Basic Math Examples

$\frac{6}{8} - \frac{7}{10} \cdot (y + \frac{4}{9})$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $6$ and $8$ .

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Step 1.1.1

Factor $2$ out of $6$ .

$\frac{2 (3)}{8} - \frac{7}{10} \cdot (y + \frac{4}{9})$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $2$ out of $8$ .

$\frac{2 \cdot 3}{2 \cdot 4} - \frac{7}{10} \cdot (y + \frac{4}{9})$

Step 1.1.2.2

Cancel the common factor.

$\frac{2 \cdot 3}{2 \cdot 4} - \frac{7}{10} \cdot (y + \frac{4}{9})$

Step 1.1.2.3

Rewrite the expression.

$\frac{3}{4} - \frac{7}{10} \cdot (y + \frac{4}{9})$

Step 1.2

To write $y$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{3}{4} - \frac{7}{10} \cdot (y \cdot \frac{9}{9} + \frac{4}{9})$

Step 1.3

Combine $y$ and $\frac{9}{9}$ .

$\frac{3}{4} - \frac{7}{10} \cdot (\frac{y \cdot 9}{9} + \frac{4}{9})$

Step 1.4

Combine the numerators over the common denominator.

$\frac{3}{4} - \frac{7}{10} \cdot \frac{y \cdot 9 + 4}{9}$

Step 1.5

Move $9$ to the left of $y$ .

$\frac{3}{4} - \frac{7}{10} \cdot \frac{9 y + 4}{9}$

Step 1.6

Multiply $- \frac{7}{10} \cdot \frac{9 y + 4}{9}$ .

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Step 1.6.1

Multiply $\frac{9 y + 4}{9}$ by $\frac{7}{10}$ .

$\frac{3}{4} - \frac{(9 y + 4) \cdot 7}{9 \cdot 10}$

Step 1.6.2

Multiply $9$ by $10$ .

$\frac{3}{4} - \frac{(9 y + 4) \cdot 7}{90}$

Step 1.7

Move $7$ to the left of $9 y + 4$ .

$\frac{3}{4} - \frac{7 (9 y + 4)}{90}$

Step 2

To write $\frac{3}{4}$ as a fraction with a common denominator, multiply by $\frac{45}{45}$ .

$\frac{3}{4} \cdot \frac{45}{45} - \frac{7 (9 y + 4)}{90}$

Step 3

To write $- \frac{7 (9 y + 4)}{90}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3}{4} \cdot \frac{45}{45} - \frac{7 (9 y + 4)}{90} \cdot \frac{2}{2}$

Step 4

Write each expression with a common denominator of $180$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{3}{4}$ by $\frac{45}{45}$ .

$\frac{3 \cdot 45}{4 \cdot 45} - \frac{7 (9 y + 4)}{90} \cdot \frac{2}{2}$

Step 4.2

Multiply $4$ by $45$ .

$\frac{3 \cdot 45}{180} - \frac{7 (9 y + 4)}{90} \cdot \frac{2}{2}$

Step 4.3

Multiply $\frac{7 (9 y + 4)}{90}$ by $\frac{2}{2}$ .

$\frac{3 \cdot 45}{180} - \frac{7 (9 y + 4) \cdot 2}{90 \cdot 2}$

Step 4.4

Multiply $90$ by $2$ .

$\frac{3 \cdot 45}{180} - \frac{7 (9 y + 4) \cdot 2}{180}$

Step 5

Combine the numerators over the common denominator.

$\frac{3 \cdot 45 - 7 (9 y + 4) \cdot 2}{180}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $3$ by $45$ .

$\frac{135 - 7 (9 y + 4) \cdot 2}{180}$

Step 6.2

Apply the distributive property.

$\frac{135 + (- 7 (9 y) - 7 \cdot 4) \cdot 2}{180}$

Step 6.3

Multiply $9$ by $- 7$ .

$\frac{135 + (- 63 y - 7 \cdot 4) \cdot 2}{180}$

Step 6.4

Multiply $- 7$ by $4$ .

$\frac{135 + (- 63 y - 28) \cdot 2}{180}$

Step 6.5

Apply the distributive property.

$\frac{135 - 63 y \cdot 2 - 28 \cdot 2}{180}$

Step 6.6

Multiply $2$ by $- 63$ .

$\frac{135 - 126 y - 28 \cdot 2}{180}$

Step 6.7

Multiply $- 28$ by $2$ .

$\frac{135 - 126 y - 56}{180}$

Step 6.8

Subtract $56$ from $135$ .

$\frac{- 126 y + 79}{180}$

Step 7

Simplify with factoring out.

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Step 7.1

Factor $- 1$ out of $- 126 y$ .

$\frac{- (126 y) + 79}{180}$

Step 7.2

Rewrite $79$ as $- 1 (- 79)$ .

$\frac{- (126 y) - 1 (- 79)}{180}$

Step 7.3

Factor $- 1$ out of $- (126 y) - 1 (- 79)$ .

$\frac{- (126 y - 79)}{180}$

Step 7.4

Simplify the expression.

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Step 7.4.1

Rewrite $- (126 y - 79)$ as $- 1 (126 y - 79)$ .

$\frac{- 1 (126 y - 79)}{180}$

Step 7.4.2

Move the negative in front of the fraction.

$- \frac{126 y - 79}{180}$