Solve 1/2div5/8+1/4*3/5quadfrac{3}{4}

$$\frac { 1 } { 2 } \div \frac { 5 } { 8 } + \frac { 1 } { 4 } \times \frac { 3 } { 5 } \quad \frac { 3 } { 4 }$$

Evaluate

$$\frac{73}{80}=0.9125$$

Solution Steps

Divide \frac{1}{2} by \frac{5}{8} by multiplying \frac{1}{2} by the reciprocal of \frac{5}{8}.

$$\frac{1}{2}\times \frac{8}{5}+\frac{1}{4}\times \frac{3}{5}\times \frac{3}{4}$$

Multiply \frac{1}{2} times \frac{8}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 8}{2\times 5}+\frac{1}{4}\times \frac{3}{5}\times \frac{3}{4}$$

Do the multiplications in the fraction \frac{1\times 8}{2\times 5}.

$$\frac{8}{10}+\frac{1}{4}\times \frac{3}{5}\times \frac{3}{4}$$

Reduce the fraction \frac{8}{10} to lowest terms by extracting and canceling out 2.

$$\frac{4}{5}+\frac{1}{4}\times \frac{3}{5}\times \frac{3}{4}$$

Multiply \frac{1}{4} times \frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4}{5}+\frac{1\times 3}{4\times 5}\times \frac{3}{4}$$

Do the multiplications in the fraction \frac{1\times 3}{4\times 5}.

$$\frac{4}{5}+\frac{3}{20}\times \frac{3}{4}$$

Multiply \frac{3}{20} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4}{5}+\frac{3\times 3}{20\times 4}$$

Do the multiplications in the fraction \frac{3\times 3}{20\times 4}.

$$\frac{4}{5}+\frac{9}{80}$$

Least common multiple of 5 and 80 is 80. Convert \frac{4}{5} and \frac{9}{80} to fractions with denominator 80.

$$\frac{64}{80}+\frac{9}{80}$$

Since \frac{64}{80} and \frac{9}{80} have the same denominator, add them by adding their numerators.

$$\frac{64+9}{80}$$

Add 64 and 9 to get 73.

$$\frac{73}{80}$$

Factor

$$\frac{73}{2 ^ {4} \cdot 5} = 0.9125$$