Fractions. Using Mixed Numbers and Improper Fractions


Using Mixed Numbers and Improper Fractions

A mixed number represents the sum of an integer and a fraction.
In fractional form: 3\frac{1}{4}=\frac{4\times 3+1}{4}=\frac{13}{4}.
When \; 3\frac{1}{4} is written as the fraction \; 3\frac{13}{4} it is called an improper fraction.
Improper fractions are fractions whose numerator is greater than the denominator.
It is often easier to change mixed numerals to improper fractions when
simplifying an expression.

E X A M P L E :
Simplify \; 8\frac{2}{3}+\frac{1}{6}.
 \large =\frac{3\times 8+2}{3}=\frac{24+2}{3}=\frac{26}{3}.\; \; \; Change to an improper fraction first.
 \large \frac{26}{3}\times \frac{6}{1}.\; \; \; Multipl by the reciprocal of \frac{1}{6}.
 \large \frac{26\times 6}{3}=\frac{26\times 2}{1}=52.\; \; \; (Answer)

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