Solve 5/9\div(1/3+1/4)OF15/7 | Equatix

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Question

$$5/9 \div (1/3+1/4)OF15/7$$

Evaluate

$\frac{20F_{15}O}{147}$

Solution Steps

Least common multiple of $3$ and $4$ is $12$. Convert $\frac{1}{3}$ and $\frac{1}{4}$ to fractions with denominator $12$.

$$\frac{\frac{\frac{5}{9}}{\frac{4}{12}+\frac{3}{12}}OF_{15}}{7}$$

Since $\frac{4}{12}$ and $\frac{3}{12}$ have the same denominator, add them by adding their numerators.

$$\frac{\frac{\frac{5}{9}}{\frac{4+3}{12}}OF_{15}}{7}$$

Add $4$ and $3$ to get $7$.

$$\frac{\frac{\frac{5}{9}}{\frac{7}{12}}OF_{15}}{7}$$

Divide $\frac{5}{9}$ by $\frac{7}{12}$ by multiplying $\frac{5}{9}$ by the reciprocal of $\frac{7}{12}$.

$$\frac{\frac{5}{9}\times \frac{12}{7}OF_{15}}{7}$$

Multiply $\frac{5}{9}$ times $\frac{12}{7}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{5\times 12}{9\times 7}OF_{15}}{7}$$

Do the multiplications in the fraction $\frac{5\times 12}{9\times 7}$.

$$\frac{\frac{60}{63}OF_{15}}{7}$$

Reduce the fraction $\frac{60}{63}$ to lowest terms by extracting and canceling out $3$.

$$\frac{\frac{20}{21}OF_{15}}{7}$$

Divide $\frac{20}{21}OF_{15}$ by $7$ to get $\frac{20}{147}OF_{15}$.

$$\frac{20}{147}OF_{15}$$

Show Solution

Differentiate w.r.t. O

$\frac{20F_{15}}{147}$