Solve 16\div3+5\div7\times2+4\times6-3\times12\div2+4\div9+7

Question

$$16 \div 3+5 \div 7 \times 2+4 \times 6-3 \times 12 \div 2+4 \div 9+7$$

Evaluate

$\frac{1273}{63}\approx 20.206349206$

Solution Steps

Express $\frac{5}{7}\times 2$ as a single fraction.

$$\frac{16}{3}+\frac{5\times 2}{7}+4\times 6-\frac{3\times 12}{2}+\frac{4}{9}+7$$

Multiply $5$ and $2$ to get $10$.

$$\frac{16}{3}+\frac{10}{7}+4\times 6-\frac{3\times 12}{2}+\frac{4}{9}+7$$

Least common multiple of $3$ and $7$ is $21$. Convert $\frac{16}{3}$ and $\frac{10}{7}$ to fractions with denominator $21$.

$$\frac{112}{21}+\frac{30}{21}+4\times 6-\frac{3\times 12}{2}+\frac{4}{9}+7$$

Since $\frac{112}{21}$ and $\frac{30}{21}$ have the same denominator, add them by adding their numerators.

$$\frac{112+30}{21}+4\times 6-\frac{3\times 12}{2}+\frac{4}{9}+7$$

Add $112$ and $30$ to get $142$.

$$\frac{142}{21}+4\times 6-\frac{3\times 12}{2}+\frac{4}{9}+7$$

Multiply $4$ and $6$ to get $24$.

$$\frac{142}{21}+24-\frac{3\times 12}{2}+\frac{4}{9}+7$$

Convert $24$ to fraction $\frac{504}{21}$.

$$\frac{142}{21}+\frac{504}{21}-\frac{3\times 12}{2}+\frac{4}{9}+7$$

Since $\frac{142}{21}$ and $\frac{504}{21}$ have the same denominator, add them by adding their numerators.

$$\frac{142+504}{21}-\frac{3\times 12}{2}+\frac{4}{9}+7$$

Add $142$ and $504$ to get $646$.

$$\frac{646}{21}-\frac{3\times 12}{2}+\frac{4}{9}+7$$

Multiply $3$ and $12$ to get $36$.

$$\frac{646}{21}-\frac{36}{2}+\frac{4}{9}+7$$

Divide $36$ by $2$ to get $18$.

$$\frac{646}{21}-18+\frac{4}{9}+7$$

Convert $18$ to fraction $\frac{378}{21}$.

$$\frac{646}{21}-\frac{378}{21}+\frac{4}{9}+7$$

Since $\frac{646}{21}$ and $\frac{378}{21}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{646-378}{21}+\frac{4}{9}+7$$

Subtract $378$ from $646$ to get $268$.

$$\frac{268}{21}+\frac{4}{9}+7$$

Least common multiple of $21$ and $9$ is $63$. Convert $\frac{268}{21}$ and $\frac{4}{9}$ to fractions with denominator $63$.

$$\frac{804}{63}+\frac{28}{63}+7$$

Since $\frac{804}{63}$ and $\frac{28}{63}$ have the same denominator, add them by adding their numerators.

$$\frac{804+28}{63}+7$$

Add $804$ and $28$ to get $832$.

$$\frac{832}{63}+7$$

Convert $7$ to fraction $\frac{441}{63}$.

$$\frac{832}{63}+\frac{441}{63}$$

Since $\frac{832}{63}$ and $\frac{441}{63}$ have the same denominator, add them by adding their numerators.

$$\frac{832+441}{63}$$

Add $832$ and $441$ to get $1273$.

$$\frac{1273}{63}$$

Show Solution

Factor

$\frac{19 \cdot 67}{3 ^ {2} \cdot 7} = 20\frac{13}{63} = 20.206349206349206$

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