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

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

Verify

Solution Steps

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

$$\frac{5}{7}+\frac{7}{11}+\frac{4}{10}=\frac{10}{14}+\frac{7}{11}+\frac{4}{10}$$

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

$$\frac{55}{77}+\frac{49}{77}+\frac{4}{10}=\frac{10}{14}+\frac{7}{11}+\frac{4}{10}$$

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

$$\frac{55+49}{77}+\frac{4}{10}=\frac{10}{14}+\frac{7}{11}+\frac{4}{10}$$

Add 55 and 49 to get 104.

$$\frac{104}{77}+\frac{4}{10}=\frac{10}{14}+\frac{7}{11}+\frac{4}{10}$$

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

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

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

$$\frac{520}{385}+\frac{154}{385}=\frac{10}{14}+\frac{7}{11}+\frac{4}{10}$$

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

$$\frac{520+154}{385}=\frac{10}{14}+\frac{7}{11}+\frac{4}{10}$$

Add 520 and 154 to get 674.

$$\frac{674}{385}=\frac{10}{14}+\frac{7}{11}+\frac{4}{10}$$

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

$$\frac{674}{385}=\frac{5}{7}+\frac{7}{11}+\frac{4}{10}$$

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

$$\frac{674}{385}=\frac{55}{77}+\frac{49}{77}+\frac{4}{10}$$

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

$$\frac{674}{385}=\frac{55+49}{77}+\frac{4}{10}$$

Add 55 and 49 to get 104.

$$\frac{674}{385}=\frac{104}{77}+\frac{4}{10}$$

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

$$\frac{674}{385}=\frac{104}{77}+\frac{2}{5}$$

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

$$\frac{674}{385}=\frac{520}{385}+\frac{154}{385}$$

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

$$\frac{674}{385}=\frac{520+154}{385}$$

Add 520 and 154 to get 674.

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

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

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