Pre-Algebra Examples

$- \frac{12}{37} \cdot {(\frac{5}{6} - \frac{7}{12})}^{2}$

Step 1

To write $\frac{5}{6}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{12}{37} \cdot {(\frac{5}{6} \cdot \frac{2}{2} - \frac{7}{12})}^{2}$

Step 2

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

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Step 2.1

Multiply $\frac{5}{6}$ by $\frac{2}{2}$ .

$- \frac{12}{37} \cdot {(\frac{5 \cdot 2}{6 \cdot 2} - \frac{7}{12})}^{2}$

Step 2.2

Multiply $6$ by $2$ .

$- \frac{12}{37} \cdot {(\frac{5 \cdot 2}{12} - \frac{7}{12})}^{2}$

Step 3

Combine the numerators over the common denominator.

$- \frac{12}{37} \cdot {(\frac{5 \cdot 2 - 7}{12})}^{2}$

Step 4

Simplify the numerator.

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Step 4.1

Multiply $5$ by $2$ .

$- \frac{12}{37} \cdot {(\frac{10 - 7}{12})}^{2}$

Step 4.2

Subtract $7$ from $10$ .

$- \frac{12}{37} \cdot {(\frac{3}{12})}^{2}$

Step 5

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

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Step 5.1

Factor $3$ out of $3$ .

$- \frac{12}{37} \cdot {(\frac{3 (1)}{12})}^{2}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $3$ out of $12$ .

$- \frac{12}{37} \cdot {(\frac{3 \cdot 1}{3 \cdot 4})}^{2}$

Step 5.2.2

Cancel the common factor.

$- \frac{12}{37} \cdot {(\frac{3 \cdot 1}{3 \cdot 4})}^{2}$

Step 5.2.3

Rewrite the expression.

$- \frac{12}{37} \cdot {(\frac{1}{4})}^{2}$

Step 6

Simplify the expression.

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Step 6.1

Apply the product rule to $\frac{1}{4}$ .

$- \frac{12}{37} \cdot \frac{1^{2}}{4^{2}}$

Step 6.2

One to any power is one.

$- \frac{12}{37} \cdot \frac{1}{4^{2}}$

Step 6.3

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

$- \frac{12}{37} \cdot \frac{1}{16}$

Step 7

Cancel the common factor of $4$ .

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Step 7.1

Move the leading negative in $- \frac{12}{37}$ into the numerator.

$\frac{- 12}{37} \cdot \frac{1}{16}$

Step 7.2

Factor $4$ out of $- 12$ .

$\frac{4 (- 3)}{37} \cdot \frac{1}{16}$

Step 7.3

Factor $4$ out of $16$ .

$\frac{4 \cdot - 3}{37} \cdot \frac{1}{4 \cdot 4}$

Step 7.4

Cancel the common factor.

$\frac{4 \cdot - 3}{37} \cdot \frac{1}{4 \cdot 4}$

Step 7.5

Rewrite the expression.

$\frac{- 3}{37} \cdot \frac{1}{4}$

Step 8

Multiply $\frac{- 3}{37}$ by $\frac{1}{4}$ .

$\frac{- 3}{37 \cdot 4}$

Step 9

Simplify the expression.

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Step 9.1

Multiply $37$ by $4$ .

$\frac{- 3}{148}$

Step 9.2

Move the negative in front of the fraction.

$- \frac{3}{148}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$- \frac{3}{148}$

Decimal Form:

$- 0.02\overline{027}$