Basic Math Examples

15 \div 2 (7 + (68 - 15 \cdot 33 + 45^{2} \div 16 \div 3) \cdot 15) + 19

$15 \div 2 (7 + (68 - 15 \cdot 33 + 45^{2} \div 16 \div 3) \cdot 15) + 19$

Step 1

Simplify each term.

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Step 1.1

Rewrite the division as a fraction.

\frac{15}{2} (7 + (68 - 15 \cdot 33 + 45^{2} \div 16 \div 3) \cdot 15) + 19

$\frac{15}{2} (7 + (68 - 15 \cdot 33 + 45^{2} \div 16 \div 3) \cdot 15) + 19$

Step 1.2

Simplify each term.

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Step 1.2.1

Find the common denominator.

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Step 1.2.1.1

Write

68

$68$ as a fraction with denominator

1

$1$ .

\frac{15}{2} (7 + (\frac{68}{1} - 15 \cdot 33 + 45^{2} \div 16 \div 3) \cdot 15) + 19

$\frac{15}{2} (7 + (\frac{68}{1} - 15 \cdot 33 + 45^{2} \div 16 \div 3) \cdot 15) + 19$

Step 1.2.1.2

Multiply

\frac{68}{1}

$\frac{68}{1}$ by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{15}{2} (7 + (\frac{68}{1} \cdot \frac{3}{3} - 15 \cdot 33 + 45^{2} \div 16 \div 3) \cdot 15) + 19

$\frac{15}{2} (7 + (\frac{68}{1} \cdot \frac{3}{3} - 15 \cdot 33 + 45^{2} \div 16 \div 3) \cdot 15) + 19$

Step 1.2.1.3

Multiply

\frac{68}{1}

$\frac{68}{1}$ by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{15}{2} (7 + (\frac{68 \cdot 3}{3} - 15 \cdot 33 + 45^{2} \div 16 \div 3) \cdot 15) + 19

$\frac{15}{2} (7 + (\frac{68 \cdot 3}{3} - 15 \cdot 33 + 45^{2} \div 16 \div 3) \cdot 15) + 19$

Step 1.2.1.4

Write

- 15 \cdot 33

$- 15 \cdot 33$ as a fraction with denominator

1

$1$ .

\frac{15}{2} (7 + (\frac{68 \cdot 3}{3} + \frac{- 15 \cdot 33}{1} + 45^{2} \div 16 \div 3) \cdot 15) + 19

$\frac{15}{2} (7 + (\frac{68 \cdot 3}{3} + \frac{- 15 \cdot 33}{1} + 45^{2} \div 16 \div 3) \cdot 15) + 19$

Step 1.2.1.5

Multiply

\frac{- 15 \cdot 33}{1}

$\frac{- 15 \cdot 33}{1}$ by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{15}{2} (7 + (\frac{68 \cdot 3}{3} + \frac{- 15 \cdot 33}{1} \cdot \frac{3}{3} + 45^{2} \div 16 \div 3) \cdot 15) + 19

$\frac{15}{2} (7 + (\frac{68 \cdot 3}{3} + \frac{- 15 \cdot 33}{1} \cdot \frac{3}{3} + 45^{2} \div 16 \div 3) \cdot 15) + 19$

Step 1.2.1.6

Multiply

\frac{- 15 \cdot 33}{1}

$\frac{- 15 \cdot 33}{1}$ by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{15}{2} (7 + (\frac{68 \cdot 3}{3} + \frac{- 15 \cdot 33 \cdot 3}{3} + 45^{2} \div 16 \div 3) \cdot 15) + 19

$\frac{15}{2} (7 + (\frac{68 \cdot 3}{3} + \frac{- 15 \cdot 33 \cdot 3}{3} + 45^{2} \div 16 \div 3) \cdot 15) + 19$

\frac{15}{2} (7 + (\frac{68 \cdot 3}{3} + \frac{- 15 \cdot 33 \cdot 3}{3} + 45^{2} \div 16 \div 3) \cdot 15) + 19

$\frac{15}{2} (7 + (\frac{68 \cdot 3}{3} + \frac{- 15 \cdot 33 \cdot 3}{3} + 45^{2} \div 16 \div 3) \cdot 15) + 19$

Step 1.2.2

Combine the numerators over the common denominator.

\frac{15}{2} (7 + \frac{68 \cdot 3 - 15 \cdot 33 \cdot 3 + 45^{2} \div 16}{3} \cdot 15) + 19

$\frac{15}{2} (7 + \frac{68 \cdot 3 - 15 \cdot 33 \cdot 3 + 45^{2} \div 16}{3} \cdot 15) + 19$

Step 1.2.3

Find the common denominator.

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Step 1.2.3.1

Write

68 \cdot 3

$68 \cdot 3$ as a fraction with denominator

1

$1$ .

\frac{15}{2} (7 + \frac{\frac{68 \cdot 3}{1} - 15 \cdot 33 \cdot 3 + 45^{2} \div 16}{3} \cdot 15) + 19

$\frac{15}{2} (7 + \frac{\frac{68 \cdot 3}{1} - 15 \cdot 33 \cdot 3 + 45^{2} \div 16}{3} \cdot 15) + 19$

Step 1.2.3.2

Multiply

\frac{68 \cdot 3}{1}

$\frac{68 \cdot 3}{1}$ by

$\frac{16}{16}$ .

$\frac{15}{2} (7 + \frac{\frac{68 \cdot 3}{1} \cdot \frac{16}{16} - 15 \cdot 33 \cdot 3 + 45^{2} \div 16}{3} \cdot 15) + 19$

Step 1.2.3.3

Multiply

$\frac{68 \cdot 3}{1}$ by

$\frac{16}{16}$ .

$\frac{15}{2} (7 + \frac{\frac{68 \cdot 3 \cdot 16}{16} - 15 \cdot 33 \cdot 3 + 45^{2} \div 16}{3} \cdot 15) + 19$

Step 1.2.3.4

Write

$- 15 \cdot 33 \cdot 3$ as a fraction with denominator

$1$ .

$\frac{15}{2} (7 + \frac{\frac{68 \cdot 3 \cdot 16}{16} + \frac{- 15 \cdot 33 \cdot 3}{1} + 45^{2} \div 16}{3} \cdot 15) + 19$

Step 1.2.3.5

Multiply

$\frac{- 15 \cdot 33 \cdot 3}{1}$ by

$\frac{16}{16}$ .

$\frac{15}{2} (7 + \frac{\frac{68 \cdot 3 \cdot 16}{16} + \frac{- 15 \cdot 33 \cdot 3}{1} \cdot \frac{16}{16} + 45^{2} \div 16}{3} \cdot 15) + 19$

Step 1.2.3.6

Multiply

$\frac{- 15 \cdot 33 \cdot 3}{1}$ by

$\frac{16}{16}$ .

$\frac{15}{2} (7 + \frac{\frac{68 \cdot 3 \cdot 16}{16} + \frac{- 15 \cdot 33 \cdot 3 \cdot 16}{16} + 45^{2} \div 16}{3} \cdot 15) + 19$

Step 1.2.4

Combine the numerators over the common denominator.

$\frac{15}{2} (7 + \frac{\frac{68 \cdot 3 \cdot 16 - 15 \cdot 33 \cdot 3 \cdot 16 + 45^{2}}{16}}{3} \cdot 15) + 19$

Step 1.2.5

Simplify each term.

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Step 1.2.5.1

Multiply

$68 \cdot 3 \cdot 16$ .

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Step 1.2.5.1.1

Multiply

$68$ by

$3$ .

$\frac{15}{2} (7 + \frac{\frac{204 \cdot 16 - 15 \cdot 33 \cdot 3 \cdot 16 + 45^{2}}{16}}{3} \cdot 15) + 19$

Step 1.2.5.1.2

Multiply

$204$ by

$16$ .

$\frac{15}{2} (7 + \frac{\frac{3264 - 15 \cdot 33 \cdot 3 \cdot 16 + 45^{2}}{16}}{3} \cdot 15) + 19$

Step 1.2.5.2

Multiply

$- 15 \cdot 33 \cdot 3 \cdot 16$ .

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Step 1.2.5.2.1

Multiply

$- 15$ by

$33$ .

$\frac{15}{2} (7 + \frac{\frac{3264 - 495 \cdot 3 \cdot 16 + 45^{2}}{16}}{3} \cdot 15) + 19$

Step 1.2.5.2.2

Multiply

$- 495$ by

$3$ .

$\frac{15}{2} (7 + \frac{\frac{3264 - 1485 \cdot 16 + 45^{2}}{16}}{3} \cdot 15) + 19$

Step 1.2.5.2.3

Multiply

$- 1485$ by

$16$ .

$\frac{15}{2} (7 + \frac{\frac{3264 - 23760 + 45^{2}}{16}}{3} \cdot 15) + 19$

Step 1.2.5.3

Raise

$45$ to the power of

$2$ .

$\frac{15}{2} (7 + \frac{\frac{3264 - 23760 + 2025}{16}}{3} \cdot 15) + 19$

Step 1.2.6

Subtract

$23760$ from

$3264$ .

$\frac{15}{2} (7 + \frac{\frac{- 20496 + 2025}{16}}{3} \cdot 15) + 19$

Step 1.2.7

Add

$- 20496$ and

$2025$ .

$\frac{15}{2} (7 + \frac{\frac{- 18471}{16}}{3} \cdot 15) + 19$

Step 1.2.8

Move the negative in front of the fraction.

$\frac{15}{2} (7 + \frac{- \frac{18471}{16}}{3} \cdot 15) + 19$

Step 1.2.9

Cancel the common factor of

$3$ .

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Step 1.2.9.1

Factor

$3$ out of

$15$ .

$\frac{15}{2} (7 + \frac{- \frac{18471}{16}}{3} \cdot (3 (5))) + 19$

Step 1.2.9.2

Cancel the common factor.

$\frac{15}{2} (7 + \frac{- \frac{18471}{16}}{3} \cdot (3 \cdot 5)) + 19$

Step 1.2.9.3

Rewrite the expression.

$\frac{15}{2} (7 - \frac{18471}{16} \cdot 5) + 19$

Step 1.2.10

Multiply

$5$ by

$- 1$ .

$\frac{15}{2} (7 - 5 (\frac{18471}{16})) + 19$

Step 1.2.11

Combine

$- 5$ and

$\frac{18471}{16}$ .

$\frac{15}{2} (7 + \frac{- 5 \cdot 18471}{16}) + 19$

Step 1.2.12

Multiply

$- 5$ by

$18471$ .

$\frac{15}{2} (7 + \frac{- 92355}{16}) + 19$

Step 1.2.13

Move the negative in front of the fraction.

$\frac{15}{2} (7 - \frac{92355}{16}) + 19$

Step 1.3

To write

$7$ as a fraction with a common denominator, multiply by

$\frac{16}{16}$ .

$\frac{15}{2} (7 \cdot \frac{16}{16} - \frac{92355}{16}) + 19$

Step 1.4

Combine

$7$ and

$\frac{16}{16}$ .

$\frac{15}{2} (\frac{7 \cdot 16}{16} - \frac{92355}{16}) + 19$

Step 1.5

Combine the numerators over the common denominator.

$\frac{15}{2} \cdot \frac{7 \cdot 16 - 92355}{16} + 19$

Step 1.6

Simplify the numerator.

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Step 1.6.1

Multiply

$7$ by

$16$ .

$\frac{15}{2} \cdot \frac{112 - 92355}{16} + 19$

Step 1.6.2

Subtract

$92355$ from

$112$ .

$\frac{15}{2} \cdot \frac{- 92243}{16} + 19$

Step 1.7

Move the negative in front of the fraction.

$\frac{15}{2} (- \frac{92243}{16}) + 19$

Step 1.8

Multiply

$\frac{15}{2} (- \frac{92243}{16})$ .

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Step 1.8.1

Multiply

$\frac{15}{2}$ by

$\frac{92243}{16}$ .

$- \frac{15 \cdot 92243}{2 \cdot 16} + 19$

Step 1.8.2

Multiply

$15$ by

$92243$ .

$- \frac{1383645}{2 \cdot 16} + 19$

Step 1.8.3

Multiply

$2$ by

$16$ .

$- \frac{1383645}{32} + 19$

Step 2

To write

$19$ as a fraction with a common denominator, multiply by

$\frac{32}{32}$ .

$- \frac{1383645}{32} + 19 \cdot \frac{32}{32}$

Step 3

Combine

$19$ and

$\frac{32}{32}$ .

$- \frac{1383645}{32} + \frac{19 \cdot 32}{32}$

Step 4

Combine the numerators over the common denominator.

$\frac{- 1383645 + 19 \cdot 32}{32}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply

$19$ by

$32$ .

$\frac{- 1383645 + 608}{32}$

Step 5.2

Add

$- 1383645$ and

$608$ .

$\frac{- 1383037}{32}$

Step 6

Move the negative in front of the fraction.

$- \frac{1383037}{32}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{1383037}{32}$

Decimal Form:

$- 43219.90625$

Mixed Number Form:

$- 43219 \frac{29}{32}$