Pre-Algebra Examples

$3 (- \frac{5}{24}) + {(\frac{3}{8})}^{2}$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $3$ .

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Step 1.1.1

Move the leading negative in $- \frac{5}{24}$ into the numerator.

$3 (\frac{- 5}{24}) + {(\frac{3}{8})}^{2}$

Step 1.1.2

Factor $3$ out of $24$ .

$3 \frac{- 5}{3 (8)} + {(\frac{3}{8})}^{2}$

Step 1.1.3

Cancel the common factor.

$3 \frac{- 5}{3 \cdot 8} + {(\frac{3}{8})}^{2}$

Step 1.1.4

Rewrite the expression.

$\frac{- 5}{8} + {(\frac{3}{8})}^{2}$

Step 1.2

Move the negative in front of the fraction.

$- \frac{5}{8} + {(\frac{3}{8})}^{2}$

Step 1.3

Apply the product rule to $\frac{3}{8}$ .

$- \frac{5}{8} + \frac{3^{2}}{8^{2}}$

Step 1.4

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

$- \frac{5}{8} + \frac{9}{8^{2}}$

Step 1.5

Raise $8$ to the power of $2$ .

$- \frac{5}{8} + \frac{9}{64}$

Step 2

To write $- \frac{5}{8}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$- \frac{5}{8} \cdot \frac{8}{8} + \frac{9}{64}$

Step 3

Write each expression with a common denominator of $64$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{5}{8}$ by $\frac{8}{8}$ .

$- \frac{5 \cdot 8}{8 \cdot 8} + \frac{9}{64}$

Step 3.2

Multiply $8$ by $8$ .

$- \frac{5 \cdot 8}{64} + \frac{9}{64}$

Step 4

Combine the numerators over the common denominator.

$\frac{- 5 \cdot 8 + 9}{64}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $- 5$ by $8$ .

$\frac{- 40 + 9}{64}$

Step 5.2

Add $- 40$ and $9$ .

$\frac{- 31}{64}$

Step 6

Move the negative in front of the fraction.

$- \frac{31}{64}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{31}{64}$

Decimal Form:

$- 0.484375$