Basic Math Examples

${(\frac{1}{2} + \frac{1}{3})}^{2} \cdot 144 - \frac{5}{8} \div 10 \frac{1}{2}$

Step 1

Convert $10 \frac{1}{2}$ to an improper fraction.

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Step 1.1

A mixed number is an addition of its whole and fractional parts.

${(\frac{1}{2} + \frac{1}{3})}^{2} \cdot 144 - \frac{5}{8} \div (10 + \frac{1}{2})$

Step 1.2

Add $10$ and $\frac{1}{2}$ .

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Step 1.2.1

To write $10$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

${(\frac{1}{2} + \frac{1}{3})}^{2} \cdot 144 - \frac{5}{8} \div (10 \cdot \frac{2}{2} + \frac{1}{2})$

Step 1.2.2

Combine $10$ and $\frac{2}{2}$ .

${(\frac{1}{2} + \frac{1}{3})}^{2} \cdot 144 - \frac{5}{8} \div (\frac{10 \cdot 2}{2} + \frac{1}{2})$

Step 1.2.3

Combine the numerators over the common denominator.

${(\frac{1}{2} + \frac{1}{3})}^{2} \cdot 144 - \frac{5}{8} \div \frac{10 \cdot 2 + 1}{2}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $10$ by $2$ .

${(\frac{1}{2} + \frac{1}{3})}^{2} \cdot 144 - \frac{5}{8} \div \frac{20 + 1}{2}$

Step 1.2.4.2

Add $20$ and $1$ .

${(\frac{1}{2} + \frac{1}{3})}^{2} \cdot 144 - \frac{5}{8} \div \frac{21}{2}$

Step 2

Simplify each term.

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Step 2.1

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

${(\frac{1}{2} \cdot \frac{3}{3} + \frac{1}{3})}^{2} \cdot 144 - \frac{5}{8} \div \frac{21}{2}$

Step 2.2

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

${(\frac{1}{2} \cdot \frac{3}{3} + \frac{1}{3} \cdot \frac{2}{2})}^{2} \cdot 144 - \frac{5}{8} \div \frac{21}{2}$

Step 2.3

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.3.1

Multiply $\frac{1}{2}$ by $\frac{3}{3}$ .

${(\frac{3}{2 \cdot 3} + \frac{1}{3} \cdot \frac{2}{2})}^{2} \cdot 144 - \frac{5}{8} \div \frac{21}{2}$

Step 2.3.2

Multiply $2$ by $3$ .

${(\frac{3}{6} + \frac{1}{3} \cdot \frac{2}{2})}^{2} \cdot 144 - \frac{5}{8} \div \frac{21}{2}$

Step 2.3.3

Multiply $\frac{1}{3}$ by $\frac{2}{2}$ .

${(\frac{3}{6} + \frac{2}{3 \cdot 2})}^{2} \cdot 144 - \frac{5}{8} \div \frac{21}{2}$

Step 2.3.4

Multiply $3$ by $2$ .

${(\frac{3}{6} + \frac{2}{6})}^{2} \cdot 144 - \frac{5}{8} \div \frac{21}{2}$

Step 2.4

Combine the numerators over the common denominator.

${(\frac{3 + 2}{6})}^{2} \cdot 144 - \frac{5}{8} \div \frac{21}{2}$

Step 2.5

Add $3$ and $2$ .

${(\frac{5}{6})}^{2} \cdot 144 - \frac{5}{8} \div \frac{21}{2}$

Step 2.6

Apply the product rule to $\frac{5}{6}$ .

$\frac{5^{2}}{6^{2}} \cdot 144 - \frac{5}{8} \div \frac{21}{2}$

Step 2.7

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

$\frac{25}{6^{2}} \cdot 144 - \frac{5}{8} \div \frac{21}{2}$

Step 2.8

Raise $6$ to the power of $2$ .

$\frac{25}{36} \cdot 144 - \frac{5}{8} \div \frac{21}{2}$

Step 2.9

Cancel the common factor of $36$ .

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Step 2.9.1

Factor $36$ out of $144$ .

$\frac{25}{36} \cdot (36 (4)) - \frac{5}{8} \div \frac{21}{2}$

Step 2.9.2

Cancel the common factor.

$\frac{25}{36} \cdot (36 \cdot 4) - \frac{5}{8} \div \frac{21}{2}$

Step 2.9.3

Rewrite the expression.

$25 \cdot 4 - \frac{5}{8} \div \frac{21}{2}$

Step 2.10

Multiply $25$ by $4$ .

$100 - \frac{5}{8} \div \frac{21}{2}$

Step 2.11

To divide by a fraction, multiply by its reciprocal.

$100 - (\frac{5}{8} \cdot \frac{2}{21})$

Step 2.12

Cancel the common factor of $2$ .

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Step 2.12.1

Factor $2$ out of $8$ .

$100 - (\frac{5}{2 (4)} \cdot \frac{2}{21})$

Step 2.12.2

Cancel the common factor.

$100 - (\frac{5}{2 \cdot 4} \cdot \frac{2}{21})$

Step 2.12.3

Rewrite the expression.

$100 - (\frac{5}{4} \cdot \frac{1}{21})$

Step 2.13

Multiply $\frac{5}{4}$ by $\frac{1}{21}$ .

$100 - \frac{5}{4 \cdot 21}$

Step 2.14

Multiply $4$ by $21$ .

$100 - \frac{5}{84}$

Step 3

To write $100$ as a fraction with a common denominator, multiply by $\frac{84}{84}$ .

$100 \cdot \frac{84}{84} - \frac{5}{84}$

Step 4

Combine $100$ and $\frac{84}{84}$ .

$\frac{100 \cdot 84}{84} - \frac{5}{84}$

Step 5

Combine the numerators over the common denominator.

$\frac{100 \cdot 84 - 5}{84}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $100$ by $84$ .

$\frac{8400 - 5}{84}$

Step 6.2

Subtract $5$ from $8400$ .

$\frac{8395}{84}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{8395}{84}$

Decimal Form:

$99.94047619 \dots$

Mixed Number Form:

$99 \frac{79}{84}$