Basic Math Examples

$\frac{5}{24} - {(\frac{1}{4})}^{2} + \frac{2}{3}$

Step 1

Find the common denominator.

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Step 1.1

Write $- {(\frac{1}{4})}^{2}$ as a fraction with denominator $1$ .

$\frac{5}{24} + \frac{- {(\frac{1}{4})}^{2}}{1} + \frac{2}{3}$

Step 1.2

Multiply $\frac{- {(\frac{1}{4})}^{2}}{1}$ by $\frac{24}{24}$ .

$\frac{5}{24} + \frac{- {(\frac{1}{4})}^{2}}{1} \cdot \frac{24}{24} + \frac{2}{3}$

Step 1.3

Multiply $\frac{- {(\frac{1}{4})}^{2}}{1}$ by $\frac{24}{24}$ .

$\frac{5}{24} + \frac{- {(\frac{1}{4})}^{2} \cdot 24}{24} + \frac{2}{3}$

Step 1.4

Multiply $\frac{2}{3}$ by $\frac{8}{8}$ .

$\frac{5}{24} + \frac{- {(\frac{1}{4})}^{2} \cdot 24}{24} + \frac{2}{3} \cdot \frac{8}{8}$

Step 1.5

Multiply $\frac{2}{3}$ by $\frac{8}{8}$ .

$\frac{5}{24} + \frac{- {(\frac{1}{4})}^{2} \cdot 24}{24} + \frac{2 \cdot 8}{3 \cdot 8}$

Step 1.6

Multiply $3$ by $8$ .

$\frac{5}{24} + \frac{- {(\frac{1}{4})}^{2} \cdot 24}{24} + \frac{2 \cdot 8}{24}$

Step 2

Combine the numerators over the common denominator.

$\frac{5 - {(\frac{1}{4})}^{2} \cdot 24 + 2 \cdot 8}{24}$

Step 3

Simplify each term.

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Step 3.1

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

$\frac{5 - \frac{1^{2}}{4^{2}} \cdot 24 + 2 \cdot 8}{24}$

Step 3.2

One to any power is one.

$\frac{5 - \frac{1}{4^{2}} \cdot 24 + 2 \cdot 8}{24}$

Step 3.3

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

$\frac{5 - \frac{1}{16} \cdot 24 + 2 \cdot 8}{24}$

Step 3.4

Cancel the common factor of $8$ .

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Step 3.4.1

Move the leading negative in $- \frac{1}{16}$ into the numerator.

$\frac{5 + \frac{- 1}{16} \cdot 24 + 2 \cdot 8}{24}$

Step 3.4.2

Factor $8$ out of $16$ .

$\frac{5 + \frac{- 1}{8 (2)} \cdot 24 + 2 \cdot 8}{24}$

Step 3.4.3

Factor $8$ out of $24$ .

$\frac{5 + \frac{- 1}{8 \cdot 2} \cdot (8 \cdot 3) + 2 \cdot 8}{24}$

Step 3.4.4

Cancel the common factor.

$\frac{5 + \frac{- 1}{8 \cdot 2} \cdot (8 \cdot 3) + 2 \cdot 8}{24}$

Step 3.4.5

Rewrite the expression.

$\frac{5 + \frac{- 1}{2} \cdot 3 + 2 \cdot 8}{24}$

Step 3.5

Combine $\frac{- 1}{2}$ and $3$ .

$\frac{5 + \frac{- 1 \cdot 3}{2} + 2 \cdot 8}{24}$

Step 3.6

Multiply $- 1$ by $3$ .

$\frac{5 + \frac{- 3}{2} + 2 \cdot 8}{24}$

Step 3.7

Move the negative in front of the fraction.

$\frac{5 - \frac{3}{2} + 2 \cdot 8}{24}$

Step 3.8

Multiply $2$ by $8$ .

$\frac{5 - \frac{3}{2} + 16}{24}$

Step 4

Find the common denominator.

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Step 4.1

Write $5$ as a fraction with denominator $1$ .

$\frac{\frac{5}{1} - \frac{3}{2} + 16}{24}$

Step 4.2

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

$\frac{\frac{5}{1} \cdot \frac{2}{2} - \frac{3}{2} + 16}{24}$

Step 4.3

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

$\frac{\frac{5 \cdot 2}{2} - \frac{3}{2} + 16}{24}$

Step 4.4

Write $16$ as a fraction with denominator $1$ .

$\frac{\frac{5 \cdot 2}{2} - \frac{3}{2} + \frac{16}{1}}{24}$

Step 4.5

Multiply $\frac{16}{1}$ by $\frac{2}{2}$ .

$\frac{\frac{5 \cdot 2}{2} - \frac{3}{2} + \frac{16}{1} \cdot \frac{2}{2}}{24}$

Step 4.6

Multiply $\frac{16}{1}$ by $\frac{2}{2}$ .

$\frac{\frac{5 \cdot 2}{2} - \frac{3}{2} + \frac{16 \cdot 2}{2}}{24}$

Step 5

Combine the numerators over the common denominator.

$\frac{\frac{5 \cdot 2 - 3 + 16 \cdot 2}{2}}{24}$

Step 6

Simplify each term.

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Step 6.1

Multiply $5$ by $2$ .

$\frac{\frac{10 - 3 + 16 \cdot 2}{2}}{24}$

Step 6.2

Multiply $16$ by $2$ .

$\frac{\frac{10 - 3 + 32}{2}}{24}$

Step 7

Simplify by adding and subtracting.

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Step 7.1

Subtract $3$ from $10$ .

$\frac{\frac{7 + 32}{2}}{24}$

Step 7.2

Add $7$ and $32$ .

$\frac{\frac{39}{2}}{24}$

Step 8

Multiply the numerator by the reciprocal of the denominator.

$\frac{39}{2} \cdot \frac{1}{24}$

Step 9

Cancel the common factor of $3$ .

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Step 9.1

Factor $3$ out of $39$ .

$\frac{3 (13)}{2} \cdot \frac{1}{24}$

Step 9.2

Factor $3$ out of $24$ .

$\frac{3 \cdot 13}{2} \cdot \frac{1}{3 \cdot 8}$

Step 9.3

Cancel the common factor.

$\frac{3 \cdot 13}{2} \cdot \frac{1}{3 \cdot 8}$

Step 9.4

Rewrite the expression.

$\frac{13}{2} \cdot \frac{1}{8}$

Step 10

Multiply $\frac{13}{2}$ by $\frac{1}{8}$ .

$\frac{13}{2 \cdot 8}$

Step 11

Multiply $2$ by $8$ .

$\frac{13}{16}$

Step 12

The result can be shown in multiple forms.

Exact Form:

$\frac{13}{16}$

Decimal Form:

$0.8125$