Solve 23*(1/76-1/53)

$$23 \times ( \frac { 1 } { 76 } - \frac { 1 } { 53 } )$$

Evaluate

$$-\frac{529}{4028}\approx -0.131330685$$

Solution Steps

Least common multiple of 76 and 53 is 4028. Convert \frac{1}{76} and \frac{1}{53} to fractions with denominator 4028.

$$23\left(\frac{53}{4028}-\frac{76}{4028}\right)$$

Since \frac{53}{4028} and \frac{76}{4028} have the same denominator, subtract them by subtracting their numerators.

$$23\times \frac{53-76}{4028}$$

Subtract 76 from 53 to get -23.

$$23\left(-\frac{23}{4028}\right)$$

Express 23\left(-\frac{23}{4028}\right) as a single fraction.

$$\frac{23\left(-23\right)}{4028}$$

Multiply 23 and -23 to get -529.

$$\frac{-529}{4028}$$

Fraction \frac{-529}{4028} can be rewritten as -\frac{529}{4028} by extracting the negative sign.

$$-\frac{529}{4028}$$

Factor

$$-\frac{529}{4028} = -0.13133068520357497$$