Adding Fractions with Unlike Denominators: 2/5 and 1/4

Video Solution

Solution Steps

00:00 Solve

00:03 We want to find the least common denominator

00:06 Multiply each fraction by the other denominator to find the common denominator

00:09 Remember to multiply both numerator and denominator

00:24 Calculate the multiplications

00:30 Add under the common denominator

00:34 Calculate the numerator

00:38 And this is the solution to the question

Step-by-Step Solution

To solve the problem, let's follow a structured approach:

Step 1: Determine the least common multiple (LCM) of the denominators (5 and 4). The LCM of 5 and 4 is 20.
Step 2: Adjust each fraction to have the common denominator of 20.
For $\frac{2}{5}$ , multiply both numerator and denominator by 4 to get $\frac{8}{20}$ .
For $\frac{1}{4}$ , multiply both numerator and denominator by 5 to get $\frac{5}{20}$ .
Step 3: Now, add the two fractions:
$\frac{8}{20} + \frac{5}{20} = \frac{8 + 5}{20} = \frac{13}{20}$ .
Step 4: Verify if the fraction needs simplification. In this case, $\frac{13}{20}$ is already in its simplest form.

The resulting fraction after adding $\frac{2}{5}$ and $\frac{1}{4}$ is $\frac{13}{20}$ .