Solve 132/9-(47/15-12/3)=111/5

$$13 \frac { 2 } { 9 } - ( 4 \frac { 7 } { 15 } - 1 \frac { 2 } { 3 } ) = 11 \frac { 1 } { 5 }$$

Verify

Solution Steps

Multiply both sides of the equation by 45, the least common multiple of 9,15,3,5.

$$5\left(13\times 9+2\right)-45\left(\frac{4\times 15+7}{15}-\frac{1\times 3+2}{3}\right)=9\left(11\times 5+1\right)$$

Multiply 13 and 9 to get 117.

$$5\left(117+2\right)-45\left(\frac{4\times 15+7}{15}-\frac{1\times 3+2}{3}\right)=9\left(11\times 5+1\right)$$

Add 117 and 2 to get 119.

$$5\times 119-45\left(\frac{4\times 15+7}{15}-\frac{1\times 3+2}{3}\right)=9\left(11\times 5+1\right)$$

Multiply 5 and 119 to get 595.

$$595-45\left(\frac{4\times 15+7}{15}-\frac{1\times 3+2}{3}\right)=9\left(11\times 5+1\right)$$

Multiply 4 and 15 to get 60.

$$595-45\left(\frac{60+7}{15}-\frac{1\times 3+2}{3}\right)=9\left(11\times 5+1\right)$$

Add 60 and 7 to get 67.

$$595-45\left(\frac{67}{15}-\frac{1\times 3+2}{3}\right)=9\left(11\times 5+1\right)$$

Multiply 1 and 3 to get 3.

$$595-45\left(\frac{67}{15}-\frac{3+2}{3}\right)=9\left(11\times 5+1\right)$$

Add 3 and 2 to get 5.

$$595-45\left(\frac{67}{15}-\frac{5}{3}\right)=9\left(11\times 5+1\right)$$

Least common multiple of 15 and 3 is 15. Convert \frac{67}{15} and \frac{5}{3} to fractions with denominator 15.

$$595-45\left(\frac{67}{15}-\frac{25}{15}\right)=9\left(11\times 5+1\right)$$

Since \frac{67}{15} and \frac{25}{15} have the same denominator, subtract them by subtracting their numerators.

$$595-45\times \frac{67-25}{15}=9\left(11\times 5+1\right)$$

Subtract 25 from 67 to get 42.

$$595-45\times \frac{42}{15}=9\left(11\times 5+1\right)$$

Reduce the fraction \frac{42}{15} to lowest terms by extracting and canceling out 3.

$$595-45\times \frac{14}{5}=9\left(11\times 5+1\right)$$

Express 45\times \frac{14}{5} as a single fraction.

$$595-\frac{45\times 14}{5}=9\left(11\times 5+1\right)$$

Multiply 45 and 14 to get 630.

$$595-\frac{630}{5}=9\left(11\times 5+1\right)$$

Divide 630 by 5 to get 126.

$$595-126=9\left(11\times 5+1\right)$$

Subtract 126 from 595 to get 469.

$$469=9\left(11\times 5+1\right)$$

Multiply 11 and 5 to get 55.

$$469=9\left(55+1\right)$$

Add 55 and 1 to get 56.

$$469=9\times 56$$

Multiply 9 and 56 to get 504.

$$469=504$$

Compare 469 and 504.

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