Basic Math Examples

$\frac{3 - 7 a}{24} - \frac{4 a - 7}{12} + \frac{3 a + 6}{4}$

Step 1

To write $- \frac{4 a - 7}{12}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3 - 7 a}{24} - \frac{4 a - 7}{12} \cdot \frac{2}{2} + \frac{3 a + 6}{4}$

Step 2

Write each expression with a common denominator of $24$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.1

Multiply $\frac{4 a - 7}{12}$ by $\frac{2}{2}$ .

$\frac{3 - 7 a}{24} - \frac{(4 a - 7) \cdot 2}{12 \cdot 2} + \frac{3 a + 6}{4}$

Step 2.2

Multiply $12$ by $2$ .

$\frac{3 - 7 a}{24} - \frac{(4 a - 7) \cdot 2}{24} + \frac{3 a + 6}{4}$

Step 3

Combine the numerators over the common denominator.

$\frac{3 - 7 a - (4 a - 7) \cdot 2}{24} + \frac{3 a + 6}{4}$

Step 4

To write $\frac{3 a + 6}{4}$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{3 - 7 a - (4 a - 7) \cdot 2}{24} + \frac{3 a + 6}{4} \cdot \frac{6}{6}$

Step 5

Write each expression with a common denominator of $24$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.1

Multiply $\frac{3 a + 6}{4}$ by $\frac{6}{6}$ .

$\frac{3 - 7 a - (4 a - 7) \cdot 2}{24} + \frac{(3 a + 6) \cdot 6}{4 \cdot 6}$

Step 5.2

Multiply $4$ by $6$ .

$\frac{3 - 7 a - (4 a - 7) \cdot 2}{24} + \frac{(3 a + 6) \cdot 6}{24}$

Step 6

Combine the numerators over the common denominator.

$\frac{3 - 7 a - (4 a - 7) \cdot 2 + (3 a + 6) \cdot 6}{24}$

Step 7

Reorder terms.

$\frac{- 7 a - 1 \cdot 2 (4 a - 7) + 6 (3 a + 6) + 3}{24}$

Step 8

Rewrite $\frac{- 7 a - 1 \cdot 2 (4 a - 7) + 6 (3 a + 6) + 3}{24}$ in a factored form.

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Step 8.1

Multiply $- 1$ by $2$ .

$\frac{- 7 a - 2 (4 a - 7) + 6 (3 a + 6) + 3}{24}$

Step 8.2

Apply the distributive property.

$\frac{- 7 a - 2 (4 a) - 2 \cdot - 7 + 6 (3 a + 6) + 3}{24}$

Step 8.3

Multiply $4$ by $- 2$ .

$\frac{- 7 a - 8 a - 2 \cdot - 7 + 6 (3 a + 6) + 3}{24}$

Step 8.4

Multiply $- 2$ by $- 7$ .

$\frac{- 7 a - 8 a + 14 + 6 (3 a + 6) + 3}{24}$

Step 8.5

Apply the distributive property.

$\frac{- 7 a - 8 a + 14 + 6 (3 a) + 6 \cdot 6 + 3}{24}$

Step 8.6

Multiply $3$ by $6$ .

$\frac{- 7 a - 8 a + 14 + 18 a + 6 \cdot 6 + 3}{24}$

Step 8.7

Multiply $6$ by $6$ .

$\frac{- 7 a - 8 a + 14 + 18 a + 36 + 3}{24}$

Step 8.8

Subtract $8 a$ from $- 7 a$ .

$\frac{- 15 a + 14 + 18 a + 36 + 3}{24}$

Step 8.9

Add $- 15 a$ and $18 a$ .

$\frac{3 a + 14 + 36 + 3}{24}$

Step 8.10

Add $14$ and $36$ .

$\frac{3 a + 50 + 3}{24}$

Step 8.11

Add $50$ and $3$ .

$\frac{3 a + 53}{24}$