Basic Math Examples

$\frac{22}{25} b - \frac{3}{5} + \frac{4}{15} b - \frac{1}{3}$

Step 1

Simplify each term.

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Step 1.1

Combine $\frac{22}{25}$ and $b$ .

$\frac{22 b}{25} - \frac{3}{5} + \frac{4}{15} b - \frac{1}{3}$

Step 1.2

Combine $\frac{4}{15}$ and $b$ .

$\frac{22 b}{25} - \frac{3}{5} + \frac{4 b}{15} - \frac{1}{3}$

Step 2

To write $\frac{22 b}{25}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{22 b}{25} \cdot \frac{3}{3} + \frac{4 b}{15} - \frac{3}{5} - \frac{1}{3}$

Step 3

To write $\frac{4 b}{15}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{22 b}{25} \cdot \frac{3}{3} + \frac{4 b}{15} \cdot \frac{5}{5} - \frac{3}{5} - \frac{1}{3}$

Step 4

Write each expression with a common denominator of $75$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{22 b}{25}$ by $\frac{3}{3}$ .

$\frac{22 b \cdot 3}{25 \cdot 3} + \frac{4 b}{15} \cdot \frac{5}{5} - \frac{3}{5} - \frac{1}{3}$

Step 4.2

Multiply $25$ by $3$ .

$\frac{22 b \cdot 3}{75} + \frac{4 b}{15} \cdot \frac{5}{5} - \frac{3}{5} - \frac{1}{3}$

Step 4.3

Multiply $\frac{4 b}{15}$ by $\frac{5}{5}$ .

$\frac{22 b \cdot 3}{75} + \frac{4 b \cdot 5}{15 \cdot 5} - \frac{3}{5} - \frac{1}{3}$

Step 4.4

Multiply $15$ by $5$ .

$\frac{22 b \cdot 3}{75} + \frac{4 b \cdot 5}{75} - \frac{3}{5} - \frac{1}{3}$

Step 5

Combine the numerators over the common denominator.

$\frac{22 b \cdot 3 + 4 b \cdot 5}{75} - \frac{3}{5} - \frac{1}{3}$

Step 6

Find the common denominator.

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Step 6.1

Multiply $\frac{3}{5}$ by $\frac{15}{15}$ .

$\frac{22 b \cdot 3 + 4 b \cdot 5}{75} - (\frac{3}{5} \cdot \frac{15}{15}) - \frac{1}{3}$

Step 6.2

Multiply $\frac{3}{5}$ by $\frac{15}{15}$ .

$\frac{22 b \cdot 3 + 4 b \cdot 5}{75} - \frac{3 \cdot 15}{5 \cdot 15} - \frac{1}{3}$

Step 6.3

Multiply $\frac{1}{3}$ by $\frac{25}{25}$ .

$\frac{22 b \cdot 3 + 4 b \cdot 5}{75} - \frac{3 \cdot 15}{5 \cdot 15} - (\frac{1}{3} \cdot \frac{25}{25})$

Step 6.4

Multiply $\frac{1}{3}$ by $\frac{25}{25}$ .

$\frac{22 b \cdot 3 + 4 b \cdot 5}{75} - \frac{3 \cdot 15}{5 \cdot 15} - \frac{25}{3 \cdot 25}$

Step 6.5

Multiply $5$ by $15$ .

$\frac{22 b \cdot 3 + 4 b \cdot 5}{75} - \frac{3 \cdot 15}{75} - \frac{25}{3 \cdot 25}$

Step 6.6

Multiply $3$ by $25$ .

$\frac{22 b \cdot 3 + 4 b \cdot 5}{75} - \frac{3 \cdot 15}{75} - \frac{25}{75}$

Step 7

Combine the numerators over the common denominator.

$\frac{22 b \cdot 3 + 4 b \cdot 5 - 3 \cdot 15 - 25}{75}$

Step 8

Simplify each term.

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Step 8.1

Multiply $3$ by $22$ .

$\frac{66 b + 4 b \cdot 5 - 3 \cdot 15 - 25}{75}$

Step 8.2

Multiply $5$ by $4$ .

$\frac{66 b + 20 b - 3 \cdot 15 - 25}{75}$

Step 8.3

Multiply $- 3$ by $15$ .

$\frac{66 b + 20 b - 45 - 25}{75}$

Step 9

Simplify terms.

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Step 9.1

Add $66 b$ and $20 b$ .

$\frac{86 b - 45 - 25}{75}$

Step 9.2

Subtract $25$ from $- 45$ .

$\frac{86 b - 70}{75}$

Step 9.3

Factor $2$ out of $86 b - 70$ .

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Step 9.3.1

Factor $2$ out of $86 b$ .

$\frac{2 (43 b) - 70}{75}$

Step 9.3.2

Factor $2$ out of $- 70$ .

$\frac{2 (43 b) + 2 (- 35)}{75}$

Step 9.3.3

Factor $2$ out of $2 (43 b) + 2 (- 35)$ .

$\frac{2 (43 b - 35)}{75}$