Algebra Examples

$\frac{1}{4} b + \frac{4}{3} b + \frac{7}{12}$

Step 1

Simplify each term.

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Step 1.1

Combine $\frac{1}{4}$ and $b$ .

$\frac{b}{4} + \frac{4}{3} b + \frac{7}{12}$

Step 1.2

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

$\frac{b}{4} + \frac{4 b}{3} + \frac{7}{12}$

Step 2

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

$\frac{b}{4} \cdot \frac{3}{3} + \frac{4 b}{3} + \frac{7}{12}$

Step 3

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

$\frac{b}{4} \cdot \frac{3}{3} + \frac{4 b}{3} \cdot \frac{4}{4} + \frac{7}{12}$

Step 4

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

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

$\frac{b \cdot 3}{4 \cdot 3} + \frac{4 b}{3} \cdot \frac{4}{4} + \frac{7}{12}$

Step 4.2

Multiply $4$ by $3$ .

$\frac{b \cdot 3}{12} + \frac{4 b}{3} \cdot \frac{4}{4} + \frac{7}{12}$

Step 4.3

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

$\frac{b \cdot 3}{12} + \frac{4 b \cdot 4}{3 \cdot 4} + \frac{7}{12}$

Step 4.4

Multiply $3$ by $4$ .

$\frac{b \cdot 3}{12} + \frac{4 b \cdot 4}{12} + \frac{7}{12}$

Step 5

Simplify terms.

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Step 5.1

Combine the numerators over the common denominator.

$\frac{b \cdot 3 + 4 b \cdot 4}{12} + \frac{7}{12}$

Step 5.2

Combine the numerators over the common denominator.

$\frac{b \cdot 3 + 4 b \cdot 4 + 7}{12}$

Step 6

Simplify each term.

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Step 6.1

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

$\frac{3 \cdot b + 4 b \cdot 4 + 7}{12}$

Step 6.2

Multiply $4$ by $4$ .

$\frac{3 b + 16 b + 7}{12}$

Step 7

Add $3 b$ and $16 b$ .

$\frac{19 b + 7}{12}$