Basic Math Examples

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

Step 1

Find the common denominator.

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Step 1.1

Write ${(1.9)}^{3}$ as a fraction with denominator $1$ .

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

Step 1.2

Multiply $\frac{{(1.9)}^{3}}{1}$ by $\frac{43}{43}$ .

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

Step 1.3

Multiply $\frac{{(1.9)}^{3}}{1}$ by $\frac{43}{43}$ .

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

Step 1.4

Write ${(2.1)}^{2}$ as a fraction with denominator $1$ .

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

Step 1.5

Multiply $\frac{{(2.1)}^{2}}{1}$ by $\frac{43}{43}$ .

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

Step 1.6

Multiply $\frac{{(2.1)}^{2}}{1}$ by $\frac{43}{43}$ .

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

Step 1.7

Multiply $13.158 \div 2.15$ by $\frac{\frac{43}{2.15}}{\frac{43}{2.15}}$ .

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

Step 1.8

Multiply $13.158 \div 2.15$ by $\frac{\frac{43}{2.15}}{\frac{43}{2.15}}$ .

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

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 $6.12$ .

$20.498\overline{9}$