Solve ( ) 10 1/10 + [4\{7/10 + (1/5 + 1/4)\}]

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Question

$$10 \frac { 1 } { 10 } + [ 4 \{ \frac { 7 } { 10 } + ( \frac { 1 } { 5 } + \frac { 1 } { 4 } ) \} ]$$

Evaluate

$\frac{147}{10}=14.7$

Solution Steps

Multiply $10$ and $10$ to get $100$.

$$\frac{100+1}{10}+4\left(\frac{7}{10}+\frac{1}{5}+\frac{1}{4}\right)$$

Add $100$ and $1$ to get $101$.

$$\frac{101}{10}+4\left(\frac{7}{10}+\frac{1}{5}+\frac{1}{4}\right)$$

Least common multiple of $10$ and $5$ is $10$. Convert $\frac{7}{10}$ and $\frac{1}{5}$ to fractions with denominator $10$.

$$\frac{101}{10}+4\left(\frac{7}{10}+\frac{2}{10}+\frac{1}{4}\right)$$

Since $\frac{7}{10}$ and $\frac{2}{10}$ have the same denominator, add them by adding their numerators.

$$\frac{101}{10}+4\left(\frac{7+2}{10}+\frac{1}{4}\right)$$

Add $7$ and $2$ to get $9$.

$$\frac{101}{10}+4\left(\frac{9}{10}+\frac{1}{4}\right)$$

Least common multiple of $10$ and $4$ is $20$. Convert $\frac{9}{10}$ and $\frac{1}{4}$ to fractions with denominator $20$.

$$\frac{101}{10}+4\left(\frac{18}{20}+\frac{5}{20}\right)$$

Since $\frac{18}{20}$ and $\frac{5}{20}$ have the same denominator, add them by adding their numerators.

$$\frac{101}{10}+4\times \frac{18+5}{20}$$

Add $18$ and $5$ to get $23$.

$$\frac{101}{10}+4\times \frac{23}{20}$$

Express $4\times \frac{23}{20}$ as a single fraction.

$$\frac{101}{10}+\frac{4\times 23}{20}$$

Multiply $4$ and $23$ to get $92$.

$$\frac{101}{10}+\frac{92}{20}$$

Reduce the fraction $\frac{92}{20}$ to lowest terms by extracting and canceling out $4$.

$$\frac{101}{10}+\frac{23}{5}$$

Least common multiple of $10$ and $5$ is $10$. Convert $\frac{101}{10}$ and $\frac{23}{5}$ to fractions with denominator $10$.

$$\frac{101}{10}+\frac{46}{10}$$

Since $\frac{101}{10}$ and $\frac{46}{10}$ have the same denominator, add them by adding their numerators.

$$\frac{101+46}{10}$$

Add $101$ and $46$ to get $147$.

$$\frac{147}{10}$$

Show Solution

Factor

$\frac{3 \cdot 7 ^ {2}}{2 \cdot 5} = 14\frac{7}{10} = 14.7$