Solve 1-3/8-4/3/frac{5{4}}=

$$1 - \frac { \frac { 3 } { 8 } - \frac { 4 } { 3 } } { \frac { 5 } { 4 } } =$$

Evaluate

$$\frac{53}{30}\approx 1.766666667$$

Solution Steps

Least common multiple of 8 and 3 is 24. Convert \frac{3}{8} and \frac{4}{3} to fractions with denominator 24.

$$1-\frac{\frac{9}{24}-\frac{32}{24}}{\frac{5}{4}}$$

Since \frac{9}{24} and \frac{32}{24} have the same denominator, subtract them by subtracting their numerators.

$$1-\frac{\frac{9-32}{24}}{\frac{5}{4}}$$

Subtract 32 from 9 to get -23.

$$1-\frac{-\frac{23}{24}}{\frac{5}{4}}$$

Divide -\frac{23}{24} by \frac{5}{4} by multiplying -\frac{23}{24} by the reciprocal of \frac{5}{4}.

$$1-\left(-\frac{23}{24}\times \frac{4}{5}\right)$$

Multiply -\frac{23}{24} times \frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

$$1-\frac{-23\times 4}{24\times 5}$$

Do the multiplications in the fraction \frac{-23\times 4}{24\times 5}.

$$1-\frac{-92}{120}$$

Reduce the fraction \frac{-92}{120} to lowest terms by extracting and canceling out 4.

$$1-\left(-\frac{23}{30}\right)$$

The opposite of -\frac{23}{30} is \frac{23}{30}.

$$1+\frac{23}{30}$$

Convert 1 to fraction \frac{30}{30}.

$$\frac{30}{30}+\frac{23}{30}$$

Since \frac{30}{30} and \frac{23}{30} have the same denominator, add them by adding their numerators.

$$\frac{30+23}{30}$$

Add 30 and 23 to get 53.

$$\frac{53}{30}$$

Factor

$$\frac{53}{2 \cdot 3 \cdot 5} = 1\frac{23}{30} = 1.7666666666666666$$