Basic Math Examples

\frac{60}{b} = \frac{30}{100}

$\frac{60}{b} = \frac{30}{100}$

Step 1

Cancel the common factor of

30

$30$ and

100

$100$ .

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Step 1.1

Factor

10

$10$ out of

30

$30$ .

\frac{60}{b} = \frac{10 (3)}{100}

$\frac{60}{b} = \frac{10 (3)}{100}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor

10

$10$ out of

100

$100$ .

\frac{60}{b} = \frac{10 \cdot 3}{10 \cdot 10}

$\frac{60}{b} = \frac{10 \cdot 3}{10 \cdot 10}$

Step 1.2.2

Cancel the common factor.

\frac{60}{b} = \frac{10 \cdot 3}{10 \cdot 10}

$\frac{60}{b} = \frac{10 \cdot 3}{10 \cdot 10}$

Step 1.2.3

Rewrite the expression.

\frac{60}{b} = \frac{3}{10}

$\frac{60}{b} = \frac{3}{10}$

\frac{60}{b} = \frac{3}{10}

$\frac{60}{b} = \frac{3}{10}$

\frac{60}{b} = \frac{3}{10}

$\frac{60}{b} = \frac{3}{10}$

Step 2

Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.

60 \cdot 10 = b \cdot 3

$60 \cdot 10 = b \cdot 3$

Step 3

Solve the equation for

b

$b$ .

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Step 3.1

Rewrite the equation as

b \cdot 3 = 60 \cdot 10

$b \cdot 3 = 60 \cdot 10$ .

b \cdot 3 = 60 \cdot 10

$b \cdot 3 = 60 \cdot 10$

Step 3.2

Multiply

60

$60$ by

10

$10$ .

b \cdot 3 = 600

$b \cdot 3 = 600$

Step 3.3

Divide each term in

b \cdot 3 = 600

$b \cdot 3 = 600$ by

3

$3$ and simplify.

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Step 3.3.1

Divide each term in

b \cdot 3 = 600

$b \cdot 3 = 600$ by

3

$3$ .

\frac{b \cdot 3}{3} = \frac{600}{3}

$\frac{b \cdot 3}{3} = \frac{600}{3}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of

3

$3$ .

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Step 3.3.2.1.1

Cancel the common factor.

\frac{b \cdot 3}{3} = \frac{600}{3}

$\frac{b \cdot 3}{3} = \frac{600}{3}$

Step 3.3.2.1.2

Divide

b

$b$ by

1

$1$ .

b = \frac{600}{3}

$b = \frac{600}{3}$

b = \frac{600}{3}

$b = \frac{600}{3}$

b = \frac{600}{3}

$b = \frac{600}{3}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Divide

600

$600$ by

3

$3$ .

b = 200

$b = 200$

b = 200

$b = 200$

b = 200

$b = 200$

b = 200

$b = 200$