Solve 23/4:1/7-22/6-(-5)

$$\frac { 2 \frac { 3 } { 4 } : \frac { 1 } { 7 } - 22 } { 6 - ( - 5 ) }$$

Evaluate

$$-\frac{1}{4}=-0.25$$

Solution Steps

Divide \frac{2\times 4+3}{4} by \frac{1}{7} by multiplying \frac{2\times 4+3}{4} by the reciprocal of \frac{1}{7}.

$$\frac{\frac{\left(2\times 4+3\right)\times 7}{4}-22}{6-\left(-5\right)}$$

Multiply 2 and 4 to get 8.

$$\frac{\frac{\left(8+3\right)\times 7}{4}-22}{6-\left(-5\right)}$$

Add 8 and 3 to get 11.

$$\frac{\frac{11\times 7}{4}-22}{6-\left(-5\right)}$$

Multiply 11 and 7 to get 77.

$$\frac{\frac{77}{4}-22}{6-\left(-5\right)}$$

Convert 22 to fraction \frac{88}{4}.

$$\frac{\frac{77}{4}-\frac{88}{4}}{6-\left(-5\right)}$$

Since \frac{77}{4} and \frac{88}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{77-88}{4}}{6-\left(-5\right)}$$

Subtract 88 from 77 to get -11.

$$\frac{-\frac{11}{4}}{6-\left(-5\right)}$$

The opposite of -5 is 5.

$$\frac{-\frac{11}{4}}{6+5}$$

Add 6 and 5 to get 11.

$$\frac{-\frac{11}{4}}{11}$$

Express \frac{-\frac{11}{4}}{11} as a single fraction.

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

Multiply 4 and 11 to get 44.

$$\frac{-11}{44}$$

Reduce the fraction \frac{-11}{44} to lowest terms by extracting and canceling out 11.

$$-\frac{1}{4}$$

Factor

$$-\frac{1}{4} = -0.25$$