Solve (10/14+7/11)+4/10=10/14*(frac{7}{11}+frac{4}{10})

$$( \frac { 10 } { 14 } + \frac { 7 } { 11 } ) + \frac { 4 } { 10 } = \frac { 10 } { 14 } \cdot ( \frac { 7 } { 11 } + \frac { 4 } { 10 } )$$

Verify

Solution Steps

Reduce the fraction \frac{10}{14} to lowest terms by extracting and canceling out 2.

$$\frac{5}{7}+\frac{7}{11}+\frac{4}{10}=\frac{10}{14}\left(\frac{7}{11}+\frac{4}{10}\right)$$

Least common multiple of 7 and 11 is 77. Convert \frac{5}{7} and \frac{7}{11} to fractions with denominator 77.

$$\frac{55}{77}+\frac{49}{77}+\frac{4}{10}=\frac{10}{14}\left(\frac{7}{11}+\frac{4}{10}\right)$$

Since \frac{55}{77} and \frac{49}{77} have the same denominator, add them by adding their numerators.

$$\frac{55+49}{77}+\frac{4}{10}=\frac{10}{14}\left(\frac{7}{11}+\frac{4}{10}\right)$$

Add 55 and 49 to get 104.

$$\frac{104}{77}+\frac{4}{10}=\frac{10}{14}\left(\frac{7}{11}+\frac{4}{10}\right)$$

Reduce the fraction \frac{4}{10} to lowest terms by extracting and canceling out 2.

$$\frac{104}{77}+\frac{2}{5}=\frac{10}{14}\left(\frac{7}{11}+\frac{4}{10}\right)$$

Least common multiple of 77 and 5 is 385. Convert \frac{104}{77} and \frac{2}{5} to fractions with denominator 385.

$$\frac{520}{385}+\frac{154}{385}=\frac{10}{14}\left(\frac{7}{11}+\frac{4}{10}\right)$$

Since \frac{520}{385} and \frac{154}{385} have the same denominator, add them by adding their numerators.

$$\frac{520+154}{385}=\frac{10}{14}\left(\frac{7}{11}+\frac{4}{10}\right)$$

Add 520 and 154 to get 674.

$$\frac{674}{385}=\frac{10}{14}\left(\frac{7}{11}+\frac{4}{10}\right)$$

Reduce the fraction \frac{10}{14} to lowest terms by extracting and canceling out 2.

$$\frac{674}{385}=\frac{5}{7}\left(\frac{7}{11}+\frac{4}{10}\right)$$

Reduce the fraction \frac{4}{10} to lowest terms by extracting and canceling out 2.

$$\frac{674}{385}=\frac{5}{7}\left(\frac{7}{11}+\frac{2}{5}\right)$$

Least common multiple of 11 and 5 is 55. Convert \frac{7}{11} and \frac{2}{5} to fractions with denominator 55.

$$\frac{674}{385}=\frac{5}{7}\left(\frac{35}{55}+\frac{22}{55}\right)$$

Since \frac{35}{55} and \frac{22}{55} have the same denominator, add them by adding their numerators.

$$\frac{674}{385}=\frac{5}{7}\times \frac{35+22}{55}$$

Add 35 and 22 to get 57.

$$\frac{674}{385}=\frac{5}{7}\times \frac{57}{55}$$

Multiply \frac{5}{7} times \frac{57}{55} by multiplying numerator times numerator and denominator times denominator.

$$\frac{674}{385}=\frac{5\times 57}{7\times 55}$$

Do the multiplications in the fraction \frac{5\times 57}{7\times 55}.

$$\frac{674}{385}=\frac{285}{385}$$

Compare \frac{674}{385} and \frac{285}{385}.

$$\text{false}$$