Solve k/delta-k/5/frac{k{5}}*100

$$\frac { \frac { k } { \delta } - \frac { k } { 5 } } { \frac { k } { 5 } } \times 100$$

Evaluate

$$-100+\frac{500}{\delta }$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \delta and 5 is 5\delta . Multiply \frac{k}{\delta } times \frac{5}{5}. Multiply \frac{k}{5} times \frac{\delta }{\delta }.

$$\frac{\frac{5k}{5\delta }-\frac{k\delta }{5\delta }}{\frac{k}{5}}\times 100$$

Since \frac{5k}{5\delta } and \frac{k\delta }{5\delta } have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5k-k\delta }{5\delta }}{\frac{k}{5}}\times 100$$

Divide \frac{5k-k\delta }{5\delta } by \frac{k}{5} by multiplying \frac{5k-k\delta }{5\delta } by the reciprocal of \frac{k}{5}.

$$\frac{\left(5k-k\delta \right)\times 5}{5\delta k}\times 100$$

Cancel out 5 in both numerator and denominator.

$$\frac{-k\delta +5k}{k\delta }\times 100$$

Factor the expressions that are not already factored in \frac{-k\delta +5k}{k\delta }.

$$\frac{k\left(-\delta +5\right)}{k\delta }\times 100$$

Cancel out k in both numerator and denominator.

$$\frac{-\delta +5}{\delta }\times 100$$

Express \frac{-\delta +5}{\delta }\times 100 as a single fraction.

$$\frac{\left(-\delta +5\right)\times 100}{\delta }$$

Use the distributive property to multiply -\delta +5 by 100.

$$\frac{-100\delta +500}{\delta }$$

Expand

$$-100+\frac{500}{\delta }$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \delta and 5 is 5\delta . Multiply \frac{k}{\delta } times \frac{5}{5}. Multiply \frac{k}{5} times \frac{\delta }{\delta }.

$$\frac{\frac{5k}{5\delta }-\frac{k\delta }{5\delta }}{\frac{k}{5}}\times 100$$

Since \frac{5k}{5\delta } and \frac{k\delta }{5\delta } have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5k-k\delta }{5\delta }}{\frac{k}{5}}\times 100$$

Divide \frac{5k-k\delta }{5\delta } by \frac{k}{5} by multiplying \frac{5k-k\delta }{5\delta } by the reciprocal of \frac{k}{5}.

$$\frac{\left(5k-k\delta \right)\times 5}{5\delta k}\times 100$$

Cancel out 5 in both numerator and denominator.

$$\frac{-k\delta +5k}{k\delta }\times 100$$

Factor the expressions that are not already factored in \frac{-k\delta +5k}{k\delta }.

$$\frac{k\left(-\delta +5\right)}{k\delta }\times 100$$

Cancel out k in both numerator and denominator.

$$\frac{-\delta +5}{\delta }\times 100$$

Express \frac{-\delta +5}{\delta }\times 100 as a single fraction.

$$\frac{\left(-\delta +5\right)\times 100}{\delta }$$

Use the distributive property to multiply -\delta +5 by 100.

$$\frac{-100\delta +500}{\delta }$$