Basic Math Examples

$6 a - \frac{3}{8} a + 2 + \frac{1}{4} - \frac{3}{4} a$

Step 1

Combine $a$ and $\frac{3}{8}$ .

$6 a - \frac{a \cdot 3}{8} + 2 + \frac{1}{4} - \frac{3}{4} a$

Step 2

Move $3$ to the left of $a$ .

$6 a - \frac{3 \cdot a}{8} + 2 + \frac{1}{4} - \frac{3}{4} a$

Step 3

Multiply $3$ by $a$ .

$6 a - \frac{3 a}{8} + 2 + \frac{1}{4} - \frac{3}{4} a$

Step 4

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

$6 a - \frac{3 a}{8} + 2 + \frac{1}{4} - \frac{a \cdot 3}{4}$

Step 5

Move $3$ to the left of $a$ .

$6 a - \frac{3 a}{8} + 2 + \frac{1}{4} - \frac{3 \cdot a}{4}$

Step 6

Multiply $3$ by $a$ .

$6 a - \frac{3 a}{8} + 2 + \frac{1}{4} - \frac{3 a}{4}$

Step 7

To write $6 a$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$6 a \cdot \frac{8}{8} - \frac{3 a}{8} + 2 + \frac{1}{4} - \frac{3 a}{4}$

Step 8

Combine $6 a$ and $\frac{8}{8}$ .

$\frac{6 a \cdot 8}{8} - \frac{3 a}{8} + 2 + \frac{1}{4} - \frac{3 a}{4}$

Step 9

Combine the numerators over the common denominator.

$\frac{6 a \cdot 8 - 3 a}{8} + 2 + \frac{1}{4} - \frac{3 a}{4}$

Step 10

To write $2$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{6 a \cdot 8 - 3 a}{8} + 2 \cdot \frac{8}{8} + \frac{1}{4} - \frac{3 a}{4}$

Step 11

Combine $2$ and $\frac{8}{8}$ .

$\frac{6 a \cdot 8 - 3 a}{8} + \frac{2 \cdot 8}{8} + \frac{1}{4} - \frac{3 a}{4}$

Step 12

Combine the numerators over the common denominator.

$\frac{6 a \cdot 8 - 3 a + 2 \cdot 8}{8} + \frac{1}{4} - \frac{3 a}{4}$

Step 13

To write $\frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{6 a \cdot 8 - 3 a + 2 \cdot 8}{8} + \frac{1}{4} \cdot \frac{2}{2} - \frac{3 a}{4}$

Step 14

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 14.1

Multiply $\frac{1}{4}$ by $\frac{2}{2}$ .

$\frac{6 a \cdot 8 - 3 a + 2 \cdot 8}{8} + \frac{2}{4 \cdot 2} - \frac{3 a}{4}$

Step 14.2

Multiply $4$ by $2$ .

$\frac{6 a \cdot 8 - 3 a + 2 \cdot 8}{8} + \frac{2}{8} - \frac{3 a}{4}$

Step 15

Combine the numerators over the common denominator.

$\frac{6 a \cdot 8 - 3 a + 2 \cdot 8 + 2}{8} - \frac{3 a}{4}$

Step 16

To write $- \frac{3 a}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{6 a \cdot 8 - 3 a + 2 \cdot 8 + 2}{8} - \frac{3 a}{4} \cdot \frac{2}{2}$

Step 17

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 17.1

Multiply $\frac{3 a}{4}$ by $\frac{2}{2}$ .

$\frac{6 a \cdot 8 - 3 a + 2 \cdot 8 + 2}{8} - \frac{3 a \cdot 2}{4 \cdot 2}$

Step 17.2

Multiply $4$ by $2$ .

$\frac{6 a \cdot 8 - 3 a + 2 \cdot 8 + 2}{8} - \frac{3 a \cdot 2}{8}$

Step 18

Combine the numerators over the common denominator.

$\frac{6 a \cdot 8 - 3 a + 2 \cdot 8 + 2 - 3 a \cdot 2}{8}$

Step 19

Reorder terms.

$\frac{- 3 a + 6 \cdot 8 a - 3 \cdot 2 a + 2 \cdot 8 + 2}{8}$

Step 20

Rewrite $\frac{- 3 a + 6 \cdot 8 a - 3 \cdot 2 a + 2 \cdot 8 + 2}{8}$ in a factored form.

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Step 20.1

Multiply $6$ by $8$ .

$\frac{- 3 a + 48 a - 3 \cdot 2 a + 2 \cdot 8 + 2}{8}$

Step 20.2

Multiply $- 3$ by $2$ .

$\frac{- 3 a + 48 a - 6 a + 2 \cdot 8 + 2}{8}$

Step 20.3

Multiply $2$ by $8$ .

$\frac{- 3 a + 48 a - 6 a + 16 + 2}{8}$

Step 20.4

Add $- 3 a$ and $48 a$ .

$\frac{45 a - 6 a + 16 + 2}{8}$

Step 20.5

Subtract $6 a$ from $45 a$ .

$\frac{39 a + 16 + 2}{8}$

Step 20.6

Add $16$ and $2$ .

$\frac{39 a + 18}{8}$

Step 20.7

Factor $3$ out of $39 a + 18$ .

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Step 20.7.1

Factor $3$ out of $39 a$ .

$\frac{3 (13 a) + 18}{8}$

Step 20.7.2

Factor $3$ out of $18$ .

$\frac{3 (13 a) + 3 (6)}{8}$

Step 20.7.3

Factor $3$ out of $3 (13 a) + 3 (6)$ .

$\frac{3 (13 a + 6)}{8}$