Basic Math Examples

$\frac{1}{3.179 \cdot 10^{3}} = \frac{1}{1.017 \cdot 10^{6}} + \frac{1}{z}$

Step 1

Rewrite the equation as

$\frac{1}{1.017 \cdot 10^{6}} + \frac{1}{z} = \frac{1}{3.179 \cdot 10^{3}}$ .

$\frac{1}{1.017 \cdot 10^{6}} + \frac{1}{z} = \frac{1}{3.179 \cdot 10^{3}}$

Step 2

Simplify

$\frac{1}{1.017 \cdot 10^{6}} + \frac{1}{z}$ .

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Step 2.1

Divide using scientific notation.

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Step 2.1.1

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

$(\frac{1}{1.017}) (\frac{1}{10^{6}}) + \frac{1}{z} = \frac{1}{3.179 \cdot 10^{3}}$

Step 2.1.2

Divide

$1$ by

$1.017$ .

$0.98328416 \frac{1}{10^{6}} + \frac{1}{z} = \frac{1}{3.179 \cdot 10^{3}}$

Step 2.1.3

Move

$10^{6}$ to the numerator using the negative exponent rule

$\frac{1}{b^{n}} = b^{- n}$ .

$0.98328416 \cdot 10^{- 6} + \frac{1}{z} = \frac{1}{3.179 \cdot 10^{3}}$

Step 2.2

Move the decimal point in

$0.98328416$ to the right by

$1$ place and decrease the power of

$10^{- 6}$ by

$1$ .

$9.83284169 \cdot 10^{- 7} + \frac{1}{z} = \frac{1}{3.179 \cdot 10^{3}}$

Step 3

Simplify

$\frac{1}{3.179 \cdot 10^{3}}$ .

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Step 3.1

Divide using scientific notation.

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Step 3.1.1

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

$9.83284169 \cdot 10^{- 7} + \frac{1}{z} = (\frac{1}{3.179}) (\frac{1}{10^{3}})$

Step 3.1.2

Divide

$1$ by

$3.179$ .

$9.83284169 \cdot 10^{- 7} + \frac{1}{z} = 0.31456432 \frac{1}{10^{3}}$

Step 3.1.3

Move

$10^{3}$ to the numerator using the negative exponent rule

$\frac{1}{b^{n}} = b^{- n}$ .

$9.83284169 \cdot 10^{- 7} + \frac{1}{z} = 0.31456432 \cdot 10^{- 3}$

Step 3.2

Move the decimal point in

$0.31456432$ to the right by

$1$ place and decrease the power of

$10^{- 3}$ by

$1$ .

$9.83284169 \cdot 10^{- 7} + \frac{1}{z} = 3.14564328 \cdot 10^{- 4}$

Step 4

Move all terms not containing

$z$ to the right side of the equation.

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Step 4.1

Subtract

$9.83284169 \cdot 10^{- 7}$ from both sides of the equation.

$\frac{1}{z} = 3.14564328 \cdot 10^{- 4} - 9.83284169 \cdot 10^{- 7}$

Step 4.2

Move the decimal point in

$- 9.83284169$ to the left by

$3$ places and increase the power of

$10^{- 7}$ by

$3$ .

$\frac{1}{z} = 3.14564328 \cdot 10^{- 4} - 0.00983284 \cdot 10^{- 4}$

Step 4.3

Factor

$10^{- 4}$ out of

$3.14564328 \cdot 10^{- 4} - 0.00983284 \cdot 10^{- 4}$ .

$\frac{1}{z} = (3.14564328 - 0.00983284) \cdot 10^{- 4}$

Step 4.4

Subtract

$0.00983284$ from

$3.14564328$ .

$\frac{1}{z} = 3.13581044 \cdot 10^{- 4}$

Step 5

Find the LCD of the terms in the equation.

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Step 5.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$z, 1, 1$

Step 5.2

The LCM of one and any expression is the expression.

$z$

Step 6

Multiply each term in

$\frac{1}{z} = 3.13581044 \cdot 10^{- 4}$ by

$z$ to eliminate the fractions.

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Step 6.1

Multiply each term in

$\frac{1}{z} = 3.13581044 \cdot 10^{- 4}$ by

$z$ .

$\frac{1}{z} z = 3.13581044 \cdot 10^{- 4} z$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of

$z$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{1}{z} z = 3.13581044 \cdot 10^{- 4} z$

Step 6.2.1.2

Rewrite the expression.

$1 = 3.13581044 \cdot 10^{- 4} z$

Step 6.3

Simplify the right side.

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Step 6.3.1

Reorder factors in

$3.13581044 \cdot 10^{- 4} z$ .

$1 = 3.13581044 z \cdot 10^{- 4}$

Step 7

Solve the equation.

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Step 7.1

Rewrite the equation as

$3.13581044 z \cdot 10^{- 4} = 1$ .

$3.13581044 z \cdot 10^{- 4} = 1$

Step 7.2

Divide each term in

$3.13581044 z \cdot 10^{- 4} = 1$ by

$3.13581044 \cdot 10^{- 4}$ and simplify.

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Step 7.2.1

Divide each term in

$3.13581044 z \cdot 10^{- 4} = 1$ by

$3.13581044 \cdot 10^{- 4}$ .

$\frac{3.13581044 z \cdot 10^{- 4}}{3.13581044 \cdot 10^{- 4}} = \frac{1}{3.13581044 \cdot 10^{- 4}}$

Step 7.2.2

Simplify the left side.

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Step 7.2.2.1

Cancel the common factor of

$3.13581044$ .

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Step 7.2.2.1.1

Cancel the common factor.

$\frac{3.13581044 z \cdot 10^{- 4}}{3.13581044 \cdot 10^{- 4}} = \frac{1}{3.13581044 \cdot 10^{- 4}}$

Step 7.2.2.1.2

Rewrite the expression.

$\frac{z \cdot 10^{- 4}}{10^{- 4}} = \frac{1}{3.13581044 \cdot 10^{- 4}}$

Step 7.2.2.2

Cancel the common factor of

$10^{- 4}$ .

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Step 7.2.2.2.1

Cancel the common factor.

$\frac{z \cdot 10^{- 4}}{10^{- 4}} = \frac{1}{3.13581044 \cdot 10^{- 4}}$

Step 7.2.2.2.2

Divide

$z$ by

$1$ .

$z = \frac{1}{3.13581044 \cdot 10^{- 4}}$

Step 7.2.3

Simplify the right side.

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Step 7.2.3.1

Divide using scientific notation.

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Step 7.2.3.1.1

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

$z = (\frac{1}{3.13581044}) (\frac{1}{10^{- 4}})$

Step 7.2.3.1.2

Divide

$1$ by

$3.13581044$ .

$z = 0.31889682 \frac{1}{10^{- 4}}$

Step 7.2.3.1.3

Move

$10^{- 4}$ to the numerator using the negative exponent rule

$\frac{1}{b^{- n}} = b^{n}$ .

$z = 0.31889682 \cdot 10^{4}$

Step 7.2.3.2

Move the decimal point in

$0.31889682$ to the right by

$1$ place and decrease the power of

$10^{4}$ by

$1$ .

$z = 3.18896826 \cdot 10^{3}$

Step 8

The result can be shown in multiple forms.

Scientific Notation:

$z = 3.18896826 \cdot 10^{3}$

Expanded Form:

$z = 3188.96826954$