Basic Math Examples

$- \frac{3}{2} a - \frac{1}{8} b + \frac{7}{4} a + 2 b$

Step 1

Simplify each term.

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Step 1.1

Combine $a$ and $\frac{3}{2}$ .

$- \frac{a \cdot 3}{2} - \frac{1}{8} b + \frac{7}{4} a + 2 b$

Step 1.2

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

$- \frac{3 \cdot a}{2} - \frac{1}{8} b + \frac{7}{4} a + 2 b$

Step 1.3

Combine $b$ and $\frac{1}{8}$ .

$- \frac{3 a}{2} - \frac{b}{8} + \frac{7}{4} a + 2 b$

Step 1.4

Combine $\frac{7}{4}$ and $a$ .

$- \frac{3 a}{2} - \frac{b}{8} + \frac{7 a}{4} + 2 b$

Step 2

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

$- \frac{b}{8} - \frac{3 a}{2} \cdot \frac{2}{2} + \frac{7 a}{4} + 2 b$

Step 3

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

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

$- \frac{b}{8} - \frac{3 a \cdot 2}{2 \cdot 2} + \frac{7 a}{4} + 2 b$

Step 3.2

Multiply $2$ by $2$ .

$- \frac{b}{8} - \frac{3 a \cdot 2}{4} + \frac{7 a}{4} + 2 b$

Step 4

Combine the numerators over the common denominator.

$- \frac{b}{8} + \frac{- 3 a \cdot 2 + 7 a}{4} + 2 b$

Step 5

Simplify each term.

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Step 5.1

Simplify the numerator.

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Step 5.1.1

Factor $a$ out of $- 3 a \cdot 2 + 7 a$ .

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Step 5.1.1.1

Factor $a$ out of $- 3 a \cdot 2$ .

$- \frac{b}{8} + \frac{a (- 3 \cdot 2) + 7 a}{4} + 2 b$

Step 5.1.1.2

Factor $a$ out of $7 a$ .

$- \frac{b}{8} + \frac{a (- 3 \cdot 2) + a \cdot 7}{4} + 2 b$

Step 5.1.1.3

Factor $a$ out of $a (- 3 \cdot 2) + a \cdot 7$ .

$- \frac{b}{8} + \frac{a (- 3 \cdot 2 + 7)}{4} + 2 b$

Step 5.1.2

Multiply $- 3$ by $2$ .

$- \frac{b}{8} + \frac{a (- 6 + 7)}{4} + 2 b$

Step 5.1.3

Add $- 6$ and $7$ .

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

Step 5.2

Multiply $a$ by $1$ .

$- \frac{b}{8} + \frac{a}{4} + 2 b$

Step 6

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

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

Step 7

Simplify terms.

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Step 7.1

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

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

Step 7.2

Combine the numerators over the common denominator.

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

Step 8

Simplify each term.

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Step 8.1

Simplify the numerator.

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Step 8.1.1

Factor $b$ out of $- b + 2 b \cdot 8$ .

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Step 8.1.1.1

Factor $b$ out of $- b$ .

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

Step 8.1.1.2

Factor $b$ out of $2 b \cdot 8$ .

$\frac{a}{4} + \frac{b \cdot - 1 + b (2 \cdot 8)}{8}$

Step 8.1.1.3

Factor $b$ out of $b \cdot - 1 + b (2 \cdot 8)$ .

$\frac{a}{4} + \frac{b (- 1 + 2 \cdot 8)}{8}$

Step 8.1.2

Multiply $2$ by $8$ .

$\frac{a}{4} + \frac{b (- 1 + 16)}{8}$

Step 8.1.3

Add $- 1$ and $16$ .

$\frac{a}{4} + \frac{b \cdot 15}{8}$

Step 8.2

Move $15$ to the left of $b$ .

$\frac{a}{4} + \frac{15 b}{8}$