1Cademy - Solving $$\frac{144}{a} = \frac{9}{4}$$

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Proportion

Example

Solving $\frac{144}{a} = \frac{9}{4}$

Solve the proportion $\frac{144}{a} = \frac{9}{4}$ .

Because the variable $a$ appears in a denominator, the value $a = 0$ must be excluded — it would make the left-hand expression undefined.

Step 1 — Multiply both sides by the LCD. The denominators are $a$ and $4$ . The LCD is $4a$ . Multiply both sides by $4a$ :

$4a \cdot \frac{144}{a} = 4a \cdot \frac{9}{4}$

Step 2 — Remove common factors on each side. On the left, $a$ cancels with the denominator, giving $4 \cdot 144 = 576$ . On the right, $4$ cancels with the denominator, giving $9a$ :

$576 = 9a$

Step 3 — Divide both sides by $9$ :

$\frac{576}{9} = \frac{9a}{9}$

$64 = a$

Step 4 — Check. Substitute $a = 64$ into the original proportion:

$\frac{144}{64} = \frac{9 \cdot 16}{4 \cdot 16} = \frac{9}{4}$ ✓

The solution is $a = 64$ . Unlike proportions where the variable sits in a numerator, here the variable appears in a denominator, so the LCD contains the variable ( $4a$ ). After clearing fractions, the equation reduces to a simple linear equation that is solved by dividing both sides by the coefficient.

Updated 2026-04-21

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OpenStax Elementary Algebra

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