Basic Math Examples

{(1.9)}^{3} + {(2.1)}^{2} + 13.158 \div 2.15 + 3.11

${(1.9)}^{3} + {(2.1)}^{2} + 13.158 \div 2.15 + 3.11$

Step 1

Find the common denominator.

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Step 1.1

Write

{(1.9)}^{3}

${(1.9)}^{3}$ as a fraction with denominator

1

$1$ .

\frac{{(1.9)}^{3}}{1} + {(2.1)}^{2} + 13.158 \div 2.15 + 3.11

$\frac{{(1.9)}^{3}}{1} + {(2.1)}^{2} + 13.158 \div 2.15 + 3.11$

Step 1.2

Multiply

\frac{{(1.9)}^{3}}{1}

$\frac{{(1.9)}^{3}}{1}$ by

\frac{43}{43}

$\frac{43}{43}$ .

\frac{{(1.9)}^{3}}{1} \cdot \frac{43}{43} + {(2.1)}^{2} + 13.158 \div 2.15 + 3.11

$\frac{{(1.9)}^{3}}{1} \cdot \frac{43}{43} + {(2.1)}^{2} + 13.158 \div 2.15 + 3.11$

Step 1.3

Multiply

\frac{{(1.9)}^{3}}{1}

$\frac{{(1.9)}^{3}}{1}$ by

\frac{43}{43}

$\frac{43}{43}$ .

\frac{{(1.9)}^{3} \cdot 43}{43} + {(2.1)}^{2} + 13.158 \div 2.15 + 3.11

$\frac{{(1.9)}^{3} \cdot 43}{43} + {(2.1)}^{2} + 13.158 \div 2.15 + 3.11$

Step 1.4

Write

{(2.1)}^{2}

${(2.1)}^{2}$ as a fraction with denominator

1

$1$ .

\frac{{(1.9)}^{3} \cdot 43}{43} + \frac{{(2.1)}^{2}}{1} + 13.158 \div 2.15 + 3.11

$\frac{{(1.9)}^{3} \cdot 43}{43} + \frac{{(2.1)}^{2}}{1} + 13.158 \div 2.15 + 3.11$

Step 1.5

Multiply

\frac{{(2.1)}^{2}}{1}

$\frac{{(2.1)}^{2}}{1}$ by

\frac{43}{43}

$\frac{43}{43}$ .

\frac{{(1.9)}^{3} \cdot 43}{43} + \frac{{(2.1)}^{2}}{1} \cdot \frac{43}{43} + 13.158 \div 2.15 + 3.11

$\frac{{(1.9)}^{3} \cdot 43}{43} + \frac{{(2.1)}^{2}}{1} \cdot \frac{43}{43} + 13.158 \div 2.15 + 3.11$

Step 1.6

Multiply

\frac{{(2.1)}^{2}}{1}

$\frac{{(2.1)}^{2}}{1}$ by

\frac{43}{43}

$\frac{43}{43}$ .

\frac{{(1.9)}^{3} \cdot 43}{43} + \frac{{(2.1)}^{2} \cdot 43}{43} + 13.158 \div 2.15 + 3.11

$\frac{{(1.9)}^{3} \cdot 43}{43} + \frac{{(2.1)}^{2} \cdot 43}{43} + 13.158 \div 2.15 + 3.11$

Step 1.7

Multiply

13.158 \div 2.15

$13.158 \div 2.15$ by

\frac{\frac{43}{2.15}}{\frac{43}{2.15}}

$\frac{\frac{43}{2.15}}{\frac{43}{2.15}}$ .

\frac{{(1.9)}^{3} \cdot 43}{43} + \frac{{(2.1)}^{2} \cdot 43}{43} + 13.158 \div 2.15 \cdot \frac{\frac{43}{2.15}}{\frac{43}{2.15}} + 3.11

$\frac{{(1.9)}^{3} \cdot 43}{43} + \frac{{(2.1)}^{2} \cdot 43}{43} + 13.158 \div 2.15 \cdot \frac{\frac{43}{2.15}}{\frac{43}{2.15}} + 3.11$

Step 1.8

Multiply

13.158 \div 2.15

$13.158 \div 2.15$ by

\frac{\frac{43}{2.15}}{\frac{43}{2.15}}

$\frac{\frac{43}{2.15}}{\frac{43}{2.15}}$ .

\frac{{(1.9)}^{3} \cdot 43}{43} + \frac{{(2.1)}^{2} \cdot 43}{43} + \frac{13.158 (\frac{43}{2.15})}{2.15 (\frac{43}{2.15})} + 3.11

$\frac{{(1.9)}^{3} \cdot 43}{43} + \frac{{(2.1)}^{2} \cdot 43}{43} + \frac{13.158 (\frac{43}{2.15})}{2.15 (\frac{43}{2.15})} + 3.11$

Step 1.9

Write

$3.11$ as a fraction with denominator

$1$ .

$\frac{{(1.9)}^{3} \cdot 43}{43} + \frac{{(2.1)}^{2} \cdot 43}{43} + \frac{13.158 (\frac{43}{2.15})}{2.15 (\frac{43}{2.15})} + \frac{3.11}{1}$

Step 1.10

Multiply

$\frac{3.11}{1}$ by

$\frac{43}{43}$ .

$\frac{{(1.9)}^{3} \cdot 43}{43} + \frac{{(2.1)}^{2} \cdot 43}{43} + \frac{13.158 (\frac{43}{2.15})}{2.15 (\frac{43}{2.15})} + \frac{3.11}{1} \cdot \frac{43}{43}$

Step 1.11

Multiply

$\frac{3.11}{1}$ by

$\frac{43}{43}$ .

$\frac{{(1.9)}^{3} \cdot 43}{43} + \frac{{(2.1)}^{2} \cdot 43}{43} + \frac{13.158 (\frac{43}{2.15})}{2.15 (\frac{43}{2.15})} + \frac{3.11 \cdot 43}{43}$

Step 1.12

Combine

$2.15$ and

$\frac{43}{2.15}$ .

$\frac{{(1.9)}^{3} \cdot 43}{43} + \frac{{(2.1)}^{2} \cdot 43}{43} + \frac{13.158 (\frac{43}{2.15})}{\frac{2.15 \cdot 43}{2.15}} + \frac{3.11 \cdot 43}{43}$

Step 1.13

Multiply

$2.15$ by

$43$ .

$\frac{{(1.9)}^{3} \cdot 43}{43} + \frac{{(2.1)}^{2} \cdot 43}{43} + \frac{13.158 (\frac{43}{2.15})}{\frac{92.45}{2.15}} + \frac{3.11 \cdot 43}{43}$

Step 2

Combine the numerators over the common denominator.

$\frac{{(1.9)}^{3} \cdot 43 + {(2.1)}^{2} \cdot 43 + 3.11 \cdot 43}{43} + \frac{13.158 (\frac{43}{2.15})}{\frac{92.45}{2.15}}$

Step 3

Simplify each term.

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Step 3.1

Raise

$1.9$ to the power of

$3$ .

$\frac{6.859 \cdot 43 + {(2.1)}^{2} \cdot 43 + 3.11 \cdot 43}{43} + \frac{13.158 (\frac{43}{2.15})}{\frac{92.45}{2.15}}$

Step 3.2

Multiply

$6.859$ by

$43$ .

$\frac{294.937 + {(2.1)}^{2} \cdot 43 + 3.11 \cdot 43}{43} + \frac{13.158 (\frac{43}{2.15})}{\frac{92.45}{2.15}}$

Step 3.3

Raise

$2.1$ to the power of

$2$ .

$\frac{294.937 + 4.41 \cdot 43 + 3.11 \cdot 43}{43} + \frac{13.158 (\frac{43}{2.15})}{\frac{92.45}{2.15}}$

Step 3.4

Multiply

$4.41$ by

$43$ .

$\frac{294.937 + 189.63 + 3.11 \cdot 43}{43} + \frac{13.158 (\frac{43}{2.15})}{\frac{92.45}{2.15}}$

Step 3.5

Multiply

$3.11$ by

$43$ .

$\frac{294.937 + 189.63 + 133.73}{43} + \frac{13.158 (\frac{43}{2.15})}{\frac{92.45}{2.15}}$

Step 4

Simplify by adding numbers.

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Step 4.1

Add

$294.937$ and

$189.63$ .

$\frac{484.567 + 133.73}{43} + \frac{13.158 (\frac{43}{2.15})}{\frac{92.45}{2.15}}$

Step 4.2

Add

$484.567$ and

$133.73$ .

$\frac{618.297}{43} + \frac{13.158 (\frac{43}{2.15})}{\frac{92.45}{2.15}}$

Step 5

Simplify each term.

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Step 5.1

Divide

$618.297$ by

$43$ .

$14.379 + \frac{13.158 (\frac{43}{2.15})}{\frac{92.45}{2.15}}$

Step 5.2

Multiply the numerator by the reciprocal of the denominator.

$14.379 + 13.158 (\frac{43}{2.15}) \frac{2.15}{92.45}$

Step 5.3

Divide

$43$ by

$2.15$ .

$14.379 + 13.158 \cdot 20 \frac{2.15}{92.45}$

Step 5.4

Multiply

$13.158$ by

$20$ .

$14.379 + 263.16 (\frac{2.15}{92.45})$

Step 5.5

Divide

$2.15$ by

$92.45$ .

$14.379 + 263.16 \cdot 0.02325581$

Step 5.6

Multiply

$263.16$ by

$0.02325581$ .

$14.379 + 6.12$

Step 6

Add

$14.379$ and

$6.12$ .

$20.498\overline{9}$