Solve the Fraction Subtraction: 5/4 - 3/8 Step-by-Step

To solve this problem, we'll perform the following steps:

• Step 1: Find the Least Common Denominator (LCD) between $4$ and $8$.
• Step 2: Convert both fractions to have this common denominator.
• Step 3: Subtract the numerators, keeping the denominator the same.

Let's apply these steps starting with the first one.

Step 1: Find the Least Common Denominator
The denominators are $4$ and $8$. The least common denominator is the smallest number that both denominators divide into evenly. In this case, the LCD is $8$ because it is the smallest number that is a multiple of both $4$ and $8$.

Step 2: Convert fractions to have the same denominator of $8$
- The fraction $\frac{5}{4}$ needs to be converted to a denominator of $8$. To do this, multiply both the numerator and denominator by $2$:

$\frac{5}{4} \times \frac{2}{2} = \frac{10}{8}$

- The fraction $\frac{3}{8}$ already has the denominator $8$, so it remains unchanged as $\frac{3}{8}$.

Step 3: Subtract the numerators
Now that the fractions have the same denominator, subtract the numerators:

$\frac{10}{8} - \frac{3}{8} = \frac{10 - 3}{8} = \frac{7}{8}$

Therefore, the solution to $\frac{5}{4} - \frac{3}{8}$ is $\frac{7}{8}$.