Solve 9 + (1.6/3.2) + \{1.8(5.2 - 1.7)\}

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Question

$$2.9+(1.6\div3.2)+\{1.8\times(5.2-1.7)\}$$

Evaluate

$9.7$

Solution Steps

Expand $\frac{1.6}{3.2}$ by multiplying both numerator and the denominator by $10$.

$$2.9+\frac{16}{32}+1.8\left(5.2-1.7\right)$$

Reduce the fraction $\frac{16}{32}$ to lowest terms by extracting and canceling out $16$.

$$2.9+\frac{1}{2}+1.8\left(5.2-1.7\right)$$

Convert decimal number $2.9$ to fraction $\frac{29}{10}$.

$$\frac{29}{10}+\frac{1}{2}+1.8\left(5.2-1.7\right)$$

Least common multiple of $10$ and $2$ is $10$. Convert $\frac{29}{10}$ and $\frac{1}{2}$ to fractions with denominator $10$.

$$\frac{29}{10}+\frac{5}{10}+1.8\left(5.2-1.7\right)$$

Since $\frac{29}{10}$ and $\frac{5}{10}$ have the same denominator, add them by adding their numerators.

$$\frac{29+5}{10}+1.8\left(5.2-1.7\right)$$

Add $29$ and $5$ to get $34$.

$$\frac{34}{10}+1.8\left(5.2-1.7\right)$$

Reduce the fraction $\frac{34}{10}$ to lowest terms by extracting and canceling out $2$.

$$\frac{17}{5}+1.8\left(5.2-1.7\right)$$

Subtract $1.7$ from $5.2$ to get $3.5$.

$$\frac{17}{5}+1.8\times 3.5$$

Multiply $1.8$ and $3.5$ to get $6.3$.

$$\frac{17}{5}+6.3$$

Convert decimal number $6.3$ to fraction $\frac{63}{10}$.

$$\frac{17}{5}+\frac{63}{10}$$

Least common multiple of $5$ and $10$ is $10$. Convert $\frac{17}{5}$ and $\frac{63}{10}$ to fractions with denominator $10$.

$$\frac{34}{10}+\frac{63}{10}$$

Since $\frac{34}{10}$ and $\frac{63}{10}$ have the same denominator, add them by adding their numerators.

$$\frac{34+63}{10}$$

Add $34$ and $63$ to get $97$.

$$\frac{97}{10}$$

Show Solution

Factor

$\frac{97}{2 \cdot 5} = 9\frac{7}{10} = 9.7$