# Question #1a0d7

Mar 20, 2017

$\text{the number is } 36$

#### Explanation:

If we let the number be represented by n

Change the fractions to eqivalent fractions with a $\textcolor{b l u e}{\text{common denominator}}$

$\Rightarrow \frac{1}{3} = \frac{1}{3} \times \frac{4}{4} = \frac{4}{12} \text{ and } \frac{1}{4} = \frac{1}{4} \times \frac{3}{3} = \frac{3}{12}$

$\Rightarrow \frac{4}{12} x - \frac{3}{12} x = 3 \leftarrow \textcolor{red}{\text{ difference}}$

Since the fractions have a common denominator we can subtract the numerators while leaving the denominator as it is.

$\Rightarrow \frac{4 x}{12} - \frac{3 x}{12} = \frac{x}{12}$

$\Rightarrow \frac{x}{12} = 3$

multiply both sides by 12

${\cancel{12}}^{1} \times \frac{x}{\cancel{12}} ^ 1 = 12 \times 3$

$\Rightarrow x = 36$

$\textcolor{b l u e}{\text{As a check}}$

$\frac{1}{3} \times 36 - \frac{1}{4} \times 36 = 12 - 9 = 3 \to \text{ True}$

$\Rightarrow \text{ The number is } 36$

Mar 20, 2017

36

#### Explanation:

Let the number be x
One third of the number is $\frac{x}{3}$ and one fourth of the number is $\frac{x}{4}$. The difference between the two is $\frac{x}{3} - \frac{x}{4}$, which is equal to 3
ie $\frac{x}{3} - \frac{x}{4} = 3$
The Lowest common Multiple, (LCM) of the denominators namely , is 12
Multiplying through out by 12, we get,

$\frac{x}{3} \cdot 12 - \frac{x}{4} \cdot 12 = 3 \cdot 12$
or
$4 x - 3 x = 36$
ie $x = 36$