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

Q: Why can't I just add 3 + 2 and 4 + 5?

Because fractions represent parts of different wholes! $ \frac{3}{4} $ means 3 parts out of 4, while $ \frac{2}{5} $ means 2 parts out of 5. You need equal-sized pieces first.

Q: How do I find the LCD of 4 and 5?

Since 4 and 5 share no common factors (they're relatively prime), their LCD is simply 4 × 5 = 20. For other numbers, find the smallest number that both denominators divide into evenly.

Q: Is 23/20 really the final answer since it's greater than 1?

Yes! $ \frac{23}{20} $ equals 1 hour and 3 minutes (1.15 hours), which makes perfect sense when adding $ \frac{3}{4} $ hour (45 min) and $ \frac{2}{5} $ hour (24 min).

Q: Do I need to convert this to a mixed number?

Not unless the problem asks for it! $ \frac{23}{20} $ is perfectly acceptable as an improper fraction. If needed, it converts to $ 1\frac{3}{20} $ hours.

Q: What if the LCD is really big?

Don't worry! Even large LCDs work the same way. Just multiply each fraction's numerator and denominator by whatever makes the denominator equal the LCD, then add normally.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

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 written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

Pete spends $\frac{3}{4}$ of an hour doing his Spanish homework and $\frac{2}{5}$ of an hour doing his science assignments.

How much time does he spend on homework in total (expressed as a fraction of an hour)?

2

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: $\frac{23}{20}$ .

3

Final Answer

$\frac{23}{20}$

Key Points to Remember

Essential concepts to master this topic

Rule: Find the least common denominator before adding fractions
Technique: Convert $\frac{3}{4}$ to $\frac{15}{20}$ and $\frac{2}{5}$ to $\frac{8}{20}$
Check: Add numerators only: 15 + 8 = 23, keep denominator 20 ✓

Common Mistakes

Avoid these frequent errors

Adding numerators and denominators separately
Don't add 3/4 + 2/5 as (3+2)/(4+5) = 5/9! This completely ignores fraction equivalence rules and gives a wrong answer. Always find the LCD first, convert both fractions, then add only the numerators.

Practice Quiz

Test your knowledge with interactive questions

$$ $\frac{4}{5}+\frac{1}{5}=$

FAQ

Everything you need to know about this question

Why can't I just add 3 + 2 and 4 + 5?

+

Because fractions represent parts of different wholes! $\frac{3}{4}$ means 3 parts out of 4, while $\frac{2}{5}$ means 2 parts out of 5. You need equal-sized pieces first.

How do I find the LCD of 4 and 5?

+

Since 4 and 5 share no common factors (they're relatively prime), their LCD is simply 4 × 5 = 20. For other numbers, find the smallest number that both denominators divide into evenly.

Is 23/20 really the final answer since it's greater than 1?

+

Yes! $\frac{23}{20}$ equals 1 hour and 3 minutes (1.15 hours), which makes perfect sense when adding $\frac{3}{4}$ hour (45 min) and $\frac{2}{5}$ hour (24 min).

Do I need to convert this to a mixed number?

+

Not unless the problem asks for it! $\frac{23}{20}$ is perfectly acceptable as an improper fraction. If needed, it converts to $1\frac{3}{20}$ hours.

What if the LCD is really big?

+

Don't worry! Even large LCDs work the same way. Just multiply each fraction's numerator and denominator by whatever makes the denominator equal the LCD, then add normally.

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