Solve 1/357-1/246|+|1/246-358/357|=

$$\frac { 1 } { 357 } - \frac { 1 } { 246 } | + | \frac { 1 } { 246 } - \frac { 358 } { 357 } | =$$

Evaluate

$$-\frac{1295}{1028772}\approx -0.001258782$$

Solution Steps

Least common multiple of 246 and 357 is 29274. Convert \frac{1}{246} and \frac{358}{357} to fractions with denominator 29274.

$$\frac{1}{357}-\frac{1}{246}||\frac{119}{29274}-\frac{29356}{29274}||$$

Since \frac{119}{29274} and \frac{29356}{29274} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{357}-\frac{1}{246}||\frac{119-29356}{29274}||$$

Subtract 29356 from 119 to get -29237.

$$\frac{1}{357}-\frac{1}{246}||-\frac{29237}{29274}||$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{29237}{29274} is \frac{29237}{29274}.

$$\frac{1}{357}-\frac{1}{246}|\frac{29237}{29274}|$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of \frac{29237}{29274} is \frac{29237}{29274}.

$$\frac{1}{357}-\frac{1}{246}\times \frac{29237}{29274}$$

Multiply \frac{1}{246} times \frac{29237}{29274} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{357}-\frac{1\times 29237}{246\times 29274}$$

Do the multiplications in the fraction \frac{1\times 29237}{246\times 29274}.

$$\frac{1}{357}-\frac{29237}{7201404}$$

Least common multiple of 357 and 7201404 is 7201404. Convert \frac{1}{357} and \frac{29237}{7201404} to fractions with denominator 7201404.

$$\frac{20172}{7201404}-\frac{29237}{7201404}$$

Since \frac{20172}{7201404} and \frac{29237}{7201404} have the same denominator, subtract them by subtracting their numerators.

$$\frac{20172-29237}{7201404}$$

Subtract 29237 from 20172 to get -9065.

$$\frac{-9065}{7201404}$$

Reduce the fraction \frac{-9065}{7201404} to lowest terms by extracting and canceling out 7.

$$-\frac{1295}{1028772}$$

Factor

$$-\frac{1295}{1028772} = -0.0012587823152263086$$