Solve 25/14+3^2501n/21-63/10

$$2 \frac { 5 } { 14 } + 3 ^ { 2 } \frac { 501 n } { 21 } - 6 \frac { 3 } { 10 }$$

Evaluate

$$\frac{1503n}{7}-\frac{138}{35}$$

Solution Steps

Multiply 2 and 14 to get 28.

$$\frac{28+5}{14}+3^{2}\times \frac{501n}{21}-\frac{6\times 10+3}{10}$$

Add 28 and 5 to get 33.

$$\frac{33}{14}+3^{2}\times \frac{501n}{21}-\frac{6\times 10+3}{10}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{33}{14}+9\times \frac{501n}{21}-\frac{6\times 10+3}{10}$$

Divide 501n by 21 to get \frac{167}{7}n.

$$\frac{33}{14}+9\times \frac{167}{7}n-\frac{6\times 10+3}{10}$$

Express 9\times \frac{167}{7} as a single fraction.

$$\frac{33}{14}+\frac{9\times 167}{7}n-\frac{6\times 10+3}{10}$$

Multiply 9 and 167 to get 1503.

$$\frac{33}{14}+\frac{1503}{7}n-\frac{6\times 10+3}{10}$$

Multiply 6 and 10 to get 60.

$$\frac{33}{14}+\frac{1503}{7}n-\frac{60+3}{10}$$

Add 60 and 3 to get 63.

$$\frac{33}{14}+\frac{1503}{7}n-\frac{63}{10}$$

Least common multiple of 14 and 10 is 70. Convert \frac{33}{14} and \frac{63}{10} to fractions with denominator 70.

$$\frac{165}{70}+\frac{1503}{7}n-\frac{441}{70}$$

Since \frac{165}{70} and \frac{441}{70} have the same denominator, subtract them by subtracting their numerators.

$$\frac{165-441}{70}+\frac{1503}{7}n$$

Subtract 441 from 165 to get -276.

$$\frac{-276}{70}+\frac{1503}{7}n$$

Reduce the fraction \frac{-276}{70} to lowest terms by extracting and canceling out 2.

$$-\frac{138}{35}+\frac{1503}{7}n$$

Expand

$$\frac{1503n}{7}-\frac{138}{35}$$

Solution Steps

Multiply 2 and 14 to get 28.

$$\frac{28+5}{14}+3^{2}\times \frac{501n}{21}-\frac{6\times 10+3}{10}$$

Add 28 and 5 to get 33.

$$\frac{33}{14}+3^{2}\times \frac{501n}{21}-\frac{6\times 10+3}{10}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{33}{14}+9\times \frac{501n}{21}-\frac{6\times 10+3}{10}$$

Divide 501n by 21 to get \frac{167}{7}n.

$$\frac{33}{14}+9\times \frac{167}{7}n-\frac{6\times 10+3}{10}$$

Express 9\times \frac{167}{7} as a single fraction.

$$\frac{33}{14}+\frac{9\times 167}{7}n-\frac{6\times 10+3}{10}$$

Multiply 9 and 167 to get 1503.

$$\frac{33}{14}+\frac{1503}{7}n-\frac{6\times 10+3}{10}$$

Multiply 6 and 10 to get 60.

$$\frac{33}{14}+\frac{1503}{7}n-\frac{60+3}{10}$$

Add 60 and 3 to get 63.

$$\frac{33}{14}+\frac{1503}{7}n-\frac{63}{10}$$

Least common multiple of 14 and 10 is 70. Convert \frac{33}{14} and \frac{63}{10} to fractions with denominator 70.

$$\frac{165}{70}+\frac{1503}{7}n-\frac{441}{70}$$

Since \frac{165}{70} and \frac{441}{70} have the same denominator, subtract them by subtracting their numerators.

$$\frac{165-441}{70}+\frac{1503}{7}n$$

Subtract 441 from 165 to get -276.

$$\frac{-276}{70}+\frac{1503}{7}n$$

Reduce the fraction \frac{-276}{70} to lowest terms by extracting and canceling out 2.

$$-\frac{138}{35}+\frac{1503}{7}n$$