Basic Math Examples

$(\frac{7}{8} - \frac{1}{4}) - \frac{2}{3} \cdot {(\frac{3}{4})}^{2}$

Step 1

Simplify each term.

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Step 1.1

Apply the product rule to $\frac{3}{4}$ .

$\frac{7}{8} - \frac{1}{4} - \frac{2}{3} \cdot \frac{3^{2}}{4^{2}}$

Step 1.2

Raise $3$ to the power of $2$ .

$\frac{7}{8} - \frac{1}{4} - \frac{2}{3} \cdot \frac{9}{4^{2}}$

Step 1.3

Raise $4$ to the power of $2$ .

$\frac{7}{8} - \frac{1}{4} - \frac{2}{3} \cdot \frac{9}{16}$

Step 1.4

Cancel the common factor of $2$ .

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Step 1.4.1

Move the leading negative in $- \frac{2}{3}$ into the numerator.

$\frac{7}{8} - \frac{1}{4} + \frac{- 2}{3} \cdot \frac{9}{16}$

Step 1.4.2

Factor $2$ out of $- 2$ .

$\frac{7}{8} - \frac{1}{4} + \frac{2 (- 1)}{3} \cdot \frac{9}{16}$

Step 1.4.3

Factor $2$ out of $16$ .

$\frac{7}{8} - \frac{1}{4} + \frac{2 \cdot - 1}{3} \cdot \frac{9}{2 \cdot 8}$

Step 1.4.4

Cancel the common factor.

$\frac{7}{8} - \frac{1}{4} + \frac{2 \cdot - 1}{3} \cdot \frac{9}{2 \cdot 8}$

Step 1.4.5

Rewrite the expression.

$\frac{7}{8} - \frac{1}{4} + \frac{- 1}{3} \cdot \frac{9}{8}$

Step 1.5

Cancel the common factor of $3$ .

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Step 1.5.1

Factor $3$ out of $9$ .

$\frac{7}{8} - \frac{1}{4} + \frac{- 1}{3} \cdot \frac{3 (3)}{8}$

Step 1.5.2

Cancel the common factor.

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

Step 1.5.3

Rewrite the expression.

$\frac{7}{8} - \frac{1}{4} - 1 \cdot \frac{3}{8}$

Step 1.6

Rewrite $- 1 (\frac{3}{8})$ as $- (\frac{3}{8})$ .

$\frac{7}{8} - \frac{1}{4} - \frac{3}{8}$

Step 2

Combine fractions.

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Step 2.1

Combine the numerators over the common denominator.

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

Step 2.2

Subtract $3$ from $7$ .

$\frac{4}{8} + \frac{- 1}{4}$

Step 3

Simplify each term.

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Step 3.1

Cancel the common factor of $4$ and $8$ .

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Step 3.1.1

Factor $4$ out of $4$ .

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

Step 3.1.2

Cancel the common factors.

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Step 3.1.2.1

Factor $4$ out of $8$ .

$\frac{4 \cdot 1}{4 \cdot 2} + \frac{- 1}{4}$

Step 3.1.2.2

Cancel the common factor.

$\frac{4 \cdot 1}{4 \cdot 2} + \frac{- 1}{4}$

Step 3.1.2.3

Rewrite the expression.

$\frac{1}{2} + \frac{- 1}{4}$

Step 3.2

Move the negative in front of the fraction.

$\frac{1}{2} - \frac{1}{4}$

Step 4

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{1}{2} \cdot \frac{2}{2} - \frac{1}{4}$

Step 5

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

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Step 5.1

Multiply $\frac{1}{2}$ by $\frac{2}{2}$ .

$\frac{2}{2 \cdot 2} - \frac{1}{4}$

Step 5.2

Multiply $2$ by $2$ .

$\frac{2}{4} - \frac{1}{4}$

Step 6

Combine the numerators over the common denominator.

$\frac{2 - 1}{4}$

Step 7

Subtract $1$ from $2$ .

$\frac{1}{4}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{4}$

Decimal Form:

$0.25$