Solve the Fraction Subtraction: 8/10 - 5/12 Step by Step

Solve the following exercise:

$\frac{8}{10}-\frac{5}{12}=\text{?}$

To solve this problem, we'll follow these steps:

• Step 1: Identify the least common multiple (LCM) of the denominators.
• Step 2: Convert both fractions to equivalent fractions with the common denominator.
• Step 3: Subtract the numerators of these equivalent fractions.
• Step 4: Simplify the resulting fraction if needed.

Now, let's work through each step:

Step 1: The denominators of the fractions are $10$ and $12$. The LCM of $10$ and $12$ can be determined by listing their multiples or using prime factorization.
- $10 = 2 \cdot 5$
- $12 = 2^2 \cdot 3$
The LCM is obtained by taking the highest power of each prime factor: $2^2 \cdot 3 \cdot 5 = 60$.

Step 2: Convert $\frac{8}{10}$ and $\frac{5}{12}$ to fractions with a denominator of $60$.
- Convert $\frac{8}{10}$: Multiply the numerator and the denominator by $6$ (since $\frac{60}{10} = 6$) to get $\frac{48}{60}$.
- Convert $\frac{5}{12}$: Multiply the numerator and the denominator by $5$ (since $\frac{60}{12} = 5$) to get $\frac{25}{60}$.

Step 3: Subtract the two fractions: $\frac{48}{60} - \frac{25}{60} = \frac{48 - 25}{60} = \frac{23}{60}$.

Therefore, the solution to the problem is $\frac{23}{60}$.