Solve (5/8div4/7*60/z)div1/2(frac{3}{4}text{of}frac{2}{3}div1frac{1}{2})*(frac{1}{2}+frac{3}{8})

$$( \frac { 5 } { 8 } \div \frac { 4 } { 7 } \times \frac { 60 } { z } ) \div \frac { 1 } { 2 } ( \frac { 3 } { 4 } \text { of } \frac { 2 } { 3 } \div 1 \frac { 1 } { 2 } ) \times ( \frac { 1 } { 2 } + \frac { 3 } { 8 } )$$

Evaluate

$$\frac{1225}{32z}$$

Solution Steps

Divide \frac{5}{8} by \frac{4}{7} by multiplying \frac{5}{8} by the reciprocal of \frac{4}{7}.

$$\frac{\frac{5}{8}\times \frac{7}{4}\times \frac{60}{z}}{\frac{1}{2}}\times \frac{\frac{3}{4}\times \frac{2}{3}}{\frac{1\times 2+1}{2}}\left(\frac{1}{2}+\frac{3}{8}\right)$$

Multiply \frac{5}{8} times \frac{7}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{5\times 7}{8\times 4}\times \frac{60}{z}}{\frac{1}{2}}\times \frac{\frac{3}{4}\times \frac{2}{3}}{\frac{1\times 2+1}{2}}\left(\frac{1}{2}+\frac{3}{8}\right)$$

Do the multiplications in the fraction \frac{5\times 7}{8\times 4}.

$$\frac{\frac{35}{32}\times \frac{60}{z}}{\frac{1}{2}}\times \frac{\frac{3}{4}\times \frac{2}{3}}{\frac{1\times 2+1}{2}}\left(\frac{1}{2}+\frac{3}{8}\right)$$

Multiply \frac{35}{32} times \frac{60}{z} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{35\times 60}{32z}}{\frac{1}{2}}\times \frac{\frac{3}{4}\times \frac{2}{3}}{\frac{1\times 2+1}{2}}\left(\frac{1}{2}+\frac{3}{8}\right)$$

Cancel out 4 in both numerator and denominator.

$$\frac{\frac{15\times 35}{8z}}{\frac{1}{2}}\times \frac{\frac{3}{4}\times \frac{2}{3}}{\frac{1\times 2+1}{2}}\left(\frac{1}{2}+\frac{3}{8}\right)$$

Divide \frac{15\times 35}{8z} by \frac{1}{2} by multiplying \frac{15\times 35}{8z} by the reciprocal of \frac{1}{2}.

$$\frac{15\times 35\times 2}{8z}\times \frac{\frac{3}{4}\times \frac{2}{3}}{\frac{1\times 2+1}{2}}\left(\frac{1}{2}+\frac{3}{8}\right)$$

Cancel out 2 in both numerator and denominator.

$$\frac{15\times 35}{4z}\times \frac{\frac{3}{4}\times \frac{2}{3}}{\frac{1\times 2+1}{2}}\left(\frac{1}{2}+\frac{3}{8}\right)$$

Multiply 15 and 35 to get 525.

$$\frac{525}{4z}\times \frac{\frac{3}{4}\times \frac{2}{3}}{\frac{1\times 2+1}{2}}\left(\frac{1}{2}+\frac{3}{8}\right)$$

Multiply \frac{3}{4} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{525}{4z}\times \frac{\frac{3\times 2}{4\times 3}}{\frac{1\times 2+1}{2}}\left(\frac{1}{2}+\frac{3}{8}\right)$$

Cancel out 3 in both numerator and denominator.

$$\frac{525}{4z}\times \frac{\frac{2}{4}}{\frac{1\times 2+1}{2}}\left(\frac{1}{2}+\frac{3}{8}\right)$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{525}{4z}\times \frac{\frac{1}{2}}{\frac{1\times 2+1}{2}}\left(\frac{1}{2}+\frac{3}{8}\right)$$

Multiply 1 and 2 to get 2.

$$\frac{525}{4z}\times \frac{\frac{1}{2}}{\frac{2+1}{2}}\left(\frac{1}{2}+\frac{3}{8}\right)$$

Add 2 and 1 to get 3.

$$\frac{525}{4z}\times \frac{\frac{1}{2}}{\frac{3}{2}}\left(\frac{1}{2}+\frac{3}{8}\right)$$

Divide \frac{1}{2} by \frac{3}{2} by multiplying \frac{1}{2} by the reciprocal of \frac{3}{2}.

$$\frac{525}{4z}\times \frac{1}{2}\times \frac{2}{3}\left(\frac{1}{2}+\frac{3}{8}\right)$$

Multiply \frac{1}{2} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{525}{4z}\times \frac{1\times 2}{2\times 3}\left(\frac{1}{2}+\frac{3}{8}\right)$$

Cancel out 2 in both numerator and denominator.

$$\frac{525}{4z}\times \frac{1}{3}\left(\frac{1}{2}+\frac{3}{8}\right)$$

Least common multiple of 2 and 8 is 8. Convert \frac{1}{2} and \frac{3}{8} to fractions with denominator 8.

$$\frac{525}{4z}\times \frac{1}{3}\left(\frac{4}{8}+\frac{3}{8}\right)$$

Since \frac{4}{8} and \frac{3}{8} have the same denominator, add them by adding their numerators.

$$\frac{525}{4z}\times \frac{1}{3}\times \frac{4+3}{8}$$

Add 4 and 3 to get 7.

$$\frac{525}{4z}\times \frac{1}{3}\times \frac{7}{8}$$

Multiply \frac{1}{3} times \frac{7}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{525}{4z}\times \frac{1\times 7}{3\times 8}$$

Do the multiplications in the fraction \frac{1\times 7}{3\times 8}.

$$\frac{525}{4z}\times \frac{7}{24}$$

Multiply \frac{525}{4z} times \frac{7}{24} by multiplying numerator times numerator and denominator times denominator.

$$\frac{525\times 7}{4z\times 24}$$

Cancel out 3 in both numerator and denominator.

$$\frac{7\times 175}{4\times 8z}$$

Multiply 7 and 175 to get 1225.

$$\frac{1225}{4\times 8z}$$

Multiply 4 and 8 to get 32.

$$\frac{1225}{32z}$$

Expand

$$\frac{1225}{32z}$$

Solution Steps

Divide \frac{5}{8} by \frac{4}{7} by multiplying \frac{5}{8} by the reciprocal of \frac{4}{7}.

$$\frac{\frac{5}{8}\times \frac{7}{4}\times \frac{60}{z}}{\frac{1}{2}}\times \frac{\frac{3}{4}\times \frac{2}{3}}{\frac{1\times 2+1}{2}}\left(\frac{1}{2}+\frac{3}{8}\right)$$

Multiply \frac{5}{8} times \frac{7}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{5\times 7}{8\times 4}\times \frac{60}{z}}{\frac{1}{2}}\times \frac{\frac{3}{4}\times \frac{2}{3}}{\frac{1\times 2+1}{2}}\left(\frac{1}{2}+\frac{3}{8}\right)$$

Do the multiplications in the fraction \frac{5\times 7}{8\times 4}.

$$\frac{\frac{35}{32}\times \frac{60}{z}}{\frac{1}{2}}\times \frac{\frac{3}{4}\times \frac{2}{3}}{\frac{1\times 2+1}{2}}\left(\frac{1}{2}+\frac{3}{8}\right)$$

Multiply \frac{35}{32} times \frac{60}{z} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{35\times 60}{32z}}{\frac{1}{2}}\times \frac{\frac{3}{4}\times \frac{2}{3}}{\frac{1\times 2+1}{2}}\left(\frac{1}{2}+\frac{3}{8}\right)$$

Cancel out 4 in both numerator and denominator.

$$\frac{\frac{15\times 35}{8z}}{\frac{1}{2}}\times \frac{\frac{3}{4}\times \frac{2}{3}}{\frac{1\times 2+1}{2}}\left(\frac{1}{2}+\frac{3}{8}\right)$$

Divide \frac{15\times 35}{8z} by \frac{1}{2} by multiplying \frac{15\times 35}{8z} by the reciprocal of \frac{1}{2}.

$$\frac{15\times 35\times 2}{8z}\times \frac{\frac{3}{4}\times \frac{2}{3}}{\frac{1\times 2+1}{2}}\left(\frac{1}{2}+\frac{3}{8}\right)$$

Cancel out 2 in both numerator and denominator.

$$\frac{15\times 35}{4z}\times \frac{\frac{3}{4}\times \frac{2}{3}}{\frac{1\times 2+1}{2}}\left(\frac{1}{2}+\frac{3}{8}\right)$$

Multiply 15 and 35 to get 525.

$$\frac{525}{4z}\times \frac{\frac{3}{4}\times \frac{2}{3}}{\frac{1\times 2+1}{2}}\left(\frac{1}{2}+\frac{3}{8}\right)$$

Multiply \frac{3}{4} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{525}{4z}\times \frac{\frac{3\times 2}{4\times 3}}{\frac{1\times 2+1}{2}}\left(\frac{1}{2}+\frac{3}{8}\right)$$

Cancel out 3 in both numerator and denominator.

$$\frac{525}{4z}\times \frac{\frac{2}{4}}{\frac{1\times 2+1}{2}}\left(\frac{1}{2}+\frac{3}{8}\right)$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{525}{4z}\times \frac{\frac{1}{2}}{\frac{1\times 2+1}{2}}\left(\frac{1}{2}+\frac{3}{8}\right)$$

Multiply 1 and 2 to get 2.

$$\frac{525}{4z}\times \frac{\frac{1}{2}}{\frac{2+1}{2}}\left(\frac{1}{2}+\frac{3}{8}\right)$$

Add 2 and 1 to get 3.

$$\frac{525}{4z}\times \frac{\frac{1}{2}}{\frac{3}{2}}\left(\frac{1}{2}+\frac{3}{8}\right)$$

Divide \frac{1}{2} by \frac{3}{2} by multiplying \frac{1}{2} by the reciprocal of \frac{3}{2}.

$$\frac{525}{4z}\times \frac{1}{2}\times \frac{2}{3}\left(\frac{1}{2}+\frac{3}{8}\right)$$

Multiply \frac{1}{2} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{525}{4z}\times \frac{1\times 2}{2\times 3}\left(\frac{1}{2}+\frac{3}{8}\right)$$

Cancel out 2 in both numerator and denominator.

$$\frac{525}{4z}\times \frac{1}{3}\left(\frac{1}{2}+\frac{3}{8}\right)$$

Least common multiple of 2 and 8 is 8. Convert \frac{1}{2} and \frac{3}{8} to fractions with denominator 8.

$$\frac{525}{4z}\times \frac{1}{3}\left(\frac{4}{8}+\frac{3}{8}\right)$$

Since \frac{4}{8} and \frac{3}{8} have the same denominator, add them by adding their numerators.

$$\frac{525}{4z}\times \frac{1}{3}\times \frac{4+3}{8}$$

Add 4 and 3 to get 7.

$$\frac{525}{4z}\times \frac{1}{3}\times \frac{7}{8}$$

Multiply \frac{1}{3} times \frac{7}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{525}{4z}\times \frac{1\times 7}{3\times 8}$$

Do the multiplications in the fraction \frac{1\times 7}{3\times 8}.

$$\frac{525}{4z}\times \frac{7}{24}$$

Multiply \frac{525}{4z} times \frac{7}{24} by multiplying numerator times numerator and denominator times denominator.

$$\frac{525\times 7}{4z\times 24}$$

Cancel out 3 in both numerator and denominator.

$$\frac{7\times 175}{4\times 8z}$$

Multiply 7 and 175 to get 1225.

$$\frac{1225}{4\times 8z}$$

Multiply 4 and 8 to get 32.

$$\frac{1225}{32z}$$