Solve 31/110-(21/110+1/110)

$$3 \frac { 1 } { 110 } - ( 2 \frac { 1 } { 110 } + \frac { 1 } { 110 } )$$

Evaluate

$$\frac{109}{110}\approx 0.990909091$$

Solution Steps

Multiply 3 and 110 to get 330.

$$\frac{330+1}{110}-\left(\frac{2\times 110+1}{110}+\frac{1}{110}\right)$$

Add 330 and 1 to get 331.

$$\frac{331}{110}-\left(\frac{2\times 110+1}{110}+\frac{1}{110}\right)$$

Multiply 2 and 110 to get 220.

$$\frac{331}{110}-\left(\frac{220+1}{110}+\frac{1}{110}\right)$$

Add 220 and 1 to get 221.

$$\frac{331}{110}-\left(\frac{221}{110}+\frac{1}{110}\right)$$

Since \frac{221}{110} and \frac{1}{110} have the same denominator, add them by adding their numerators.

$$\frac{331}{110}-\frac{221+1}{110}$$

Add 221 and 1 to get 222.

$$\frac{331}{110}-\frac{222}{110}$$

Since \frac{331}{110} and \frac{222}{110} have the same denominator, subtract them by subtracting their numerators.

$$\frac{331-222}{110}$$

Subtract 222 from 331 to get 109.

$$\frac{109}{110}$$

Factor

$$\frac{109}{2 \cdot 5 \cdot 11} = 0.990909090909091$$