Basic Math Examples

$\frac{r}{25} - \frac{1}{r} \div \frac{3}{25} - \frac{3}{5 r}$

Step 1

Simplify each term.

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Step 1.1

To divide by a fraction, multiply by its reciprocal.

$\frac{r}{25} - (\frac{1}{r} \cdot \frac{25}{3}) - \frac{3}{5 r}$

Step 1.2

Multiply $\frac{1}{r}$ by $\frac{25}{3}$ .

$\frac{r}{25} - \frac{25}{r \cdot 3} - \frac{3}{5 r}$

Step 1.3

Move $3$ to the left of $r$ .

$\frac{r}{25} - \frac{25}{3 r} - \frac{3}{5 r}$

Step 2

Find the common denominator.

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Step 2.1

Multiply $\frac{r}{25}$ by $\frac{3 r}{3 r}$ .

$\frac{r}{25} \cdot \frac{3 r}{3 r} - \frac{25}{3 r} - \frac{3}{5 r}$

Step 2.2

Multiply $\frac{r}{25}$ by $\frac{3 r}{3 r}$ .

$\frac{r (3 r)}{25 (3 r)} - \frac{25}{3 r} - \frac{3}{5 r}$

Step 2.3

Multiply $\frac{25}{3 r}$ by $\frac{25}{25}$ .

$\frac{r (3 r)}{25 (3 r)} - (\frac{25}{3 r} \cdot \frac{25}{25}) - \frac{3}{5 r}$

Step 2.4

Multiply $\frac{25}{3 r}$ by $\frac{25}{25}$ .

$\frac{r (3 r)}{25 (3 r)} - \frac{25 \cdot 25}{3 r \cdot 25} - \frac{3}{5 r}$

Step 2.5

Multiply $\frac{3}{5 r}$ by $\frac{15}{15}$ .

$\frac{r (3 r)}{25 (3 r)} - \frac{25 \cdot 25}{3 r \cdot 25} - (\frac{3}{5 r} \cdot \frac{15}{15})$

Step 2.6

Multiply $\frac{3}{5 r}$ by $\frac{15}{15}$ .

$\frac{r (3 r)}{25 (3 r)} - \frac{25 \cdot 25}{3 r \cdot 25} - \frac{3 \cdot 15}{5 r \cdot 15}$

Step 2.7

Reorder the factors of $25 (3 r)$ .

$\frac{r (3 r)}{3 \cdot 25 r} - \frac{25 \cdot 25}{3 r \cdot 25} - \frac{3 \cdot 15}{5 r \cdot 15}$

Step 2.8

Multiply $3$ by $25$ .

$\frac{r (3 r)}{75 r} - \frac{25 \cdot 25}{3 r \cdot 25} - \frac{3 \cdot 15}{5 r \cdot 15}$

Step 2.9

Reorder the factors of $3 r \cdot 25$ .

$\frac{r (3 r)}{75 r} - \frac{25 \cdot 25}{3 \cdot 25 r} - \frac{3 \cdot 15}{5 r \cdot 15}$

Step 2.10

Multiply $3$ by $25$ .

$\frac{r (3 r)}{75 r} - \frac{25 \cdot 25}{75 r} - \frac{3 \cdot 15}{5 r \cdot 15}$

Step 2.11

Reorder the factors of $5 r \cdot 15$ .

$\frac{r (3 r)}{75 r} - \frac{25 \cdot 25}{75 r} - \frac{3 \cdot 15}{5 \cdot 15 r}$

Step 2.12

Multiply $5$ by $15$ .

$\frac{r (3 r)}{75 r} - \frac{25 \cdot 25}{75 r} - \frac{3 \cdot 15}{75 r}$

Step 3

Combine the numerators over the common denominator.

$\frac{r (3 r) - 25 \cdot 25 - 3 \cdot 15}{75 r}$

Step 4

Simplify each term.

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Step 4.1

Rewrite using the commutative property of multiplication.

$\frac{3 r \cdot r - 25 \cdot 25 - 3 \cdot 15}{75 r}$

Step 4.2

Multiply $r$ by $r$ by adding the exponents.

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Step 4.2.1

Move $r$ .

$\frac{3 (r \cdot r) - 25 \cdot 25 - 3 \cdot 15}{75 r}$

Step 4.2.2

Multiply $r$ by $r$ .

$\frac{3 r^{2} - 25 \cdot 25 - 3 \cdot 15}{75 r}$

Step 4.3

Multiply $- 25$ by $25$ .

$\frac{3 r^{2} - 625 - 3 \cdot 15}{75 r}$

Step 4.4

Multiply $- 3$ by $15$ .

$\frac{3 r^{2} - 625 - 45}{75 r}$

Step 5

Subtract $45$ from $- 625$ .

$\frac{3 r^{2} - 670}{75 r}$