Solve 4-71/3:21/5

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

Evaluate

$$\frac{2}{3}\approx 0.666666667$$

Solution Steps

Divide \frac{7\times 3+1}{3} by \frac{2\times 5+1}{5} by multiplying \frac{7\times 3+1}{3} by the reciprocal of \frac{2\times 5+1}{5}.

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

Multiply 7 and 3 to get 21.

$$4-\frac{\left(21+1\right)\times 5}{3\left(2\times 5+1\right)}$$

Add 21 and 1 to get 22.

$$4-\frac{22\times 5}{3\left(2\times 5+1\right)}$$

Multiply 22 and 5 to get 110.

$$4-\frac{110}{3\left(2\times 5+1\right)}$$

Multiply 2 and 5 to get 10.

$$4-\frac{110}{3\left(10+1\right)}$$

Add 10 and 1 to get 11.

$$4-\frac{110}{3\times 11}$$

Multiply 3 and 11 to get 33.

$$4-\frac{110}{33}$$

Reduce the fraction \frac{110}{33} to lowest terms by extracting and canceling out 11.

$$4-\frac{10}{3}$$

Convert 4 to fraction \frac{12}{3}.

$$\frac{12}{3}-\frac{10}{3}$$

Since \frac{12}{3} and \frac{10}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{12-10}{3}$$

Subtract 10 from 12 to get 2.

$$\frac{2}{3}$$

Factor

$$\frac{2}{3} = 0.6666666666666666$$