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.
$3\frac{1}{4}=3+\frac{1}{4}.$
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)