Basic Math Examples

\frac{18}{y} = \frac{45}{100}

$\frac{18}{y} = \frac{45}{100}$

Step 1

Cancel the common factor of

45

$45$ and

100

$100$ .

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Step 1.1

Factor

5

$5$ out of

45

$45$ .

\frac{18}{y} = \frac{5 (9)}{100}

$\frac{18}{y} = \frac{5 (9)}{100}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor

5

$5$ out of

100

$100$ .

\frac{18}{y} = \frac{5 \cdot 9}{5 \cdot 20}

$\frac{18}{y} = \frac{5 \cdot 9}{5 \cdot 20}$

Step 1.2.2

Cancel the common factor.

\frac{18}{y} = \frac{5 \cdot 9}{5 \cdot 20}

$\frac{18}{y} = \frac{5 \cdot 9}{5 \cdot 20}$

Step 1.2.3

Rewrite the expression.

\frac{18}{y} = \frac{9}{20}

$\frac{18}{y} = \frac{9}{20}$

\frac{18}{y} = \frac{9}{20}

$\frac{18}{y} = \frac{9}{20}$

\frac{18}{y} = \frac{9}{20}

$\frac{18}{y} = \frac{9}{20}$

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.

18 \cdot 20 = y \cdot 9

$18 \cdot 20 = y \cdot 9$

Step 3

Solve the equation for

y

$y$ .

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Step 3.1

Rewrite the equation as

y \cdot 9 = 18 \cdot 20

$y \cdot 9 = 18 \cdot 20$ .

y \cdot 9 = 18 \cdot 20

$y \cdot 9 = 18 \cdot 20$

Step 3.2

Multiply

18

$18$ by

20

$20$ .

y \cdot 9 = 360

$y \cdot 9 = 360$

Step 3.3

Divide each term in

y \cdot 9 = 360

$y \cdot 9 = 360$ by

9

$9$ and simplify.

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Step 3.3.1

Divide each term in

y \cdot 9 = 360

$y \cdot 9 = 360$ by

9

$9$ .

\frac{y \cdot 9}{9} = \frac{360}{9}

$\frac{y \cdot 9}{9} = \frac{360}{9}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of

9

$9$ .

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Step 3.3.2.1.1

Cancel the common factor.

\frac{y \cdot 9}{9} = \frac{360}{9}

$\frac{y \cdot 9}{9} = \frac{360}{9}$

Step 3.3.2.1.2

Divide

y

$y$ by

1

$1$ .

y = \frac{360}{9}

$y = \frac{360}{9}$

y = \frac{360}{9}

$y = \frac{360}{9}$

y = \frac{360}{9}

$y = \frac{360}{9}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Divide

360

$360$ by

9

$9$ .

y = 40

$y = 40$

y = 40

$y = 40$

y = 40

$y = 40$

y = 40

$y = 40$