Basic Math Examples

$\frac{200}{{(60)}^{2}} = \frac{d}{{(72)}^{2}}$

Step 1

Rewrite the equation as $\frac{d}{72^{2}} = \frac{200}{60^{2}}$ .

$\frac{d}{72^{2}} = \frac{200}{60^{2}}$

Step 2

Multiply both sides of the equation by $72^{2}$ .

$72^{2} \frac{d}{72^{2}} = 72^{2} \frac{200}{60^{2}}$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $72^{2}$ .

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Step 3.1.1.1

Cancel the common factor.

$72^{2} \frac{d}{72^{2}} = 72^{2} \frac{200}{60^{2}}$

Step 3.1.1.2

Rewrite the expression.

$d = 72^{2} \frac{200}{60^{2}}$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $72^{2} \frac{200}{60^{2}}$ .

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Step 3.2.1.1

Evaluate the exponents.

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Step 3.2.1.1.1

Raise $72$ to the power of $2$ .

$d = 5184 \frac{200}{60^{2}}$

Step 3.2.1.1.2

Raise $60$ to the power of $2$ .

$d = 5184 (\frac{200}{3600})$

Step 3.2.1.2

Cancel the common factor of $144$ .

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Step 3.2.1.2.1

Factor $144$ out of $5184$ .

$d = 144 (36) \frac{200}{3600}$

Step 3.2.1.2.2

Factor $144$ out of $3600$ .

$d = 144 \cdot 36 \frac{200}{144 \cdot 25}$

Step 3.2.1.2.3

Cancel the common factor.

$d = 144 \cdot 36 \frac{200}{144 \cdot 25}$

Step 3.2.1.2.4

Rewrite the expression.

$d = 36 (\frac{200}{25})$

Step 3.2.1.3

Combine $36$ and $\frac{200}{25}$ .

$d = \frac{36 \cdot 200}{25}$

Step 3.2.1.4

Simplify the expression.

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Step 3.2.1.4.1

Multiply $36$ by $200$ .

$d = \frac{7200}{25}$

Step 3.2.1.4.2

Divide $7200$ by $25$ .

$d = 288$