Subtract Mixed Numbers: (+1/5) - (+3¾) Step-by-Step

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

• Convert the mixed number to an improper fraction.

• Find a common denominator for the fractions.

• Perform the subtraction.

Now, let's work through each step:

Step 1: Convert the Mixed Number
Convert $3\frac{3}{4}$ to an improper fraction:

$3\frac{3}{4} = \frac{3 \times 4 + 3}{4} = \frac{12 + 3}{4} = \frac{15}{4}$.

Step 2: Find a Common Denominator
Identify a common denominator for $\frac{1}{5}$ and $\frac{15}{4}$. The least common denominator (LCD) of 5 and 4 is 20.

Convert $\frac{1}{5}$ and $\frac{15}{4}$ to have denominator 20:

$\frac{1}{5} = \frac{1 \times 4}{5 \times 4} = \frac{4}{20}$ and $\frac{15}{4} = \frac{15 \times 5}{4 \times 5} = \frac{75}{20}$.

Step 3: Subtract the Fractions
Subtract the fractions:

$\frac{4}{20} - \frac{75}{20} = \frac{4 - 75}{20} = \frac{-71}{20}$.

The resulting fraction can be converted back to a mixed number:

$\frac{-71}{20} = -3\frac{11}{20}$.

Therefore, the solution to the problem is $-3\frac{11}{20}$.