Solve 0.4*15/16/0.4*frac{15{16}+0.25*0.8+0.35*0.5}=

$$\frac { 0.4 \times \frac { 15 } { 16 } } { 0.4 \times \frac { 15 } { 16 } + 0.25 \times 0.8 + 0.35 \times 0.5 } =$$

Evaluate

$$0.5$$

Solution Steps

Convert decimal number 0.4 to fraction \frac{4}{10}. Reduce the fraction \frac{4}{10} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{2}{5}\times \frac{15}{16}}{0.4\times \frac{15}{16}+0.25\times 0.8+0.35\times 0.5}$$

Multiply \frac{2}{5} times \frac{15}{16} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{2\times 15}{5\times 16}}{0.4\times \frac{15}{16}+0.25\times 0.8+0.35\times 0.5}$$

Do the multiplications in the fraction \frac{2\times 15}{5\times 16}.

$$\frac{\frac{30}{80}}{0.4\times \frac{15}{16}+0.25\times 0.8+0.35\times 0.5}$$

Reduce the fraction \frac{30}{80} to lowest terms by extracting and canceling out 10.

$$\frac{\frac{3}{8}}{0.4\times \frac{15}{16}+0.25\times 0.8+0.35\times 0.5}$$

Convert decimal number 0.4 to fraction \frac{4}{10}. Reduce the fraction \frac{4}{10} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{3}{8}}{\frac{2}{5}\times \frac{15}{16}+0.25\times 0.8+0.35\times 0.5}$$

Multiply \frac{2}{5} times \frac{15}{16} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{3}{8}}{\frac{2\times 15}{5\times 16}+0.25\times 0.8+0.35\times 0.5}$$

Do the multiplications in the fraction \frac{2\times 15}{5\times 16}.

$$\frac{\frac{3}{8}}{\frac{30}{80}+0.25\times 0.8+0.35\times 0.5}$$

Reduce the fraction \frac{30}{80} to lowest terms by extracting and canceling out 10.

$$\frac{\frac{3}{8}}{\frac{3}{8}+0.25\times 0.8+0.35\times 0.5}$$

Multiply 0.25 and 0.8 to get 0.2.

$$\frac{\frac{3}{8}}{\frac{3}{8}+0.2+0.35\times 0.5}$$

Convert decimal number 0.2 to fraction \frac{2}{10}. Reduce the fraction \frac{2}{10} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{3}{8}}{\frac{3}{8}+\frac{1}{5}+0.35\times 0.5}$$

Least common multiple of 8 and 5 is 40. Convert \frac{3}{8} and \frac{1}{5} to fractions with denominator 40.

$$\frac{\frac{3}{8}}{\frac{15}{40}+\frac{8}{40}+0.35\times 0.5}$$

Since \frac{15}{40} and \frac{8}{40} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3}{8}}{\frac{15+8}{40}+0.35\times 0.5}$$

Add 15 and 8 to get 23.

$$\frac{\frac{3}{8}}{\frac{23}{40}+0.35\times 0.5}$$

Multiply 0.35 and 0.5 to get 0.175.

$$\frac{\frac{3}{8}}{\frac{23}{40}+0.175}$$

Convert decimal number 0.175 to fraction \frac{175}{1000}. Reduce the fraction \frac{175}{1000} to lowest terms by extracting and canceling out 25.

$$\frac{\frac{3}{8}}{\frac{23}{40}+\frac{7}{40}}$$

Since \frac{23}{40} and \frac{7}{40} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3}{8}}{\frac{23+7}{40}}$$

Add 23 and 7 to get 30.

$$\frac{\frac{3}{8}}{\frac{30}{40}}$$

Reduce the fraction \frac{30}{40} to lowest terms by extracting and canceling out 10.

$$\frac{\frac{3}{8}}{\frac{3}{4}}$$

Divide \frac{3}{8} by \frac{3}{4} by multiplying \frac{3}{8} by the reciprocal of \frac{3}{4}.

$$\frac{3}{8}\times \frac{4}{3}$$

Multiply \frac{3}{8} times \frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 4}{8\times 3}$$

Cancel out 3 in both numerator and denominator.

$$\frac{4}{8}$$

Reduce the fraction \frac{4}{8} to lowest terms by extracting and canceling out 4.

$$\frac{1}{2}$$

Factor

$$\frac{1}{2} = 0.5$$