Solve 5/6+9/14:35/42+21/4=frac{42}{42}=frac{31}{21}

$$\frac { 5 } { 6 } + \frac { 9 } { 14 } : \frac { 35 } { 42 } + \frac { 21 } { 4 } = \frac { 42 } { 42 } = \frac { 31 } { 21 }$$

Verify

Solution Steps

Divide 42 by 42 to get 1.

$$\frac{5}{6}+\frac{\frac{9}{14}}{\frac{35}{42}}+\frac{21}{4}=1\text{ and }\frac{42}{42}=\frac{31}{21}$$

Divide 42 by 42 to get 1.

$$\frac{5}{6}+\frac{\frac{9}{14}}{\frac{35}{42}}+\frac{21}{4}=1\text{ and }1=\frac{31}{21}$$

Divide \frac{9}{14} by \frac{35}{42} by multiplying \frac{9}{14} by the reciprocal of \frac{35}{42}.

$$\frac{5}{6}+\frac{9\times 42}{14\times 35}+\frac{21}{4}=1\text{ and }1=\frac{31}{21}$$

Cancel out 14 in both numerator and denominator.

$$\frac{5}{6}+\frac{3\times 9}{35}+\frac{21}{4}=1\text{ and }1=\frac{31}{21}$$

Multiply 3 and 9 to get 27.

$$\frac{5}{6}+\frac{27}{35}+\frac{21}{4}=1\text{ and }1=\frac{31}{21}$$

Least common multiple of 6 and 35 is 210. Convert \frac{5}{6} and \frac{27}{35} to fractions with denominator 210.

$$\frac{175}{210}+\frac{162}{210}+\frac{21}{4}=1\text{ and }1=\frac{31}{21}$$

Since \frac{175}{210} and \frac{162}{210} have the same denominator, add them by adding their numerators.

$$\frac{175+162}{210}+\frac{21}{4}=1\text{ and }1=\frac{31}{21}$$

Add 175 and 162 to get 337.

$$\frac{337}{210}+\frac{21}{4}=1\text{ and }1=\frac{31}{21}$$

Least common multiple of 210 and 4 is 420. Convert \frac{337}{210} and \frac{21}{4} to fractions with denominator 420.

$$\frac{674}{420}+\frac{2205}{420}=1\text{ and }1=\frac{31}{21}$$

Since \frac{674}{420} and \frac{2205}{420} have the same denominator, add them by adding their numerators.

$$\frac{674+2205}{420}=1\text{ and }1=\frac{31}{21}$$

Add 674 and 2205 to get 2879.

$$\frac{2879}{420}=1\text{ and }1=\frac{31}{21}$$

Convert 1 to fraction \frac{420}{420}.

$$\frac{2879}{420}=\frac{420}{420}\text{ and }1=\frac{31}{21}$$

Compare \frac{2879}{420} and \frac{420}{420}.

$$\text{false}\text{ and }1=\frac{31}{21}$$

Convert 1 to fraction \frac{21}{21}.

$$\text{false}\text{ and }\frac{21}{21}=\frac{31}{21}$$

Compare \frac{21}{21} and \frac{31}{21}.

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

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

$$\text{false}$$