Basic Math Examples

$\frac{12}{15} - \frac{9}{12}$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $12$ and $15$ .

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Step 1.1.1

Factor $3$ out of $12$ .

$\frac{3 (4)}{15} - \frac{9}{12}$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $3$ out of $15$ .

$\frac{3 \cdot 4}{3 \cdot 5} - \frac{9}{12}$

Step 1.1.2.2

Cancel the common factor.

$\frac{3 \cdot 4}{3 \cdot 5} - \frac{9}{12}$

Step 1.1.2.3

Rewrite the expression.

$\frac{4}{5} - \frac{9}{12}$

Step 1.2

Cancel the common factor of $9$ and $12$ .

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Step 1.2.1

Factor $3$ out of $9$ .

$\frac{4}{5} - \frac{3 (3)}{12}$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Factor $3$ out of $12$ .

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

Step 1.2.2.2

Cancel the common factor.

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

Step 1.2.2.3

Rewrite the expression.

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

Step 2

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

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

Step 3

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

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

Step 4

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

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

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

Step 4.2

Multiply $5$ by $4$ .

$\frac{4 \cdot 4}{20} - \frac{3}{4} \cdot \frac{5}{5}$

Step 4.3

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

$\frac{4 \cdot 4}{20} - \frac{3 \cdot 5}{4 \cdot 5}$

Step 4.4

Multiply $4$ by $5$ .

$\frac{4 \cdot 4}{20} - \frac{3 \cdot 5}{20}$

Step 5

Combine the numerators over the common denominator.

$\frac{4 \cdot 4 - 3 \cdot 5}{20}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $4$ by $4$ .

$\frac{16 - 3 \cdot 5}{20}$

Step 6.2

Multiply $- 3$ by $5$ .

$\frac{16 - 15}{20}$

Step 6.3

Subtract $15$ from $16$ .

$\frac{1}{20}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{20}$

Decimal Form:

$0.05$