Basic Math Examples

$3 \cdot (10^{8} (\frac{1 km}{1000 m}) (\frac{1 mi}{1.609 km}) (\frac{60 s}{1 \min}) (\frac{16.2 \min}{1 w h i l e}))$

Step 1

Cross cancel units.

$3 \cdot (10^{8} \frac{1 km}{1000 m} \cdot \frac{1 mi}{1.609 km} \cdot \frac{60 s}{1 \min} \cdot \frac{16.2 \min}{1 w h i l e})$

Step 2

Simplify the expression.

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Step 2.1

Remove the canceled units.

$3 \cdot (10^{8} \frac{1}{1000 m} \cdot \frac{1 mi}{1.609} \cdot \frac{60 s}{1} \cdot \frac{16.2}{1 w h i l e})$

Step 2.2

Combine fractions.

$\frac{16.2 \cdot 60 s \cdot 3 \cdot 10^{8}}{w h i l e \cdot 1000 m \cdot 1.609} mi$

Step 2.3

Simplify.

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Step 2.3.1

Cancel the common factor of $0.2$ .

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Step 2.3.1.1

Factor $0.2$ out of $16.2 \cdot 60 s \cdot 3 \cdot 10^{8}$ .

$\frac{0.2 (81 \cdot 60 s \cdot 3 \cdot 10^{8})}{w h i l e \cdot 1000 m \cdot 1.609} mi$

Step 2.3.1.2

Cancel the common factor.

$\frac{0.2 (81 \cdot 60 s \cdot 3 \cdot 10^{8})}{w h i l e \cdot 1000 m \cdot 1.609} mi$

Step 2.3.1.3

Rewrite the expression.

$\frac{81 \cdot 60 s \cdot 3 \cdot 10^{8}}{w h i l e \cdot 1000 m \cdot 1.609} \cdot \frac{mi}{5}$

Step 2.3.2

Multiply $\frac{81 \cdot 60 s \cdot 3 \cdot 10^{8}}{w h i l e \cdot 1000 m \cdot 1.609}$ by $\frac{mi}{5}$ .

$\frac{81 \cdot 60 s \cdot 3 \cdot 10^{8}}{w h i l e \cdot 1000 m \cdot 1.609 \cdot 5} mi$

Step 2.3.3

Cancel the common factor of $60$ and $1000$ .

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Step 2.3.3.1

Factor $20$ out of $81 \cdot 60 s \cdot 3 \cdot 10^{8}$ .

$\frac{20 (81 \cdot 3 s \cdot 3 \cdot 10^{8})}{w h i l e \cdot 1000 m \cdot 1.609 \cdot 5} mi$

Step 2.3.3.2

Cancel the common factors.

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Step 2.3.3.2.1

Factor $20$ out of $w h i l e \cdot 1000 m \cdot 1.609 \cdot 5$ .

$\frac{20 (81 \cdot 3 s \cdot 3 \cdot 10^{8})}{20 (w h i l e \cdot 50 m \cdot 1.609 \cdot 5)} mi$

Step 2.3.3.2.2

Cancel the common factor.

$\frac{20 (81 \cdot 3 s \cdot 3 \cdot 10^{8})}{20 (w h i l e \cdot 50 m \cdot 1.609 \cdot 5)} mi$

Step 2.3.3.2.3

Rewrite the expression.

$\frac{81 \cdot 3 s \cdot 3 \cdot 10^{8}}{w h i l e \cdot 50 m \cdot 1.609 \cdot 5} mi$

Step 2.3.4

Simplify the numerator.

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Step 2.3.4.1

Multiply $81$ by $3$ .

$\frac{243 s \cdot 3 \cdot 10^{8}}{w h i l e \cdot 50 m \cdot 1.609 \cdot 5} mi$

Step 2.3.4.2

Multiply $3$ by $243$ .

$\frac{729 s \cdot 10^{8}}{w h i l e \cdot 50 m \cdot 1.609 \cdot 5} mi$

Step 2.3.5

Simplify the denominator.

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Step 2.3.5.1

Multiply $1.609$ by $e$ .

$\frac{729 s \cdot 10^{8}}{w h i l \cdot 4.37371546 \cdot 50 m \cdot 5} mi$

Step 2.3.5.2

Multiply $50$ by $4.37371546$ .

$\frac{729 s \cdot 10^{8}}{w h i l \cdot 218.68577309 m \cdot 5} mi$

Step 2.3.5.3

Multiply $5$ by $218.68577309$ .

$\frac{729 s \cdot 10^{8}}{w h i l \cdot 1093.42886549 m} mi$

Step 2.3.6

Simplify the numerator.

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Step 2.3.6.1

Raise $10$ to the power of $8$ .

$\frac{729 s \cdot 100000000}{w h i l \cdot 1093.42886549 m} mi$

Step 2.3.6.2

Multiply $100000000$ by $729$ .

$\frac{72900000000 s}{w h i l \cdot 1093.42886549 m} mi$

Step 2.3.7

Move $1093.42886549$ to the left of $w h i l$ .

$\frac{72900000000 s}{1093.42886549 \cdot (w h i l) m} mi$

Step 2.3.8

Factor $72900000000$ out of $72900000000 s$ .

$\frac{72900000000 (s)}{1093.42886549 \cdot w h i l m} mi$

Step 2.3.9

Factor $1093.42886549$ out of $1093.42886549 \cdot w h i l m$ .

$\frac{72900000000 (s)}{1093.42886549 (w h i l m)} mi$

Step 2.3.10

Separate fractions.

$\frac{72900000000}{1093.42886549} \cdot \frac{s}{w h i l m} mi$

Step 2.3.11

Divide $72900000000$ by $1093.42886549$ .

$66671003.75736034 \frac{s}{w h i l m} mi$

Step 2.3.12

Combine $66671003.75736034$ and $\frac{s}{w h i l m}$ .

$\frac{66671003.75736034 s}{w h i l m} mi$