Solve [4 1/5 * \{16/21 / (3 1/4 - 1 5/12)\}] + 4/5

Question

$$[4\frac{1}{5}\times\{\frac{16}{21}\div(3\frac{1}{4}-1\frac{5}{12})\}]+\frac{4}{5}$$

Evaluate

$\frac{28}{11}\approx 2.545454545$

Solution Steps

Multiply $4$ and $5$ to get $20$.

$$\frac{20+1}{5}\times \frac{\frac{16}{21}}{\frac{3\times 4+1}{4}-\frac{1\times 12+5}{12}}+\frac{4}{5}$$

Add $20$ and $1$ to get $21$.

$$\frac{21}{5}\times \frac{\frac{16}{21}}{\frac{3\times 4+1}{4}-\frac{1\times 12+5}{12}}+\frac{4}{5}$$

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

$$\frac{21}{5}\times \frac{\frac{16}{21}}{\frac{12+1}{4}-\frac{1\times 12+5}{12}}+\frac{4}{5}$$

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

$$\frac{21}{5}\times \frac{\frac{16}{21}}{\frac{13}{4}-\frac{1\times 12+5}{12}}+\frac{4}{5}$$

Multiply $1$ and $12$ to get $12$.

$$\frac{21}{5}\times \frac{\frac{16}{21}}{\frac{13}{4}-\frac{12+5}{12}}+\frac{4}{5}$$

Add $12$ and $5$ to get $17$.

$$\frac{21}{5}\times \frac{\frac{16}{21}}{\frac{13}{4}-\frac{17}{12}}+\frac{4}{5}$$

Least common multiple of $4$ and $12$ is $12$. Convert $\frac{13}{4}$ and $\frac{17}{12}$ to fractions with denominator $12$.

$$\frac{21}{5}\times \frac{\frac{16}{21}}{\frac{39}{12}-\frac{17}{12}}+\frac{4}{5}$$

Since $\frac{39}{12}$ and $\frac{17}{12}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{21}{5}\times \frac{\frac{16}{21}}{\frac{39-17}{12}}+\frac{4}{5}$$

Subtract $17$ from $39$ to get $22$.

$$\frac{21}{5}\times \frac{\frac{16}{21}}{\frac{22}{12}}+\frac{4}{5}$$

Reduce the fraction $\frac{22}{12}$ to lowest terms by extracting and canceling out $2$.

$$\frac{21}{5}\times \frac{\frac{16}{21}}{\frac{11}{6}}+\frac{4}{5}$$

Divide $\frac{16}{21}$ by $\frac{11}{6}$ by multiplying $\frac{16}{21}$ by the reciprocal of $\frac{11}{6}$.

$$\frac{21}{5}\times \frac{16}{21}\times \frac{6}{11}+\frac{4}{5}$$

Multiply $\frac{16}{21}$ times $\frac{6}{11}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{21}{5}\times \frac{16\times 6}{21\times 11}+\frac{4}{5}$$

Do the multiplications in the fraction $\frac{16\times 6}{21\times 11}$.

$$\frac{21}{5}\times \frac{96}{231}+\frac{4}{5}$$

Reduce the fraction $\frac{96}{231}$ to lowest terms by extracting and canceling out $3$.

$$\frac{21}{5}\times \frac{32}{77}+\frac{4}{5}$$

Multiply $\frac{21}{5}$ times $\frac{32}{77}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{21\times 32}{5\times 77}+\frac{4}{5}$$

Do the multiplications in the fraction $\frac{21\times 32}{5\times 77}$.

$$\frac{672}{385}+\frac{4}{5}$$

Reduce the fraction $\frac{672}{385}$ to lowest terms by extracting and canceling out $7$.

$$\frac{96}{55}+\frac{4}{5}$$

Least common multiple of $55$ and $5$ is $55$. Convert $\frac{96}{55}$ and $\frac{4}{5}$ to fractions with denominator $55$.

$$\frac{96}{55}+\frac{44}{55}$$

Since $\frac{96}{55}$ and $\frac{44}{55}$ have the same denominator, add them by adding their numerators.

$$\frac{96+44}{55}$$

Add $96$ and $44$ to get $140$.

$$\frac{140}{55}$$

Reduce the fraction $\frac{140}{55}$ to lowest terms by extracting and canceling out $5$.

$$\frac{28}{11}$$

Show Solution

Factor

$\frac{2 ^ {2} \cdot 7}{11} = 2\frac{6}{11} = 2.5454545454545454$

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