Solve (1/30+1/35+1/63)x/27

$$( \frac { 1 } { 30 } + \frac { 1 } { 35 } + \frac { 1 } { 63 } ) \frac { x } { 27 }$$

Evaluate

$$\frac{7x}{2430}$$

Solution Steps

Least common multiple of 30 and 35 is 210. Convert \frac{1}{30} and \frac{1}{35} to fractions with denominator 210.

$$\left(\frac{7}{210}+\frac{6}{210}+\frac{1}{63}\right)\times \frac{x}{27}$$

Since \frac{7}{210} and \frac{6}{210} have the same denominator, add them by adding their numerators.

$$\left(\frac{7+6}{210}+\frac{1}{63}\right)\times \frac{x}{27}$$

Add 7 and 6 to get 13.

$$\left(\frac{13}{210}+\frac{1}{63}\right)\times \frac{x}{27}$$

Least common multiple of 210 and 63 is 630. Convert \frac{13}{210} and \frac{1}{63} to fractions with denominator 630.

$$\left(\frac{39}{630}+\frac{10}{630}\right)\times \frac{x}{27}$$

Since \frac{39}{630} and \frac{10}{630} have the same denominator, add them by adding their numerators.

$$\frac{39+10}{630}\times \frac{x}{27}$$

Add 39 and 10 to get 49.

$$\frac{49}{630}\times \frac{x}{27}$$

Reduce the fraction \frac{49}{630} to lowest terms by extracting and canceling out 7.

$$\frac{7}{90}\times \frac{x}{27}$$

Multiply \frac{7}{90} times \frac{x}{27} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7x}{90\times 27}$$

Multiply 90 and 27 to get 2430.

$$\frac{7x}{2430}$$

Expand

$$\frac{7x}{2430}$$

Solution Steps

Least common multiple of 30 and 35 is 210. Convert \frac{1}{30} and \frac{1}{35} to fractions with denominator 210.

$$\left(\frac{7}{210}+\frac{6}{210}+\frac{1}{63}\right)\times \frac{x}{27}$$

Since \frac{7}{210} and \frac{6}{210} have the same denominator, add them by adding their numerators.

$$\left(\frac{7+6}{210}+\frac{1}{63}\right)\times \frac{x}{27}$$

Add 7 and 6 to get 13.

$$\left(\frac{13}{210}+\frac{1}{63}\right)\times \frac{x}{27}$$

Least common multiple of 210 and 63 is 630. Convert \frac{13}{210} and \frac{1}{63} to fractions with denominator 630.

$$\left(\frac{39}{630}+\frac{10}{630}\right)\times \frac{x}{27}$$

Since \frac{39}{630} and \frac{10}{630} have the same denominator, add them by adding their numerators.

$$\frac{39+10}{630}\times \frac{x}{27}$$

Add 39 and 10 to get 49.

$$\frac{49}{630}\times \frac{x}{27}$$

Reduce the fraction \frac{49}{630} to lowest terms by extracting and canceling out 7.

$$\frac{7}{90}\times \frac{x}{27}$$

Multiply \frac{7}{90} times \frac{x}{27} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7x}{90\times 27}$$

Multiply 90 and 27 to get 2430.

$$\frac{7x}{2430}$$