Basic Math Examples

$38 = \frac{a}{1.31 (10^{3})} \cdot (5655)$

Step 1

Rewrite the equation as $\frac{a}{1.31 \cdot 10^{3}} \cdot 5655 = 38$ .

$\frac{a}{1.31 \cdot 10^{3}} \cdot 5655 = 38$

Step 2

Simplify $\frac{a}{1.31 \cdot 10^{3}} \cdot 5655$ .

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Step 2.1

Combine $\frac{a}{1.31 \cdot 10^{3}}$ and $5655$ .

$\frac{a \cdot 5655}{1.31 \cdot 10^{3}} = 38$

Step 2.2

Move $5655$ to the left of $a$ .

$\frac{5655 a}{1.31 \cdot 10^{3}} = 38$

Step 3

Multiply both sides of the equation by $\frac{1.31 \cdot 10^{3}}{5655}$ .

$\frac{1.31 \cdot 10^{3}}{5655} \cdot \frac{5655 a}{1.31 \cdot 10^{3}} = \frac{1.31 \cdot 10^{3}}{5655} \cdot 38$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $\frac{1.31 \cdot 10^{3}}{5655} \cdot \frac{5655 a}{1.31 \cdot 10^{3}}$ .

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Step 4.1.1.1

Divide using scientific notation.

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Step 4.1.1.1.1

Group coefficients together and exponents together to divide numbers in scientific notation.

$(\frac{1.31}{5655}) (\frac{10^{3}}{1}) \frac{5655 a}{1.31 \cdot 10^{3}} = \frac{1.31 \cdot 10^{3}}{5655} \cdot 38$

Step 4.1.1.1.2

Divide $1.31$ by $5655$ .

$0.00023165 \frac{10^{3}}{1} \frac{5655 a}{1.31 \cdot 10^{3}} = \frac{1.31 \cdot 10^{3}}{5655} \cdot 38$

Step 4.1.1.1.3

Divide $10^{3}$ by $1$ .

$0.00023165 \cdot 10^{3} \frac{5655 a}{1.31 \cdot 10^{3}} = \frac{1.31 \cdot 10^{3}}{5655} \cdot 38$

Step 4.1.1.2

Cancel the common factor of $10^{3}$ .

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Step 4.1.1.2.1

Factor $10^{3}$ out of $0.00023165 \cdot 10^{3}$ .

$10^{3} \cdot 0.00023165 \frac{5655 a}{1.31 \cdot 10^{3}} = \frac{1.31 \cdot 10^{3}}{5655} \cdot 38$

Step 4.1.1.2.2

Factor $10^{3}$ out of $1.31 \cdot 10^{3}$ .

$10^{3} \cdot 0.00023165 \frac{5655 a}{10^{3} \cdot 1.31} = \frac{1.31 \cdot 10^{3}}{5655} \cdot 38$

Step 4.1.1.2.3

Cancel the common factor.

$10^{3} \cdot 0.00023165 \frac{5655 a}{10^{3} \cdot 1.31} = \frac{1.31 \cdot 10^{3}}{5655} \cdot 38$

Step 4.1.1.2.4

Rewrite the expression.

$0.00023165 \frac{5655 a}{1.31} = \frac{1.31 \cdot 10^{3}}{5655} \cdot 38$

Step 4.1.1.3

Combine $0.00023165$ and $\frac{5655 a}{1.31}$ .

$\frac{0.00023165 (5655 a)}{1.31} = \frac{1.31 \cdot 10^{3}}{5655} \cdot 38$

Step 4.1.1.4

Multiply $5655$ by $0.00023165$ .

$\frac{1.31 a}{1.31} = \frac{1.31 \cdot 10^{3}}{5655} \cdot 38$

Step 4.1.1.5

Factor $1.31$ out of $1.31 a$ .

$\frac{1.31 (a)}{1.31} = \frac{1.31 \cdot 10^{3}}{5655} \cdot 38$

Step 4.1.1.6

Factor $1.31$ out of $1.31$ .

$\frac{1.31 (a)}{1.31 (1)} = \frac{1.31 \cdot 10^{3}}{5655} \cdot 38$

Step 4.1.1.7

Separate fractions.

$\frac{1.31}{1.31} \cdot \frac{a}{1} = \frac{1.31 \cdot 10^{3}}{5655} \cdot 38$

Step 4.1.1.8

Divide $1.31$ by $1.31$ .

$1 \frac{a}{1} = \frac{1.31 \cdot 10^{3}}{5655} \cdot 38$

Step 4.1.1.9

Divide $a$ by $1$ .

$1 a = \frac{1.31 \cdot 10^{3}}{5655} \cdot 38$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{1.31 \cdot 10^{3}}{5655} \cdot 38$ .

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Step 4.2.1.1

Divide using scientific notation.

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Step 4.2.1.1.1

Group coefficients together and exponents together to divide numbers in scientific notation.

$1 a = (\frac{1.31}{5655}) (\frac{10^{3}}{1}) \cdot 38$

Step 4.2.1.1.2

Divide $1.31$ by $5655$ .

$1 a = 0.00023165 \frac{10^{3}}{1} \cdot 38$

Step 4.2.1.1.3

Divide $10^{3}$ by $1$ .

$1 a = 0.00023165 \cdot 10^{3} \cdot 38$

Step 4.2.1.2

Multiply $0.00023165$ by $38$ .

$1 a = 0.00880282 \cdot 10^{3}$

Step 4.2.1.3

Move the decimal point in $0.00880282$ to the right by $3$ places and decrease the power of $10^{3}$ by $3$ .

$1 a = 8.80282935 \cdot 10^{0}$

Step 4.2.1.4

Convert $8.80282935 \cdot 10^{0}$ from scientific notation.

$1 a = 8.80282935$

Step 5

Divide each term in $1 a = 8.80282935$ by $1$ and simplify.

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Step 5.1

Divide each term in $1 a = 8.80282935$ by $1$ .

$\frac{1 a}{1} = \frac{8.80282935}{1}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $1$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{1 a}{1} = \frac{8.80282935}{1}$

Step 5.2.1.2

Divide $a$ by $1$ .

$a = \frac{8.80282935}{1}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $8.80282935$ by $1$ .

$a = 8.80282935$