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Fractions Solutions

•    Fractions    must have the same    denominator    in order to add or subtract them.

• Write mixed numbers as improper fractions    BEFORE    multiplying or dividing.

• Fractions do not need to be written as mixed numbers, but they do need to be    simplified   .

• When directions say    evaluate   , calculate the value by performing the given operation on the fraction and then write it in simplest form.

• Simplest form means that the    greatest common factor    of the numerator and denominator is    one   .

Example 1

Evaluate.

$2\frac{4}{7}–\left(–\frac{2}{3}\right)$ 

Implement	Explain
$\frac{18}{7}+\frac{2}{3} \mathrm{LCD}\left(7, 3\right)=21$	Rewrite the mixed number as an improper fraction Simplify the double negative and find the LCD
$\frac{18}{7}\left(\frac{3}{3}\right)+\frac{2}{3}\left(\frac{7}{7}\right)$	Write fractions with the LCD
$\frac{54}{21}+\frac{14}{21} = \overline{)\frac{68}{21}}$	Add the numerators

Example 2

Evaluate.

$–3\frac{1}{5}÷\left(1\frac{1}{3}\right)$

Implement	Explain
$–\frac{16}{5}÷\frac{4}{3}$	Rewrite the mixed number as improper fraction
$\frac{{}^{–4}\cancel{–16}}{5}·\frac{3}{{\cancel{4}}_1}$	Take the reciprocal of the fraction after the division symbol Simplify fractions
$\overline{)–\frac{12}{5}}$