Basic Math Examples

1.92 = c (0.25 + \frac{0.72 \cdot 200 \cdot (4 p \cdot 10^{- 7}) \cdot 0.172}{10.5 \cdot 10^{- 2}})

$1.92 = c (0.25 + \frac{0.72 \cdot 200 \cdot (4 p \cdot 10^{- 7}) \cdot 0.172}{10.5 \cdot 10^{- 2}})$

Step 1

Rewrite the equation as

c (0.25 + \frac{0.72 \cdot 200 \cdot (4 p) \cdot 10^{- 7} \cdot 0.172}{10.5 \cdot 10^{- 2}}) = 1.92

$c (0.25 + \frac{0.72 \cdot 200 \cdot (4 p) \cdot 10^{- 7} \cdot 0.172}{10.5 \cdot 10^{- 2}}) = 1.92$ .

c (0.25 + \frac{0.72 \cdot 200 \cdot (4 p) \cdot 10^{- 7} \cdot 0.172}{10.5 \cdot 10^{- 2}}) = 1.92

$c (0.25 + \frac{0.72 \cdot 200 \cdot (4 p) \cdot 10^{- 7} \cdot 0.172}{10.5 \cdot 10^{- 2}}) = 1.92$

Step 2

Simplify.

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Step 2.1

Multiply

0.72

$0.72$ by

200

$200$ .

c (0.25 + \frac{144 \cdot (4 p) \cdot 10^{- 7} \cdot 0.172}{10.5 \cdot 10^{- 2}}) = 1.92

$c (0.25 + \frac{144 \cdot (4 p) \cdot 10^{- 7} \cdot 0.172}{10.5 \cdot 10^{- 2}}) = 1.92$

Step 2.2

Move the decimal point in

10.5

$10.5$ to the left by

1

$1$ place and increase the power of

10^{- 2}

$10^{- 2}$ by

1

$1$ .

c (0.25 + \frac{144 \cdot (4 p) \cdot 10^{- 7} \cdot 0.172}{1.05 \cdot 10^{- 1}}) = 1.92

$c (0.25 + \frac{144 \cdot (4 p) \cdot 10^{- 7} \cdot 0.172}{1.05 \cdot 10^{- 1}}) = 1.92$

Step 2.3

Reduce the expression

\frac{144 \cdot (4 p) \cdot 10^{- 7} \cdot 0.172}{1.05 \cdot 10^{- 1}}

$\frac{144 \cdot (4 p) \cdot 10^{- 7} \cdot 0.172}{1.05 \cdot 10^{- 1}}$ by cancelling the common factors.

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Step 2.3.1

Factor

10^{- 7}

$10^{- 7}$ out of

144 \cdot (4 p) \cdot 10^{- 7} \cdot 0.172

$144 \cdot (4 p) \cdot 10^{- 7} \cdot 0.172$ .

c (0.25 + \frac{10^{- 7} (144 \cdot (4 p) \cdot 0.172)}{1.05 \cdot 10^{- 1}}) = 1.92

$c (0.25 + \frac{10^{- 7} (144 \cdot (4 p) \cdot 0.172)}{1.05 \cdot 10^{- 1}}) = 1.92$

Step 2.3.2

Factor

10^{- 7}

$10^{- 7}$ out of

1.05 \cdot 10^{- 1}

$1.05 \cdot 10^{- 1}$ .

c (0.25 + \frac{10^{- 7} (144 \cdot (4 p) \cdot 0.172)}{10^{- 7} \cdot 1.05 \cdot 10^{6}}) = 1.92

$c (0.25 + \frac{10^{- 7} (144 \cdot (4 p) \cdot 0.172)}{10^{- 7} \cdot 1.05 \cdot 10^{6}}) = 1.92$

Step 2.3.3

Cancel the common factor.

$c (0.25 + \frac{10^{- 7} (144 \cdot (4 p) \cdot 0.172)}{10^{- 7} \cdot 1.05 \cdot 10^{6}}) = 1.92$

Step 2.3.4

Rewrite the expression.

$c (0.25 + \frac{144 \cdot (4 p) \cdot 0.172}{1.05 \cdot 10^{6}}) = 1.92$

Step 2.4

Multiply

$4$ by

$144$ .

$c (0.25 + \frac{576 \cdot p \cdot 0.172}{1.05 \cdot 10^{6}}) = 1.92$

Step 2.5

Multiply

$0.172$ by

$576$ .

$c (0.25 + \frac{99.072 \cdot p}{1.05 \cdot 10^{6}}) = 1.92$

Step 3

Divide each term in

$c (0.25 + \frac{99.072 \cdot p}{1.05 \cdot 10^{6}}) = 1.92$ by

$0.25 + \frac{99.072 \cdot p}{1.05 \cdot 10^{6}}$ and simplify.

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Step 3.1

Divide each term in

$c (0.25 + \frac{99.072 \cdot p}{1.05 \cdot 10^{6}}) = 1.92$ by

$0.25 + \frac{99.072 \cdot p}{1.05 \cdot 10^{6}}$ .

$\frac{c (0.25 + \frac{99.072 \cdot p}{1.05 \cdot 10^{6}})}{0.25 + \frac{99.072 \cdot p}{1.05 \cdot 10^{6}}} = \frac{1.92}{0.25 + \frac{99.072 \cdot p}{1.05 \cdot 10^{6}}}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of

$0.25 + \frac{99.072 \cdot p}{1.05 \cdot 10^{6}}$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{c (0.25 + \frac{99.072 \cdot p}{1.05 \cdot 10^{6}})}{0.25 + \frac{99.072 \cdot p}{1.05 \cdot 10^{6}}} = \frac{1.92}{0.25 + \frac{99.072 \cdot p}{1.05 \cdot 10^{6}}}$

Step 3.2.1.2

Divide

$c$ by

$1$ .

$c = \frac{1.92}{0.25 + \frac{99.072 \cdot p}{1.05 \cdot 10^{6}}}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Factor

$0.002$ out of

$0.25 + \frac{99.072 \cdot p}{1.05 \cdot 10^{6}}$ .

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Step 3.3.1.1

Factor

$0.002$ out of

$0.25$ .

$c = \frac{1.92}{0.002 (125) + \frac{99.072 \cdot p}{1.05 \cdot 10^{6}}}$

Step 3.3.1.2

Factor

$0.002$ out of

$\frac{99.072 \cdot p}{1.05 \cdot 10^{6}}$ .

$c = \frac{1.92}{0.002 (125) + 0.002 \frac{49536 \cdot p}{1.05 \cdot 10^{6}}}$

Step 3.3.1.3

Factor

$0.002$ out of

$0.002 (125) + 0.002 \frac{49536 \cdot p}{1.05 \cdot 10^{6}}$ .

$c = \frac{1.92}{0.002 (125 + \frac{49536 \cdot p}{1.05 \cdot 10^{6}})}$

$c = \frac{1.92}{0.002 (125 + \frac{49536 p}{1.05 \cdot 10^{6}})}$

Step 3.3.2

Factor

$1.92$ out of

$1.92$ .

$c = \frac{1.92 (1)}{0.002 (125 + \frac{49536 p}{1.05 \cdot 10^{6}})}$

Step 3.3.3

Separate fractions.

$c = \frac{1.92}{0.002} \cdot \frac{1}{125 + \frac{49536 p}{1.05 \cdot 10^{6}}}$

Step 3.3.4

Divide

$1.92$ by

$0.002$ .

$c = 960 \frac{1}{125 + \frac{49536 p}{1.05 \cdot 10^{6}}}$

Step 3.3.5

Combine

$960$ and

$\frac{1}{125 + \frac{49536 p}{1.05 \cdot 10^{6}}}$ .

$c = \frac{960}{125 + \frac{49536 p}{1.05 \cdot 10^{6}}}$