Basic Math Examples

$\frac{{(16.5)}^{2}}{4} + \frac{{(15)}^{2}}{3} + \frac{{(5.5)}^{2}}{3} - \frac{{(16.5 + 15 + 15.5)}^{2}}{10}$

Step 1

Combine the numerators over the common denominator.

$\frac{{(16.5)}^{2}}{4} + \frac{{(15)}^{2} + {(5.5)}^{2}}{3} + \frac{- {(16.5 + 15 + 15.5)}^{2}}{10}$

Step 2

Simplify each term.

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Step 2.1

Raise $15$ to the power of $2$ .

$\frac{{(16.5)}^{2}}{4} + \frac{225 + {(5.5)}^{2}}{3} + \frac{- {(16.5 + 15 + 15.5)}^{2}}{10}$

Step 2.2

Raise $5.5$ to the power of $2$ .

$\frac{{(16.5)}^{2}}{4} + \frac{225 + 30.25}{3} + \frac{- {(16.5 + 15 + 15.5)}^{2}}{10}$

Step 3

Simplify by adding numbers.

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Step 3.1

Add $225$ and $30.25$ .

$\frac{{(16.5)}^{2}}{4} + \frac{255.25}{3} + \frac{- {(16.5 + 15 + 15.5)}^{2}}{10}$

Step 3.2

Add $16.5$ and $15$ .

$\frac{{(16.5)}^{2}}{4} + \frac{255.25}{3} + \frac{- {(31.5 + 15.5)}^{2}}{10}$

Step 3.3

Add $31.5$ and $15.5$ .

$\frac{{(16.5)}^{2}}{4} + \frac{255.25}{3} + \frac{- 47^{2}}{10}$

Step 4

Find the common denominator.

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Step 4.1

Multiply $\frac{{(16.5)}^{2}}{4}$ by $\frac{15}{15}$ .

$\frac{{(16.5)}^{2}}{4} \cdot \frac{15}{15} + \frac{255.25}{3} + \frac{- 47^{2}}{10}$

Step 4.2

Multiply $\frac{{(16.5)}^{2}}{4}$ by $\frac{15}{15}$ .

$\frac{{(16.5)}^{2} \cdot 15}{4 \cdot 15} + \frac{255.25}{3} + \frac{- 47^{2}}{10}$

Step 4.3

Multiply $\frac{255.25}{3}$ by $\frac{20}{20}$ .

$\frac{{(16.5)}^{2} \cdot 15}{4 \cdot 15} + \frac{255.25}{3} \cdot \frac{20}{20} + \frac{- 47^{2}}{10}$

Step 4.4

Multiply $\frac{255.25}{3}$ by $\frac{20}{20}$ .

$\frac{{(16.5)}^{2} \cdot 15}{4 \cdot 15} + \frac{255.25 \cdot 20}{3 \cdot 20} + \frac{- 47^{2}}{10}$

Step 4.5

Multiply $\frac{- 47^{2}}{10}$ by $\frac{6}{6}$ .

$\frac{{(16.5)}^{2} \cdot 15}{4 \cdot 15} + \frac{255.25 \cdot 20}{3 \cdot 20} + \frac{- 47^{2}}{10} \cdot \frac{6}{6}$

Step 4.6

Multiply $\frac{- 47^{2}}{10}$ by $\frac{6}{6}$ .

$\frac{{(16.5)}^{2} \cdot 15}{4 \cdot 15} + \frac{255.25 \cdot 20}{3 \cdot 20} + \frac{- 47^{2} \cdot 6}{10 \cdot 6}$

Step 4.7

Multiply $4$ by $15$ .

$\frac{{(16.5)}^{2} \cdot 15}{60} + \frac{255.25 \cdot 20}{3 \cdot 20} + \frac{- 47^{2} \cdot 6}{10 \cdot 6}$

Step 4.8

Multiply $3$ by $20$ .

$\frac{{(16.5)}^{2} \cdot 15}{60} + \frac{255.25 \cdot 20}{60} + \frac{- 47^{2} \cdot 6}{10 \cdot 6}$

Step 4.9

Reorder the factors of $10 \cdot 6$ .

$\frac{{(16.5)}^{2} \cdot 15}{60} + \frac{255.25 \cdot 20}{60} + \frac{- 47^{2} \cdot 6}{6 \cdot 10}$

Step 4.10

Multiply $6$ by $10$ .

$\frac{{(16.5)}^{2} \cdot 15}{60} + \frac{255.25 \cdot 20}{60} + \frac{- 47^{2} \cdot 6}{60}$

Step 5

Combine the numerators over the common denominator.

$\frac{{(16.5)}^{2} \cdot 15 + 255.25 \cdot 20 - 47^{2} \cdot 6}{60}$

Step 6

Simplify each term.

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Step 6.1

Raise $16.5$ to the power of $2$ .

$\frac{272.25 \cdot 15 + 255.25 \cdot 20 - 47^{2} \cdot 6}{60}$

Step 6.2

Multiply $272.25$ by $15$ .

$\frac{4083.75 + 255.25 \cdot 20 - 47^{2} \cdot 6}{60}$

Step 6.3

Multiply $255.25$ by $20$ .

$\frac{4083.75 + 5105 - 47^{2} \cdot 6}{60}$

Step 6.4

Raise $47$ to the power of $2$ .

$\frac{4083.75 + 5105 - 1 \cdot 2209 \cdot 6}{60}$

Step 6.5

Multiply $- 1 \cdot 2209 \cdot 6$ .

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Step 6.5.1

Multiply $- 1$ by $2209$ .

$\frac{4083.75 + 5105 - 2209 \cdot 6}{60}$

Step 6.5.2

Multiply $- 2209$ by $6$ .

$\frac{4083.75 + 5105 - 13254}{60}$

Step 7

Simplify the expression.

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Step 7.1

Add $4083.75$ and $5105$ .

$\frac{9188.75 - 13254}{60}$

Step 7.2

Subtract $13254$ from $9188.75$ .

$\frac{- 4065.25}{60}$

Step 7.3

Divide $- 4065.25$ by $60$ .

$- 67.7541\overline{6}$