Pre-Algebra Examples

${(- \frac{5}{4})}^{2} - 7 (\frac{1}{12} - \frac{1}{3})$

Step 1

Simplify each term.

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Step 1.1

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 1.1.1

Apply the product rule to $- \frac{5}{4}$ .

${(- 1)}^{2} {(\frac{5}{4})}^{2} - 7 (\frac{1}{12} - \frac{1}{3})$

Step 1.1.2

Apply the product rule to $\frac{5}{4}$ .

${(- 1)}^{2} \frac{5^{2}}{4^{2}} - 7 (\frac{1}{12} - \frac{1}{3})$

Step 1.2

Raise $- 1$ to the power of $2$ .

$1 \frac{5^{2}}{4^{2}} - 7 (\frac{1}{12} - \frac{1}{3})$

Step 1.3

Multiply $\frac{5^{2}}{4^{2}}$ by $1$ .

$\frac{5^{2}}{4^{2}} - 7 (\frac{1}{12} - \frac{1}{3})$

Step 1.4

Raise $5$ to the power of $2$ .

$\frac{25}{4^{2}} - 7 (\frac{1}{12} - \frac{1}{3})$

Step 1.5

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

$\frac{25}{16} - 7 (\frac{1}{12} - \frac{1}{3})$

Step 1.6

To write $- \frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{25}{16} - 7 (\frac{1}{12} - \frac{1}{3} \cdot \frac{4}{4})$

Step 1.7

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

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Step 1.7.1

Multiply $\frac{1}{3}$ by $\frac{4}{4}$ .

$\frac{25}{16} - 7 (\frac{1}{12} - \frac{4}{3 \cdot 4})$

Step 1.7.2

Multiply $3$ by $4$ .

$\frac{25}{16} - 7 (\frac{1}{12} - \frac{4}{12})$

Step 1.8

Combine the numerators over the common denominator.

$\frac{25}{16} - 7 \frac{1 - 4}{12}$

Step 1.9

Subtract $4$ from $1$ .

$\frac{25}{16} - 7 (\frac{- 3}{12})$

Step 1.10

Cancel the common factor of $- 3$ and $12$ .

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Step 1.10.1

Factor $3$ out of $- 3$ .

$\frac{25}{16} - 7 \frac{3 (- 1)}{12}$

Step 1.10.2

Cancel the common factors.

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Step 1.10.2.1

Factor $3$ out of $12$ .

$\frac{25}{16} - 7 \frac{3 \cdot - 1}{3 \cdot 4}$

Step 1.10.2.2

Cancel the common factor.

$\frac{25}{16} - 7 \frac{3 \cdot - 1}{3 \cdot 4}$

Step 1.10.2.3

Rewrite the expression.

$\frac{25}{16} - 7 (\frac{- 1}{4})$

Step 1.11

Move the negative in front of the fraction.

$\frac{25}{16} - 7 (- \frac{1}{4})$

Step 1.12

Multiply $- 7 (- \frac{1}{4})$ .

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Step 1.12.1

Multiply $- 1$ by $- 7$ .

$\frac{25}{16} + 7 (\frac{1}{4})$

Step 1.12.2

Combine $7$ and $\frac{1}{4}$ .

$\frac{25}{16} + \frac{7}{4}$

Step 2

To write $\frac{7}{4}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{25}{16} + \frac{7}{4} \cdot \frac{4}{4}$

Step 3

Write each expression with a common denominator of $16$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{7}{4}$ by $\frac{4}{4}$ .

$\frac{25}{16} + \frac{7 \cdot 4}{4 \cdot 4}$

Step 3.2

Multiply $4$ by $4$ .

$\frac{25}{16} + \frac{7 \cdot 4}{16}$

Step 4

Combine the numerators over the common denominator.

$\frac{25 + 7 \cdot 4}{16}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $7$ by $4$ .

$\frac{25 + 28}{16}$

Step 5.2

Add $25$ and $28$ .

$\frac{53}{16}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{53}{16}$

Decimal Form:

$3.3125$

Mixed Number Form:

$3 \frac{5}{16}$