Solve 7/9div|1/3-4/5|=

$$\frac { 7 } { 9 } \div | \frac { 1 } { 3 } - \frac { 4 } { 5 } | =$$

Evaluate

$$\frac{5}{3}\approx 1.666666667$$

Solution Steps

Least common multiple of 3 and 5 is 15. Convert \frac{1}{3} and \frac{4}{5} to fractions with denominator 15.

$$\frac{\frac{7}{9}}{|\frac{5}{15}-\frac{12}{15}|}$$

Since \frac{5}{15} and \frac{12}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{7}{9}}{|\frac{5-12}{15}|}$$

Subtract 12 from 5 to get -7.

$$\frac{\frac{7}{9}}{|-\frac{7}{15}|}$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{7}{15} is \frac{7}{15}.

$$\frac{\frac{7}{9}}{\frac{7}{15}}$$

Divide \frac{7}{9} by \frac{7}{15} by multiplying \frac{7}{9} by the reciprocal of \frac{7}{15}.

$$\frac{7}{9}\times \frac{15}{7}$$

Multiply \frac{7}{9} times \frac{15}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 15}{9\times 7}$$

Cancel out 7 in both numerator and denominator.

$$\frac{15}{9}$$

Reduce the fraction \frac{15}{9} to lowest terms by extracting and canceling out 3.

$$\frac{5}{3}$$

Factor

$$\frac{5}{3} = 1\frac{2}{3} = 1.6666666666666667$$