Basic Math Examples

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

Step 1

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

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

Step 2

Simplify.

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Step 2.1

Multiply $0.72$ by $200$ .

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

Step 2.2

Move the decimal point in $10.5$ to the left by $1$ place and increase the power of $10^{- 2}$ by $1$ .

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

Step 2.3

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

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Step 2.3.1

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

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

Step 2.3.2

Factor $10^{- 7}$ out of $1.05 \cdot 10^{- 1}$ .

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

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

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