Basic Math Examples

$\frac{3}{4} y + 16 y - \frac{1}{3} y$

Step 1

Simplify each term.

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Step 1.1

Combine $\frac{3}{4}$ and $y$ .

$\frac{3 y}{4} + 16 y - \frac{1}{3} y$

Step 1.2

Combine $y$ and $\frac{1}{3}$ .

$\frac{3 y}{4} + 16 y - \frac{y}{3}$

Step 2

Find the common denominator.

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Step 2.1

Multiply $\frac{3 y}{4}$ by $\frac{3}{3}$ .

$\frac{3 y}{4} \cdot \frac{3}{3} + 16 y - \frac{y}{3}$

Step 2.2

Multiply $\frac{3 y}{4}$ by $\frac{3}{3}$ .

$\frac{3 y \cdot 3}{4 \cdot 3} + 16 y - \frac{y}{3}$

Step 2.3

Write $16 y$ as a fraction with denominator $1$ .

$\frac{3 y \cdot 3}{4 \cdot 3} + \frac{16 y}{1} - \frac{y}{3}$

Step 2.4

Multiply $\frac{16 y}{1}$ by $\frac{12}{12}$ .

$\frac{3 y \cdot 3}{4 \cdot 3} + \frac{16 y}{1} \cdot \frac{12}{12} - \frac{y}{3}$

Step 2.5

Multiply $\frac{16 y}{1}$ by $\frac{12}{12}$ .

$\frac{3 y \cdot 3}{4 \cdot 3} + \frac{16 y \cdot 12}{12} - \frac{y}{3}$

Step 2.6

Multiply $\frac{y}{3}$ by $\frac{4}{4}$ .

$\frac{3 y \cdot 3}{4 \cdot 3} + \frac{16 y \cdot 12}{12} - (\frac{y}{3} \cdot \frac{4}{4})$

Step 2.7

Multiply $\frac{y}{3}$ by $\frac{4}{4}$ .

$\frac{3 y \cdot 3}{4 \cdot 3} + \frac{16 y \cdot 12}{12} - \frac{y \cdot 4}{3 \cdot 4}$

Step 2.8

Reorder the factors of $4 \cdot 3$ .

$\frac{3 y \cdot 3}{3 \cdot 4} + \frac{16 y \cdot 12}{12} - \frac{y \cdot 4}{3 \cdot 4}$

Step 2.9

Multiply $3$ by $4$ .

$\frac{3 y \cdot 3}{12} + \frac{16 y \cdot 12}{12} - \frac{y \cdot 4}{3 \cdot 4}$

Step 2.10

Multiply $3$ by $4$ .

$\frac{3 y \cdot 3}{12} + \frac{16 y \cdot 12}{12} - \frac{y \cdot 4}{12}$

Step 3

Combine the numerators over the common denominator.

$\frac{3 y \cdot 3 + 16 y \cdot 12 - y \cdot 4}{12}$

Step 4

Simplify each term.

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Step 4.1

Multiply $3$ by $3$ .

$\frac{9 y + 16 y \cdot 12 - y \cdot 4}{12}$

Step 4.2

Multiply $12$ by $16$ .

$\frac{9 y + 192 y - y \cdot 4}{12}$

Step 4.3

Multiply $4$ by $- 1$ .

$\frac{9 y + 192 y - 4 y}{12}$

Step 5

Simplify by adding terms.

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Step 5.1

Add $9 y$ and $192 y$ .

$\frac{201 y - 4 y}{12}$

Step 5.2

Subtract $4 y$ from $201 y$ .

$\frac{197 y}{12}$