Solve 3/10*71/2+3/4div11/2

$$\frac { 3 } { 10 } \times 7 \frac { 1 } { 2 } + \frac { 3 } { 4 } \div 1 \frac { 1 } { 2 }$$

Evaluate

$$\frac{11}{4}=2.75$$

Solution Steps

Multiply 7 and 2 to get 14.

$$\frac{3}{10}\times \frac{14+1}{2}+\frac{\frac{3}{4}}{\frac{1\times 2+1}{2}}$$

Add 14 and 1 to get 15.

$$\frac{3}{10}\times \frac{15}{2}+\frac{\frac{3}{4}}{\frac{1\times 2+1}{2}}$$

Multiply \frac{3}{10} times \frac{15}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 15}{10\times 2}+\frac{\frac{3}{4}}{\frac{1\times 2+1}{2}}$$

Do the multiplications in the fraction \frac{3\times 15}{10\times 2}.

$$\frac{45}{20}+\frac{\frac{3}{4}}{\frac{1\times 2+1}{2}}$$

Reduce the fraction \frac{45}{20} to lowest terms by extracting and canceling out 5.

$$\frac{9}{4}+\frac{\frac{3}{4}}{\frac{1\times 2+1}{2}}$$

Divide \frac{3}{4} by \frac{1\times 2+1}{2} by multiplying \frac{3}{4} by the reciprocal of \frac{1\times 2+1}{2}.

$$\frac{9}{4}+\frac{3\times 2}{4\left(1\times 2+1\right)}$$

Cancel out 2 in both numerator and denominator.

$$\frac{9}{4}+\frac{3}{2\left(1+2\right)}$$

Add 1 and 2 to get 3.

$$\frac{9}{4}+\frac{3}{2\times 3}$$

Multiply 2 and 3 to get 6.

$$\frac{9}{4}+\frac{3}{6}$$

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

$$\frac{9}{4}+\frac{1}{2}$$

Least common multiple of 4 and 2 is 4. Convert \frac{9}{4} and \frac{1}{2} to fractions with denominator 4.

$$\frac{9}{4}+\frac{2}{4}$$

Since \frac{9}{4} and \frac{2}{4} have the same denominator, add them by adding their numerators.

$$\frac{9+2}{4}$$

Add 9 and 2 to get 11.

$$\frac{11}{4}$$

Factor

$$\frac{11}{2 ^ {2}} = 2\frac{3}{4} = 2.75$$