Basic Math Examples

$\frac{7 y}{5} + \frac{19 y}{6} - \frac{1}{12}$

Step 1

Find the common denominator.

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Step 1.1

Multiply $\frac{7 y}{5}$ by $\frac{12}{12}$ .

$\frac{7 y}{5} \cdot \frac{12}{12} + \frac{19 y}{6} - \frac{1}{12}$

Step 1.2

Multiply $\frac{7 y}{5}$ by $\frac{12}{12}$ .

$\frac{7 y \cdot 12}{5 \cdot 12} + \frac{19 y}{6} - \frac{1}{12}$

Step 1.3

Multiply $\frac{19 y}{6}$ by $\frac{10}{10}$ .

$\frac{7 y \cdot 12}{5 \cdot 12} + \frac{19 y}{6} \cdot \frac{10}{10} - \frac{1}{12}$

Step 1.4

Multiply $\frac{19 y}{6}$ by $\frac{10}{10}$ .

$\frac{7 y \cdot 12}{5 \cdot 12} + \frac{19 y \cdot 10}{6 \cdot 10} - \frac{1}{12}$

Step 1.5

Multiply $\frac{1}{12}$ by $\frac{5}{5}$ .

$\frac{7 y \cdot 12}{5 \cdot 12} + \frac{19 y \cdot 10}{6 \cdot 10} - (\frac{1}{12} \cdot \frac{5}{5})$

Step 1.6

Multiply $\frac{1}{12}$ by $\frac{5}{5}$ .

$\frac{7 y \cdot 12}{5 \cdot 12} + \frac{19 y \cdot 10}{6 \cdot 10} - \frac{5}{12 \cdot 5}$

Step 1.7

Multiply $5$ by $12$ .

$\frac{7 y \cdot 12}{60} + \frac{19 y \cdot 10}{6 \cdot 10} - \frac{5}{12 \cdot 5}$

Step 1.8

Multiply $6$ by $10$ .

$\frac{7 y \cdot 12}{60} + \frac{19 y \cdot 10}{60} - \frac{5}{12 \cdot 5}$

Step 1.9

Reorder the factors of $12 \cdot 5$ .

$\frac{7 y \cdot 12}{60} + \frac{19 y \cdot 10}{60} - \frac{5}{5 \cdot 12}$

Step 1.10

Multiply $5$ by $12$ .

$\frac{7 y \cdot 12}{60} + \frac{19 y \cdot 10}{60} - \frac{5}{60}$

Step 2

Combine the numerators over the common denominator.

$\frac{7 y \cdot 12 + 19 y \cdot 10 - 5}{60}$

Step 3

Simplify each term.

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Step 3.1

Multiply $12$ by $7$ .

$\frac{84 y + 19 y \cdot 10 - 5}{60}$

Step 3.2

Multiply $10$ by $19$ .

$\frac{84 y + 190 y - 5}{60}$

Step 4

Add $84 y$ and $190 y$ .

$\frac{274 y - 5}{60}$