Solve 4 1/3 - \{(1/4 * 2 1/2) - 17/9\}

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Question

$$4\frac{1}{3}-\{(\frac{1}{4}\times2\frac{1}{2})-\frac{17}{9}\}$$

Evaluate

$\frac{403}{72}\approx 5.597222222$

Solution Steps

Multiply $4$ and $3$ to get $12$.

$$\frac{12+1}{3}-\left(\frac{1}{4}\times \frac{2\times 2+1}{2}-\frac{17}{9}\right)$$

Add $12$ and $1$ to get $13$.

$$\frac{13}{3}-\left(\frac{1}{4}\times \frac{2\times 2+1}{2}-\frac{17}{9}\right)$$

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

$$\frac{13}{3}-\left(\frac{1}{4}\times \frac{4+1}{2}-\frac{17}{9}\right)$$

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

$$\frac{13}{3}-\left(\frac{1}{4}\times \frac{5}{2}-\frac{17}{9}\right)$$

Multiply $\frac{1}{4}$ times $\frac{5}{2}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{13}{3}-\left(\frac{1\times 5}{4\times 2}-\frac{17}{9}\right)$$

Do the multiplications in the fraction $\frac{1\times 5}{4\times 2}$.

$$\frac{13}{3}-\left(\frac{5}{8}-\frac{17}{9}\right)$$

Least common multiple of $8$ and $9$ is $72$. Convert $\frac{5}{8}$ and $\frac{17}{9}$ to fractions with denominator $72$.

$$\frac{13}{3}-\left(\frac{45}{72}-\frac{136}{72}\right)$$

Since $\frac{45}{72}$ and $\frac{136}{72}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{13}{3}-\frac{45-136}{72}$$

Subtract $136$ from $45$ to get $-91$.

$$\frac{13}{3}-\left(-\frac{91}{72}\right)$$

The opposite of $-\frac{91}{72}$ is $\frac{91}{72}$.

$$\frac{13}{3}+\frac{91}{72}$$

Least common multiple of $3$ and $72$ is $72$. Convert $\frac{13}{3}$ and $\frac{91}{72}$ to fractions with denominator $72$.

$$\frac{312}{72}+\frac{91}{72}$$

Since $\frac{312}{72}$ and $\frac{91}{72}$ have the same denominator, add them by adding their numerators.

$$\frac{312+91}{72}$$

Add $312$ and $91$ to get $403$.

$$\frac{403}{72}$$

Show Solution

Factor

$\frac{13 \cdot 31}{2 ^ {3} \cdot 3 ^ {2}} = 5\frac{43}{72} = 5.597222222222222$