Solve (11(2)/(3)-7.4)\div5(1)/(3)+1(2)/(5)

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Question

$$(11 \frac{ 2 }{ 3 } -7.4) \div 5 \frac{ 1 }{ 3 } +1 \frac{ 2 }{ 5 }$$

Evaluate

$2.2$

Solution Steps

Multiply $11$ and $3$ to get $33$.

$$\frac{\frac{33+2}{3}-7.4}{\frac{5\times 3+1}{3}}+\frac{1\times 5+2}{5}$$

Add $33$ and $2$ to get $35$.

$$\frac{\frac{35}{3}-7.4}{\frac{5\times 3+1}{3}}+\frac{1\times 5+2}{5}$$

Convert decimal number $7.4$ to fraction $\frac{74}{10}$. Reduce the fraction $\frac{74}{10}$ to lowest terms by extracting and canceling out $2$.

$$\frac{\frac{35}{3}-\frac{37}{5}}{\frac{5\times 3+1}{3}}+\frac{1\times 5+2}{5}$$

Least common multiple of $3$ and $5$ is $15$. Convert $\frac{35}{3}$ and $\frac{37}{5}$ to fractions with denominator $15$.

$$\frac{\frac{175}{15}-\frac{111}{15}}{\frac{5\times 3+1}{3}}+\frac{1\times 5+2}{5}$$

Since $\frac{175}{15}$ and $\frac{111}{15}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{175-111}{15}}{\frac{5\times 3+1}{3}}+\frac{1\times 5+2}{5}$$

Subtract $111$ from $175$ to get $64$.

$$\frac{\frac{64}{15}}{\frac{5\times 3+1}{3}}+\frac{1\times 5+2}{5}$$

Multiply $5$ and $3$ to get $15$.

$$\frac{\frac{64}{15}}{\frac{15+1}{3}}+\frac{1\times 5+2}{5}$$

Add $15$ and $1$ to get $16$.

$$\frac{\frac{64}{15}}{\frac{16}{3}}+\frac{1\times 5+2}{5}$$

Divide $\frac{64}{15}$ by $\frac{16}{3}$ by multiplying $\frac{64}{15}$ by the reciprocal of $\frac{16}{3}$.

$$\frac{64}{15}\times \frac{3}{16}+\frac{1\times 5+2}{5}$$

Multiply $\frac{64}{15}$ times $\frac{3}{16}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{64\times 3}{15\times 16}+\frac{1\times 5+2}{5}$$

Do the multiplications in the fraction $\frac{64\times 3}{15\times 16}$.

$$\frac{192}{240}+\frac{1\times 5+2}{5}$$

Reduce the fraction $\frac{192}{240}$ to lowest terms by extracting and canceling out $48$.

$$\frac{4}{5}+\frac{1\times 5+2}{5}$$

Multiply $1$ and $5$ to get $5$.

$$\frac{4}{5}+\frac{5+2}{5}$$

Add $5$ and $2$ to get $7$.

$$\frac{4}{5}+\frac{7}{5}$$

Since $\frac{4}{5}$ and $\frac{7}{5}$ have the same denominator, add them by adding their numerators.

$$\frac{4+7}{5}$$

Add $4$ and $7$ to get $11$.

$$\frac{11}{5}$$

Show Solution

Factor

$\frac{11}{5} = 2\frac{1}{5} = 2.2$