Adding Fractions: Calculate 3/4 + 2/5 Hour in Homework Time

Video Solution

Solution Steps

00:00 What fraction of the hour did Nadav dedicate to homework?

00:03 Let's add the fractions and calculate

00:06 Let's multiply each fraction by the second denominator to find the common denominator

00:09 Remember to multiply both numerator and denominator

00:20 Let's calculate the multiplications

00:23 Let's add under the common denominator

00:29 Let's calculate the numerator

00:32 And this is the solution to the question

Step-by-Step Solution

To find the total time Pete spends on his homework, we'll follow these steps:

Step 1: Identify the given fractions representing time intervals: $\frac{3}{4}$ and $\frac{2}{5}$ .
Step 2: Find the least common denominator (LCD) of the fractions.
Step 3: Convert fractions to have the same denominator.
Step 4: Add the converted fractions.
Step 5: Simplify the resulting fraction if necessary.

Let's now work through each step:

Step 1: We have the fractions $\frac{3}{4}$ (Spanish homework) and $\frac{2}{5}$ (Science assignments).

Step 2: The least common denominator of 4 and 5 is 20.

Step 3: Convert each fraction:

Convert $\frac{3}{4}$ to a fraction with denominator 20: $\frac{3 \times 5}{4 \times 5} = \frac{15}{20}$ .
Convert $\frac{2}{5}$ to a fraction with denominator 20: $\frac{2 \times 4}{5 \times 4} = \frac{8}{20}$ .

Step 4: Add the fractions: $\frac{15}{20} + \frac{8}{20} = \frac{23}{20}$ .

Step 5: The fraction $\frac{23}{20}$ is already in its simplest form.

Therefore, Pete spends a total of $\frac{23}{20}$ hours on homework.

Thus, the correct answer is choice 4: $\frac{23}{20}$ .