Algebra Examples

$2 (\frac{2}{3}) - 5 (\frac{1}{4})$

Step 1

Simplify each term.

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Step 1.1

Multiply $2 (\frac{2}{3})$ .

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Step 1.1.1

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

$\frac{2 \cdot 2}{3} - 5 (\frac{1}{4})$

Step 1.1.2

Multiply $2$ by $2$ .

$\frac{4}{3} - 5 (\frac{1}{4})$

Step 1.2

Combine $- 5$ and $\frac{1}{4}$ .

$\frac{4}{3} + \frac{- 5}{4}$

Step 1.3

Move the negative in front of the fraction.

$\frac{4}{3} - \frac{5}{4}$

Step 2

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

$\frac{4}{3} \cdot \frac{4}{4} - \frac{5}{4}$

Step 3

To write $- \frac{5}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{4}{3} \cdot \frac{4}{4} - \frac{5}{4} \cdot \frac{3}{3}$

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

$\frac{4 \cdot 4}{3 \cdot 4} - \frac{5}{4} \cdot \frac{3}{3}$

Step 4.2

Multiply $3$ by $4$ .

$\frac{4 \cdot 4}{12} - \frac{5}{4} \cdot \frac{3}{3}$

Step 4.3

Multiply $\frac{5}{4}$ by $\frac{3}{3}$ .

$\frac{4 \cdot 4}{12} - \frac{5 \cdot 3}{4 \cdot 3}$

Step 4.4

Multiply $4$ by $3$ .

$\frac{4 \cdot 4}{12} - \frac{5 \cdot 3}{12}$

Step 5

Combine the numerators over the common denominator.

$\frac{4 \cdot 4 - 5 \cdot 3}{12}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $4$ by $4$ .

$\frac{16 - 5 \cdot 3}{12}$

Step 6.2

Multiply $- 5$ by $3$ .

$\frac{16 - 15}{12}$

Step 6.3

Subtract $15$ from $16$ .

$\frac{1}{12}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{12}$

Decimal Form:

$0.08\overline{3}$