Solve 8(3)/(4)+(5)/(12)\div((1)/(3)\times2(1)/(2)-(7)/(8))

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Question

$$8 \frac{ 3 }{ 4 } + \frac{ 5 }{ 12 } \div ( \frac{ 1 }{ 3 } \times 2 \frac{ 1 }{ 2 } - \frac{ 7 }{ 8 } )$$

Evaluate

$-\frac{5}{4}=-1.25$

Solution Steps

Multiply $8$ and $4$ to get $32$.

$$\frac{32+3}{4}+\frac{\frac{5}{12}}{\frac{1}{3}\times \frac{2\times 2+1}{2}-\frac{7}{8}}$$

Add $32$ and $3$ to get $35$.

$$\frac{35}{4}+\frac{\frac{5}{12}}{\frac{1}{3}\times \frac{2\times 2+1}{2}-\frac{7}{8}}$$

Multiply $2$ and $2$ to get $4$.

$$\frac{35}{4}+\frac{\frac{5}{12}}{\frac{1}{3}\times \frac{4+1}{2}-\frac{7}{8}}$$

Add $4$ and $1$ to get $5$.

$$\frac{35}{4}+\frac{\frac{5}{12}}{\frac{1}{3}\times \frac{5}{2}-\frac{7}{8}}$$

Multiply $\frac{1}{3}$ times $\frac{5}{2}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{35}{4}+\frac{\frac{5}{12}}{\frac{1\times 5}{3\times 2}-\frac{7}{8}}$$

Do the multiplications in the fraction $\frac{1\times 5}{3\times 2}$.

$$\frac{35}{4}+\frac{\frac{5}{12}}{\frac{5}{6}-\frac{7}{8}}$$

Least common multiple of $6$ and $8$ is $24$. Convert $\frac{5}{6}$ and $\frac{7}{8}$ to fractions with denominator $24$.

$$\frac{35}{4}+\frac{\frac{5}{12}}{\frac{20}{24}-\frac{21}{24}}$$

Since $\frac{20}{24}$ and $\frac{21}{24}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{35}{4}+\frac{\frac{5}{12}}{\frac{20-21}{24}}$$

Subtract $21$ from $20$ to get $-1$.

$$\frac{35}{4}+\frac{\frac{5}{12}}{-\frac{1}{24}}$$

Divide $\frac{5}{12}$ by $-\frac{1}{24}$ by multiplying $\frac{5}{12}$ by the reciprocal of $-\frac{1}{24}$.

$$\frac{35}{4}+\frac{5}{12}\left(-24\right)$$

Express $\frac{5}{12}\left(-24\right)$ as a single fraction.

$$\frac{35}{4}+\frac{5\left(-24\right)}{12}$$

Multiply $5$ and $-24$ to get $-120$.

$$\frac{35}{4}+\frac{-120}{12}$$

Divide $-120$ by $12$ to get $-10$.

$$\frac{35}{4}-10$$

Convert $10$ to fraction $\frac{40}{4}$.

$$\frac{35}{4}-\frac{40}{4}$$

Since $\frac{35}{4}$ and $\frac{40}{4}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{35-40}{4}$$

Subtract $40$ from $35$ to get $-5$.

$$-\frac{5}{4}$$

Show Solution

Factor

$-\frac{5}{4} = -1\frac{1}{4} = -1.25$