Solve 2(1/4)-2(7/7)+7(5/3)

$$2 ( \frac { 1 } { 4 } ) - 2 ( \frac { 7 } { 7 } ) + 7 ( \frac { 5 } { 3 } )$$

Evaluate

$$\frac{61}{6}\approx 10.166666667$$

Solution Steps

Divide 7 by 7 to get 1.

$$2\times \frac{1}{4}-2\times 1+7\times \frac{5}{3}$$

Multiply 2 and \frac{1}{4} to get \frac{2}{4}.

$$\frac{2}{4}-2\times 1+7\times \frac{5}{3}$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{1}{2}-2\times 1+7\times \frac{5}{3}$$

Multiply 2 and 1 to get 2.

$$\frac{1}{2}-2+7\times \frac{5}{3}$$

Convert 2 to fraction \frac{4}{2}.

$$\frac{1}{2}-\frac{4}{2}+7\times \frac{5}{3}$$

Since \frac{1}{2} and \frac{4}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1-4}{2}+7\times \frac{5}{3}$$

Subtract 4 from 1 to get -3.

$$-\frac{3}{2}+7\times \frac{5}{3}$$

Express 7\times \frac{5}{3} as a single fraction.

$$-\frac{3}{2}+\frac{7\times 5}{3}$$

Multiply 7 and 5 to get 35.

$$-\frac{3}{2}+\frac{35}{3}$$

Least common multiple of 2 and 3 is 6. Convert -\frac{3}{2} and \frac{35}{3} to fractions with denominator 6.

$$-\frac{9}{6}+\frac{70}{6}$$

Since -\frac{9}{6} and \frac{70}{6} have the same denominator, add them by adding their numerators.

$$\frac{-9+70}{6}$$

Add -9 and 70 to get 61.

$$\frac{61}{6}$$

Factor

$$\frac{61}{2 \cdot 3} = 10\frac{1}{6} = 10.166666666666666$$