The numerator of a fraction is 3 less than its denominator. If the fraction equals $\frac{4}{5}$ , find the denominator.

Class 8Linear Equations in One VariableLinear Equations

Step-by-Step Solution

Let denominator =

x

, numerator =

x - 3. \frac{x - 3}{x} = \frac{4}{5}

→

5 (x - 3) = 4 x

→

5 x - 15 = 4 x

→

x = 15

Answer: B) 15

Multiplying both sides by the LCM of denominators turns fractions into whole numbers in one move.

Example:

\frac{x}{2} + \frac{1}{3} = \frac{5}{6}

. LCM of 2, 3, 6 = 6. Multiply every term by 6:

6 \times \frac{x}{2} + 6 \times \frac{1}{3} = 6 \times \frac{5}{6} 3 x + 2 = 53 x = 3, x = 1

.

Verify:

\frac{1}{2} + \frac{1}{3} = \frac{3}{6} + \frac{2}{6} = \frac{5}{6}

. ✓

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