Basic Math Examples

$\frac{7 y}{15} + \frac{y}{4} - \frac{15}{8}$

Step 1

Find the common denominator.

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Step 1.1

Multiply $\frac{7 y}{15}$ by $\frac{8}{8}$ .

$\frac{7 y}{15} \cdot \frac{8}{8} + \frac{y}{4} - \frac{15}{8}$

Step 1.2

Multiply $\frac{7 y}{15}$ by $\frac{8}{8}$ .

$\frac{7 y \cdot 8}{15 \cdot 8} + \frac{y}{4} - \frac{15}{8}$

Step 1.3

Multiply $\frac{y}{4}$ by $\frac{30}{30}$ .

$\frac{7 y \cdot 8}{15 \cdot 8} + \frac{y}{4} \cdot \frac{30}{30} - \frac{15}{8}$

Step 1.4

Multiply $\frac{y}{4}$ by $\frac{30}{30}$ .

$\frac{7 y \cdot 8}{15 \cdot 8} + \frac{y \cdot 30}{4 \cdot 30} - \frac{15}{8}$

Step 1.5

Multiply $\frac{15}{8}$ by $\frac{15}{15}$ .

$\frac{7 y \cdot 8}{15 \cdot 8} + \frac{y \cdot 30}{4 \cdot 30} - (\frac{15}{8} \cdot \frac{15}{15})$

Step 1.6

Multiply $\frac{15}{8}$ by $\frac{15}{15}$ .

$\frac{7 y \cdot 8}{15 \cdot 8} + \frac{y \cdot 30}{4 \cdot 30} - \frac{15 \cdot 15}{8 \cdot 15}$

Step 1.7

Reorder the factors of $15 \cdot 8$ .

$\frac{7 y \cdot 8}{8 \cdot 15} + \frac{y \cdot 30}{4 \cdot 30} - \frac{15 \cdot 15}{8 \cdot 15}$

Step 1.8

Multiply $8$ by $15$ .

$\frac{7 y \cdot 8}{120} + \frac{y \cdot 30}{4 \cdot 30} - \frac{15 \cdot 15}{8 \cdot 15}$

Step 1.9

Multiply $4$ by $30$ .

$\frac{7 y \cdot 8}{120} + \frac{y \cdot 30}{120} - \frac{15 \cdot 15}{8 \cdot 15}$

Step 1.10

Multiply $8$ by $15$ .

$\frac{7 y \cdot 8}{120} + \frac{y \cdot 30}{120} - \frac{15 \cdot 15}{120}$

Step 2

Combine the numerators over the common denominator.

$\frac{7 y \cdot 8 + y \cdot 30 - 15 \cdot 15}{120}$

Step 3

Simplify each term.

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Step 3.1

Multiply $8$ by $7$ .

$\frac{56 y + y \cdot 30 - 15 \cdot 15}{120}$

Step 3.2

Move $30$ to the left of $y$ .

$\frac{56 y + 30 \cdot y - 15 \cdot 15}{120}$

Step 3.3

Multiply $- 15$ by $15$ .

$\frac{56 y + 30 y - 225}{120}$

Step 4

Add $56 y$ and $30 y$ .

$\frac{86 y - 225}{120}$