Solve [5.17 + \{3.2(4.4/3.3 - 1.1)\}]

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Question

$$[5.17+\{3.2\times(4.4\div3.3-1.1)\}]$$

Evaluate

$\frac{71}{12}\approx 5.916666667$

Solution Steps

Expand $\frac{4.4}{3.3}$ by multiplying both numerator and the denominator by $10$.

$$5.17+3.2\left(\frac{44}{33}-1.1\right)$$

Reduce the fraction $\frac{44}{33}$ to lowest terms by extracting and canceling out $11$.

$$5.17+3.2\left(\frac{4}{3}-1.1\right)$$

Convert decimal number $1.1$ to fraction $\frac{11}{10}$.

$$5.17+3.2\left(\frac{4}{3}-\frac{11}{10}\right)$$

Least common multiple of $3$ and $10$ is $30$. Convert $\frac{4}{3}$ and $\frac{11}{10}$ to fractions with denominator $30$.

$$5.17+3.2\left(\frac{40}{30}-\frac{33}{30}\right)$$

Since $\frac{40}{30}$ and $\frac{33}{30}$ have the same denominator, subtract them by subtracting their numerators.

$$5.17+3.2\times \frac{40-33}{30}$$

Subtract $33$ from $40$ to get $7$.

$$5.17+3.2\times \frac{7}{30}$$

Convert decimal number $3.2$ to fraction $\frac{32}{10}$. Reduce the fraction $\frac{32}{10}$ to lowest terms by extracting and canceling out $2$.

$$5.17+\frac{16}{5}\times \frac{7}{30}$$

Multiply $\frac{16}{5}$ times $\frac{7}{30}$ by multiplying numerator times numerator and denominator times denominator.

$$5.17+\frac{16\times 7}{5\times 30}$$

Do the multiplications in the fraction $\frac{16\times 7}{5\times 30}$.

$$5.17+\frac{112}{150}$$

Reduce the fraction $\frac{112}{150}$ to lowest terms by extracting and canceling out $2$.

$$5.17+\frac{56}{75}$$

Convert decimal number $5.17$ to fraction $\frac{517}{100}$.

$$\frac{517}{100}+\frac{56}{75}$$

Least common multiple of $100$ and $75$ is $300$. Convert $\frac{517}{100}$ and $\frac{56}{75}$ to fractions with denominator $300$.

$$\frac{1551}{300}+\frac{224}{300}$$

Since $\frac{1551}{300}$ and $\frac{224}{300}$ have the same denominator, add them by adding their numerators.

$$\frac{1551+224}{300}$$

Add $1551$ and $224$ to get $1775$.

$$\frac{1775}{300}$$

Reduce the fraction $\frac{1775}{300}$ to lowest terms by extracting and canceling out $25$.

$$\frac{71}{12}$$

Show Solution

Factor

$\frac{71}{3 \cdot 2 ^ {2}} = 5\frac{11}{12} = 5.916666666666667$