Solve 31/63+1/14-5/21+31/252quadfrac{12}{35}

$$\frac { 31 } { 63 } + \frac { 1 } { 14 } - \frac { 5 } { 21 } + \frac { 31 } { 252 } \quad \frac { 12 } { 35 }$$

Evaluate

$$\frac{1621}{4410}\approx 0.367573696$$

Solution Steps

Least common multiple of 63 and 14 is 126. Convert \frac{31}{63} and \frac{1}{14} to fractions with denominator 126.

$$\frac{62}{126}+\frac{9}{126}-\frac{5}{21}+\frac{31}{252}\times \frac{12}{35}$$

Since \frac{62}{126} and \frac{9}{126} have the same denominator, add them by adding their numerators.

$$\frac{62+9}{126}-\frac{5}{21}+\frac{31}{252}\times \frac{12}{35}$$

Add 62 and 9 to get 71.

$$\frac{71}{126}-\frac{5}{21}+\frac{31}{252}\times \frac{12}{35}$$

Least common multiple of 126 and 21 is 126. Convert \frac{71}{126} and \frac{5}{21} to fractions with denominator 126.

$$\frac{71}{126}-\frac{30}{126}+\frac{31}{252}\times \frac{12}{35}$$

Since \frac{71}{126} and \frac{30}{126} have the same denominator, subtract them by subtracting their numerators.

$$\frac{71-30}{126}+\frac{31}{252}\times \frac{12}{35}$$

Subtract 30 from 71 to get 41.

$$\frac{41}{126}+\frac{31}{252}\times \frac{12}{35}$$

Multiply \frac{31}{252} times \frac{12}{35} by multiplying numerator times numerator and denominator times denominator.

$$\frac{41}{126}+\frac{31\times 12}{252\times 35}$$

Do the multiplications in the fraction \frac{31\times 12}{252\times 35}.

$$\frac{41}{126}+\frac{372}{8820}$$

Reduce the fraction \frac{372}{8820} to lowest terms by extracting and canceling out 12.

$$\frac{41}{126}+\frac{31}{735}$$

Least common multiple of 126 and 735 is 4410. Convert \frac{41}{126} and \frac{31}{735} to fractions with denominator 4410.

$$\frac{1435}{4410}+\frac{186}{4410}$$

Since \frac{1435}{4410} and \frac{186}{4410} have the same denominator, add them by adding their numerators.

$$\frac{1435+186}{4410}$$

Add 1435 and 186 to get 1621.

$$\frac{1621}{4410}$$

Factor

$$\frac{1621}{2 \cdot 3 ^ {2} \cdot 5 \cdot 7 ^ {2}} = 0.3675736961451247$$