Solve 8/5*(7/4+11/2)=3/4

$$\frac { 8 } { 5 } \cdot ( \frac { 7 } { 4 } + \frac { 11 } { 2 } ) = \frac { 3 } { 4 }$$

Verify

Solution Steps

Least common multiple of 4 and 2 is 4. Convert \frac{7}{4} and \frac{11}{2} to fractions with denominator 4.

$$\frac{8}{5}\left(\frac{7}{4}+\frac{22}{4}\right)=\frac{3}{4}$$

Since \frac{7}{4} and \frac{22}{4} have the same denominator, add them by adding their numerators.

$$\frac{8}{5}\times \frac{7+22}{4}=\frac{3}{4}$$

Add 7 and 22 to get 29.

$$\frac{8}{5}\times \frac{29}{4}=\frac{3}{4}$$

Multiply \frac{8}{5} times \frac{29}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8\times 29}{5\times 4}=\frac{3}{4}$$

Do the multiplications in the fraction \frac{8\times 29}{5\times 4}.

$$\frac{232}{20}=\frac{3}{4}$$

Reduce the fraction \frac{232}{20} to lowest terms by extracting and canceling out 4.

$$\frac{58}{5}=\frac{3}{4}$$

Least common multiple of 5 and 4 is 20. Convert \frac{58}{5} and \frac{3}{4} to fractions with denominator 20.

$$\frac{232}{20}=\frac{15}{20}$$

Compare \frac{232}{20} and \frac{15}{20}.

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