Solve 1/2+2/7=7/14+4/74=frac{11}{14}

$$\frac { 1 } { 2 } + \frac { 2 } { 7 } = \frac { 7 } { 14 } + \frac { 4 } { 74 } = \frac { 11 } { 14 }$$

Verify

Solution Steps

Least common multiple of 2 and 7 is 14. Convert \frac{1}{2} and \frac{2}{7} to fractions with denominator 14.

$$\frac{7}{14}+\frac{4}{14}=\frac{7}{14}+\frac{4}{74}\text{ and }\frac{7}{14}+\frac{4}{74}=\frac{11}{14}$$

Since \frac{7}{14} and \frac{4}{14} have the same denominator, add them by adding their numerators.

$$\frac{7+4}{14}=\frac{7}{14}+\frac{4}{74}\text{ and }\frac{7}{14}+\frac{4}{74}=\frac{11}{14}$$

Add 7 and 4 to get 11.

$$\frac{11}{14}=\frac{7}{14}+\frac{4}{74}\text{ and }\frac{7}{14}+\frac{4}{74}=\frac{11}{14}$$

Reduce the fraction \frac{7}{14} to lowest terms by extracting and canceling out 7.

$$\frac{11}{14}=\frac{1}{2}+\frac{4}{74}\text{ and }\frac{7}{14}+\frac{4}{74}=\frac{11}{14}$$

Reduce the fraction \frac{4}{74} to lowest terms by extracting and canceling out 2.

$$\frac{11}{14}=\frac{1}{2}+\frac{2}{37}\text{ and }\frac{7}{14}+\frac{4}{74}=\frac{11}{14}$$

Least common multiple of 2 and 37 is 74. Convert \frac{1}{2} and \frac{2}{37} to fractions with denominator 74.

$$\frac{11}{14}=\frac{37}{74}+\frac{4}{74}\text{ and }\frac{7}{14}+\frac{4}{74}=\frac{11}{14}$$

Since \frac{37}{74} and \frac{4}{74} have the same denominator, add them by adding their numerators.

$$\frac{11}{14}=\frac{37+4}{74}\text{ and }\frac{7}{14}+\frac{4}{74}=\frac{11}{14}$$

Add 37 and 4 to get 41.

$$\frac{11}{14}=\frac{41}{74}\text{ and }\frac{7}{14}+\frac{4}{74}=\frac{11}{14}$$

Least common multiple of 14 and 74 is 518. Convert \frac{11}{14} and \frac{41}{74} to fractions with denominator 518.

$$\frac{407}{518}=\frac{287}{518}\text{ and }\frac{7}{14}+\frac{4}{74}=\frac{11}{14}$$

Compare \frac{407}{518} and \frac{287}{518}.

$$\text{false}\text{ and }\frac{7}{14}+\frac{4}{74}=\frac{11}{14}$$

Reduce the fraction \frac{7}{14} to lowest terms by extracting and canceling out 7.

$$\text{false}\text{ and }\frac{1}{2}+\frac{4}{74}=\frac{11}{14}$$

Reduce the fraction \frac{4}{74} to lowest terms by extracting and canceling out 2.

$$\text{false}\text{ and }\frac{1}{2}+\frac{2}{37}=\frac{11}{14}$$

Least common multiple of 2 and 37 is 74. Convert \frac{1}{2} and \frac{2}{37} to fractions with denominator 74.

$$\text{false}\text{ and }\frac{37}{74}+\frac{4}{74}=\frac{11}{14}$$

Since \frac{37}{74} and \frac{4}{74} have the same denominator, add them by adding their numerators.

$$\text{false}\text{ and }\frac{37+4}{74}=\frac{11}{14}$$

Add 37 and 4 to get 41.

$$\text{false}\text{ and }\frac{41}{74}=\frac{11}{14}$$

Least common multiple of 74 and 14 is 518. Convert \frac{41}{74} and \frac{11}{14} to fractions with denominator 518.

$$\text{false}\text{ and }\frac{287}{518}=\frac{407}{518}$$

Compare \frac{287}{518} and \frac{407}{518}.

$$\text{false}\text{ and }\text{false}$$

The conjunction of \text{false} and \text{false} is \text{false}.

$$\text{false}$$