Solve (3)/(16)+(13)/(16)\div(29)/(15)\div(11)/(3)

Basic Math

Pre-Algebra

Algebra

Trigonometry

Calculus

Precalculus

Statistics

Finite Math

Linear Algebra

Chemistry

Question

$$\frac{ 3 }{ 16 } + \frac{ 13 }{ 16 } \div \frac{ 29 }{ 15 } \div \frac{ 11 }{ 3 }$$

Evaluate

$\frac{771}{2552}\approx 0.302115987$

Solution Steps

Divide $\frac{\frac{13}{16}}{\frac{29}{15}}$ by $\frac{11}{3}$ by multiplying $\frac{\frac{13}{16}}{\frac{29}{15}}$ by the reciprocal of $\frac{11}{3}$.

$$\frac{3}{16}+\frac{\frac{13}{16}\times 3}{\frac{29}{15}\times 11}$$

Express $\frac{13}{16}\times 3$ as a single fraction.

$$\frac{3}{16}+\frac{\frac{13\times 3}{16}}{\frac{29}{15}\times 11}$$

Multiply $13$ and $3$ to get $39$.

$$\frac{3}{16}+\frac{\frac{39}{16}}{\frac{29}{15}\times 11}$$

Express $\frac{29}{15}\times 11$ as a single fraction.

$$\frac{3}{16}+\frac{\frac{39}{16}}{\frac{29\times 11}{15}}$$

Multiply $29$ and $11$ to get $319$.

$$\frac{3}{16}+\frac{\frac{39}{16}}{\frac{319}{15}}$$

Divide $\frac{39}{16}$ by $\frac{319}{15}$ by multiplying $\frac{39}{16}$ by the reciprocal of $\frac{319}{15}$.

$$\frac{3}{16}+\frac{39}{16}\times \frac{15}{319}$$

Multiply $\frac{39}{16}$ times $\frac{15}{319}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{3}{16}+\frac{39\times 15}{16\times 319}$$

Do the multiplications in the fraction $\frac{39\times 15}{16\times 319}$.

$$\frac{3}{16}+\frac{585}{5104}$$

Least common multiple of $16$ and $5104$ is $5104$. Convert $\frac{3}{16}$ and $\frac{585}{5104}$ to fractions with denominator $5104$.

$$\frac{957}{5104}+\frac{585}{5104}$$

Since $\frac{957}{5104}$ and $\frac{585}{5104}$ have the same denominator, add them by adding their numerators.

$$\frac{957+585}{5104}$$

Add $957$ and $585$ to get $1542$.

$$\frac{1542}{5104}$$

Reduce the fraction $\frac{1542}{5104}$ to lowest terms by extracting and canceling out $2$.

$$\frac{771}{2552}$$

Show Solution

Factor

$\frac{3 \cdot 257}{2 ^ {3} \cdot 11 \cdot 29} = 0.302115987460815$