Solve 16/25*2/3+7/12-frac{9/10}{frac{15}{16}}

$$\frac{ 16 }{ 25 } \times \frac{ 2 }{ 3 } + \frac{ 7 }{ 12 } - \frac{ \frac{ 9 }{ 10 } }{ \frac{ 15 }{ 16 } }$$

Evaluate

$$\frac{1}{20}=0.05$$

Solution Steps

Multiply \frac{16}{25} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{16\times 2}{25\times 3}+\frac{7}{12}-\frac{\frac{9}{10}}{\frac{15}{16}}$$

Do the multiplications in the fraction \frac{16\times 2}{25\times 3}.

$$\frac{32}{75}+\frac{7}{12}-\frac{\frac{9}{10}}{\frac{15}{16}}$$

Least common multiple of 75 and 12 is 300. Convert \frac{32}{75} and \frac{7}{12} to fractions with denominator 300.

$$\frac{128}{300}+\frac{175}{300}-\frac{\frac{9}{10}}{\frac{15}{16}}$$

Since \frac{128}{300} and \frac{175}{300} have the same denominator, add them by adding their numerators.

$$\frac{128+175}{300}-\frac{\frac{9}{10}}{\frac{15}{16}}$$

Add 128 and 175 to get 303.

$$\frac{303}{300}-\frac{\frac{9}{10}}{\frac{15}{16}}$$

Reduce the fraction \frac{303}{300} to lowest terms by extracting and canceling out 3.

$$\frac{101}{100}-\frac{\frac{9}{10}}{\frac{15}{16}}$$

Divide \frac{9}{10} by \frac{15}{16} by multiplying \frac{9}{10} by the reciprocal of \frac{15}{16}.

$$\frac{101}{100}-\frac{9}{10}\times \frac{16}{15}$$

Multiply \frac{9}{10} times \frac{16}{15} by multiplying numerator times numerator and denominator times denominator.

$$\frac{101}{100}-\frac{9\times 16}{10\times 15}$$

Do the multiplications in the fraction \frac{9\times 16}{10\times 15}.

$$\frac{101}{100}-\frac{144}{150}$$

Reduce the fraction \frac{144}{150} to lowest terms by extracting and canceling out 6.

$$\frac{101}{100}-\frac{24}{25}$$

Least common multiple of 100 and 25 is 100. Convert \frac{101}{100} and \frac{24}{25} to fractions with denominator 100.

$$\frac{101}{100}-\frac{96}{100}$$

Since \frac{101}{100} and \frac{96}{100} have the same denominator, subtract them by subtracting their numerators.

$$\frac{101-96}{100}$$

Subtract 96 from 101 to get 5.

$$\frac{5}{100}$$

Reduce the fraction \frac{5}{100} to lowest terms by extracting and canceling out 5.

$$\frac{1}{20}$$

Factor

$$\frac{1}{2 ^ {2} \cdot 5} = 0.05$$