Operate with fractions and mixed numbers

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Operate with fractions and mixed numbers

A fraction represents division by a nonzero denominator. For addition or subtraction, rewrite the fractions with the same denominator so that their parts have equal size. Adding denominators would change the size of a part and therefore cannot describe the original sum.

To multiply fractions, multiply numerators and denominators, cancelling common factors beforehand when convenient. To divide by a nonzero fraction, multiply by its reciprocal. Cancellation is a property of products; you cannot cancel one term from a sum across a fraction bar.

Convert mixed numbers to improper fractions before multiplication or division: 1 1/2 = 3/2. Retain negative signs throughout. An exact simplified fraction is often more useful than a rounded decimal, because later calculations preserve the exact value.

Worked example: Calculate 1 1/2 ÷ 3/4.

Convert the mixed number to 3/2.

Multiply by the reciprocal: (3/2) × (4/3).

Cancel the common factor 3, then simplify 4/2.

Answer: 2.

Check your understanding: What is 2/3 + 1/4?

Answer: 11/12.

Why: The common denominator 12 gives 8/12 + 3/12, so the denominator stays 12.