Pre-Algebra Examples

$\frac{1}{5} \cdot (16 y - 2) + \frac{1}{20} \cdot (16 y + 21)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$\frac{1}{5} (16 y) + \frac{1}{5} \cdot - 2 + \frac{1}{20} \cdot (16 y + 21)$

Step 1.2

Multiply $\frac{1}{5} (16 y)$ .

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Step 1.2.1

Combine $16$ and $\frac{1}{5}$ .

$\frac{16}{5} y + \frac{1}{5} \cdot - 2 + \frac{1}{20} \cdot (16 y + 21)$

Step 1.2.2

Combine $\frac{16}{5}$ and $y$ .

$\frac{16 y}{5} + \frac{1}{5} \cdot - 2 + \frac{1}{20} \cdot (16 y + 21)$

Step 1.3

Combine $\frac{1}{5}$ and $- 2$ .

$\frac{16 y}{5} + \frac{- 2}{5} + \frac{1}{20} \cdot (16 y + 21)$

Step 1.4

Move the negative in front of the fraction.

$\frac{16 y}{5} - \frac{2}{5} + \frac{1}{20} \cdot (16 y + 21)$

Step 1.5

Apply the distributive property.

$\frac{16 y}{5} - \frac{2}{5} + \frac{1}{20} (16 y) + \frac{1}{20} \cdot 21$

Step 1.6

Cancel the common factor of $4$ .

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Step 1.6.1

Factor $4$ out of $20$ .

$\frac{16 y}{5} - \frac{2}{5} + \frac{1}{4 (5)} (16 y) + \frac{1}{20} \cdot 21$

Step 1.6.2

Factor $4$ out of $16 y$ .

$\frac{16 y}{5} - \frac{2}{5} + \frac{1}{4 (5)} (4 (4 y)) + \frac{1}{20} \cdot 21$

Step 1.6.3

Cancel the common factor.

$\frac{16 y}{5} - \frac{2}{5} + \frac{1}{4 \cdot 5} (4 (4 y)) + \frac{1}{20} \cdot 21$

Step 1.6.4

Rewrite the expression.

$\frac{16 y}{5} - \frac{2}{5} + \frac{1}{5} (4 y) + \frac{1}{20} \cdot 21$

Step 1.7

Combine $4$ and $\frac{1}{5}$ .

$\frac{16 y}{5} - \frac{2}{5} + \frac{4}{5} y + \frac{1}{20} \cdot 21$

Step 1.8

Combine $\frac{4}{5}$ and $y$ .

$\frac{16 y}{5} - \frac{2}{5} + \frac{4 y}{5} + \frac{1}{20} \cdot 21$

Step 1.9

Combine $\frac{1}{20}$ and $21$ .

$\frac{16 y}{5} - \frac{2}{5} + \frac{4 y}{5} + \frac{21}{20}$

Step 2

Simplify terms.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{16 y - 2 + 4 y}{5} + \frac{21}{20}$

Step 2.2

Add $16 y$ and $4 y$ .

$\frac{20 y - 2}{5} + \frac{21}{20}$

Step 2.3

Factor $2$ out of $20 y - 2$ .

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Step 2.3.1

Factor $2$ out of $20 y$ .

$\frac{2 (10 y) - 2}{5} + \frac{21}{20}$

Step 2.3.2

Factor $2$ out of $- 2$ .

$\frac{2 (10 y) + 2 (- 1)}{5} + \frac{21}{20}$

Step 2.3.3

Factor $2$ out of $2 (10 y) + 2 (- 1)$ .

$\frac{2 (10 y - 1)}{5} + \frac{21}{20}$

Step 3

To write $\frac{2 (10 y - 1)}{5}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{2 (10 y - 1)}{5} \cdot \frac{4}{4} + \frac{21}{20}$

Step 4

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{2 (10 y - 1)}{5}$ by $\frac{4}{4}$ .

$\frac{2 (10 y - 1) \cdot 4}{5 \cdot 4} + \frac{21}{20}$

Step 4.2

Multiply $5$ by $4$ .

$\frac{2 (10 y - 1) \cdot 4}{20} + \frac{21}{20}$

Step 5

Combine the numerators over the common denominator.

$\frac{2 (10 y - 1) \cdot 4 + 21}{20}$

Step 6

Simplify the numerator.

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Step 6.1

Apply the distributive property.

$\frac{(2 (10 y) + 2 \cdot - 1) \cdot 4 + 21}{20}$

Step 6.2

Multiply $10$ by $2$ .

$\frac{(20 y + 2 \cdot - 1) \cdot 4 + 21}{20}$

Step 6.3

Multiply $2$ by $- 1$ .

$\frac{(20 y - 2) \cdot 4 + 21}{20}$

Step 6.4

Apply the distributive property.

$\frac{20 y \cdot 4 - 2 \cdot 4 + 21}{20}$

Step 6.5

Multiply $4$ by $20$ .

$\frac{80 y - 2 \cdot 4 + 21}{20}$

Step 6.6

Multiply $- 2$ by $4$ .

$\frac{80 y - 8 + 21}{20}$

Step 6.7

Add $- 8$ and $21$ .

$\frac{80 y + 13}{20}$