator preserves the unit size. The understanding includes proper and improper fractions, mixed numbers, and positive and negative fractional quantities, with simplification, estimation, and attention to signs and reasonableness; operations on algebraic rational expressions and more advanced symbolic generalizations are not included.

Detailed Explanation: Add and subtract fractions

To add or subtract fractions, the fractions must have the same denominator. The denominator tells the size of the parts, so first rewrite equivalent fractions with a common denominator. Then add or subtract the numerators and keep the common denominator.

Example

Find:

2\frac{1}{3}-\frac{3}{4}

Step 1: Find a common denominator.

The least common multiple of $3$ and $4$ is $12$ , so use $12$ as the common denominator.

Step 2: Rewrite each fraction with denominator $12$ .

Convert $\frac{1}{3}$ :

\frac{1}{3}=\frac{4}{12}

Convert $\frac{3}{4}$ :

\frac{3}{4}=\frac{9}{12}

So the problem becomes:

2\frac{4}{12}-\frac{9}{12}

Step 3: Subtract the fractional parts.

Since $\frac{4}{12}$ is smaller than $\frac{9}{12}$ , regroup $1$ whole from $2$ :

2\frac{4}{12}=1\frac{16}{12}

Now subtract:

1\frac{16}{12}-\frac{9}{12}=1\frac{7}{12}

Therefore,

\boxed{2\frac{1}{3}-\frac{3}{4}=1\frac{7}{12}}

The answer is reasonable because $2\frac{1}{3}$ is a little more than $2$ , and subtracting about $\frac{3}{4}$ should give a result a little more than $1$ .

Learn by doing: Add and subtract fractions

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Fraction Addition - Basic (Simplifying Answers) - Two Changed Denominators

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