Box 3–5 Consequences of the Basic Properties: Formulas for the Arithmetic of Fractions

Fraction notation. The fractions 3/2 and are alternative ways of writing 3÷2. For numbers m and n, with m not 0, both n/m and denote n÷m. These are not defined when m=0.

Reciprocal of reciprocal. The reciprocal of the reciprocal of a number is the number itself. For example, and In general, for m and n not 0,

Equality. For m and s not zero, is true exactly when n×s=m×t.

Addition of fractions. Adding fractions requires that they have a common denominator, which often requires conversion to equivalent fractions. When fractions have a common denominator, their sum is the fraction whose numerator is the sum of their numerators and whose denominator is the common denominator.

For example,

In general, for m and s not zero,

Multiplication of fractions. The product of two fractions is the fraction whose numerator is the product of their numerators and whose denominator is the product of their denominators. For example,

In general, for m and s not zero,

Division of fractions. Dividing by a fraction is the same as multiplying by its reciprocal. For example, In general, for m, s, and t not zero,



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