Basic Math Examples

$\frac{2 - 8 y}{21} - \frac{2 - 7 y}{27}$

Step 1

Factor $2$ out of $2 - 8 y$ .

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Step 1.1

Factor $2$ out of $2$ .

$\frac{2 (1) - 8 y}{21} - \frac{2 - 7 y}{27}$

Step 1.2

Factor $2$ out of $- 8 y$ .

$\frac{2 (1) + 2 (- 4 y)}{21} - \frac{2 - 7 y}{27}$

Step 1.3

Factor $2$ out of $2 (1) + 2 (- 4 y)$ .

$\frac{2 (1 - 4 y)}{21} - \frac{2 - 7 y}{27}$

Step 2

To write $\frac{2 (1 - 4 y)}{21}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{2 (1 - 4 y)}{21} \cdot \frac{9}{9} - \frac{2 - 7 y}{27}$

Step 3

To write $- \frac{2 - 7 y}{27}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{2 (1 - 4 y)}{21} \cdot \frac{9}{9} - \frac{2 - 7 y}{27} \cdot \frac{7}{7}$

Step 4

Write each expression with a common denominator of $189$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{2 (1 - 4 y)}{21}$ by $\frac{9}{9}$ .

$\frac{2 (1 - 4 y) \cdot 9}{21 \cdot 9} - \frac{2 - 7 y}{27} \cdot \frac{7}{7}$

Step 4.2

Multiply $21$ by $9$ .

$\frac{2 (1 - 4 y) \cdot 9}{189} - \frac{2 - 7 y}{27} \cdot \frac{7}{7}$

Step 4.3

Multiply $\frac{2 - 7 y}{27}$ by $\frac{7}{7}$ .

$\frac{2 (1 - 4 y) \cdot 9}{189} - \frac{(2 - 7 y) \cdot 7}{27 \cdot 7}$

Step 4.4

Multiply $27$ by $7$ .

$\frac{2 (1 - 4 y) \cdot 9}{189} - \frac{(2 - 7 y) \cdot 7}{189}$

Step 5

Combine the numerators over the common denominator.

$\frac{2 (1 - 4 y) \cdot 9 - (2 - 7 y) \cdot 7}{189}$

Step 6

Simplify the numerator.

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Step 6.1

Apply the distributive property.

$\frac{(2 \cdot 1 + 2 (- 4 y)) \cdot 9 - (2 - 7 y) \cdot 7}{189}$

Step 6.2

Multiply $2$ by $1$ .

$\frac{(2 + 2 (- 4 y)) \cdot 9 - (2 - 7 y) \cdot 7}{189}$

Step 6.3

Multiply $- 4$ by $2$ .

$\frac{(2 - 8 y) \cdot 9 - (2 - 7 y) \cdot 7}{189}$

Step 6.4

Apply the distributive property.

$\frac{2 \cdot 9 - 8 y \cdot 9 - (2 - 7 y) \cdot 7}{189}$

Step 6.5

Multiply $2$ by $9$ .

$\frac{18 - 8 y \cdot 9 - (2 - 7 y) \cdot 7}{189}$

Step 6.6

Multiply $9$ by $- 8$ .

$\frac{18 - 72 y - (2 - 7 y) \cdot 7}{189}$

Step 6.7

Apply the distributive property.

$\frac{18 - 72 y + (- 1 \cdot 2 - (- 7 y)) \cdot 7}{189}$

Step 6.8

Multiply $- 1$ by $2$ .

$\frac{18 - 72 y + (- 2 - (- 7 y)) \cdot 7}{189}$

Step 6.9

Multiply $- 7$ by $- 1$ .

$\frac{18 - 72 y + (- 2 + 7 y) \cdot 7}{189}$

Step 6.10

Apply the distributive property.

$\frac{18 - 72 y - 2 \cdot 7 + 7 y \cdot 7}{189}$

Step 6.11

Multiply $- 2$ by $7$ .

$\frac{18 - 72 y - 14 + 7 y \cdot 7}{189}$

Step 6.12

Multiply $7$ by $7$ .

$\frac{18 - 72 y - 14 + 49 y}{189}$

Step 6.13

Subtract $14$ from $18$ .

$\frac{- 72 y + 4 + 49 y}{189}$

Step 6.14

Add $- 72 y$ and $49 y$ .

$\frac{- 23 y + 4}{189}$

Step 7

Simplify with factoring out.

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Step 7.1

Factor $- 1$ out of $- 23 y$ .

$\frac{- (23 y) + 4}{189}$

Step 7.2

Rewrite $4$ as $- 1 (- 4)$ .

$\frac{- (23 y) - 1 (- 4)}{189}$

Step 7.3

Factor $- 1$ out of $- (23 y) - 1 (- 4)$ .

$\frac{- (23 y - 4)}{189}$

Step 7.4

Simplify the expression.

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Step 7.4.1

Rewrite $- (23 y - 4)$ as $- 1 (23 y - 4)$ .

$\frac{- 1 (23 y - 4)}{189}$

Step 7.4.2

Move the negative in front of the fraction.

$- \frac{23 y - 4}{189}$