Solve 11/2div15/4+9/4+3/4

$$\frac{ 11 }{ 2 } \div \frac{ 15 }{ 4 } + \frac{ 9 }{ 4 } + \frac{ 3 }{ 4 }$$

Evaluate

$$\frac{67}{15}\approx 4.466666667$$

Solution Steps

Divide \frac{11}{2} by \frac{15}{4} by multiplying \frac{11}{2} by the reciprocal of \frac{15}{4}.

$$\frac{11}{2}\times \frac{4}{15}+\frac{9}{4}+\frac{3}{4}$$

Multiply \frac{11}{2} times \frac{4}{15} by multiplying numerator times numerator and denominator times denominator.

$$\frac{11\times 4}{2\times 15}+\frac{9}{4}+\frac{3}{4}$$

Do the multiplications in the fraction \frac{11\times 4}{2\times 15}.

$$\frac{44}{30}+\frac{9}{4}+\frac{3}{4}$$

Reduce the fraction \frac{44}{30} to lowest terms by extracting and canceling out 2.

$$\frac{22}{15}+\frac{9}{4}+\frac{3}{4}$$

Least common multiple of 15 and 4 is 60. Convert \frac{22}{15} and \frac{9}{4} to fractions with denominator 60.

$$\frac{88}{60}+\frac{135}{60}+\frac{3}{4}$$

Since \frac{88}{60} and \frac{135}{60} have the same denominator, add them by adding their numerators.

$$\frac{88+135}{60}+\frac{3}{4}$$

Add 88 and 135 to get 223.

$$\frac{223}{60}+\frac{3}{4}$$

Least common multiple of 60 and 4 is 60. Convert \frac{223}{60} and \frac{3}{4} to fractions with denominator 60.

$$\frac{223}{60}+\frac{45}{60}$$

Since \frac{223}{60} and \frac{45}{60} have the same denominator, add them by adding their numerators.

$$\frac{223+45}{60}$$

Add 223 and 45 to get 268.

$$\frac{268}{60}$$

Reduce the fraction \frac{268}{60} to lowest terms by extracting and canceling out 4.

$$\frac{67}{15}$$

Factor

$$\frac{67}{3 \cdot 5} = 4\frac{7}{15} = 4.466666666666667$$