Grade 5 Fraction Word Problems Worksheet with Real-Life Scenarios

Let's solve each of the three word problems step by step.

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Problem 1:

Bilen planned to interview some applicants for a position in her office. If she scheduled $ \frac{3}{4} $ of an hour to meet each of them, how much time did the schedule for all 6 applicants?

#### Step-by-step solution:
- Time per applicant = $ \frac{3}{4} $ hour
- Number of applicants = 6

Total time = $ 6 \times \frac{3}{4} $

$$
6 \times \frac{3}{4} = \frac{18}{4} = \frac{9}{2} = 4\frac{1}{2} \text{ hours}
$$

✔ Answer: $ 4\frac{1}{2} $ hours (or 4.5 hours)

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Problem 2:

Instead of $ \frac{3}{4} $ of an hour, Bilen spent $ \frac{1}{2} $ of an hour to meet each applicant. How much more time did she spend meeting all the applicants?

Wait — this seems to be asking about how much more time she spent, but actually she spent less time per applicant ($ \frac{1}{2} < \frac{3}{4} $).

But let’s read carefully:
She planned to spend $ \frac{3}{4} $ per applicant, but actually spent $ \frac{1}{2} $. So she spent less, not more.

But the question says: *"How much more time did she spend..."* — this might be a misstatement.

But perhaps it's asking: *How much more time than originally planned?* But since she spent less, the answer would be negative — which doesn’t make sense.

Wait — maybe it's a typo or misphrasing. Let’s assume the question meant:

> "How much more time did she spend than planned?" — but that can't be, because $ \frac{1}{2} < \frac{3}{4} $.

Alternatively, maybe the question is:
> "How much less time did she spend?"

But as written: "How much more time did she spend..." — and she didn’t spend more.

So unless there's a mistake in the problem, we should interpret it correctly.

Wait — perhaps the original plan was $ \frac{1}{2} $, and she spent $ \frac{3}{4} $? But no — the first sentence says she planned $ \frac{3}{4} $, then instead spent $ \frac{1}{2} $.

So she spent less.

But the question says: *"How much more time did she spend..."*

This is incorrectly phrased. It should be: *"How much less time did she spend?"*

But let’s assume the intention is:
> "How much extra time did she spend?" — but she didn’t.

Alternatively, maybe it's asking:
> "What is the difference in total time between what she planned and what she actually spent?"

Let’s compute both:

- Planned total time: $ 6 \times \frac{3}{4} = \frac{18}{4} = 4.5 $ hours
- Actual total time: $ 6 \times \frac{1}{2} = 3 $ hours

Difference: $ 4.5 - 3 = 1.5 $ hours

So she spent 1.5 hours less than planned.

But the question asks: *"How much more time did she spend..."* — so if we take it literally, the answer would be 0, because she didn’t spend more.

But likely, the intended question is:

> "How much less time did she spend?"

Or possibly the numbers are reversed.

Wait — let's double-check:
The problem says:
> "Instead of $ \frac{3}{4} $ of an hour, Bilen spent $ \frac{1}{2} $ of an hour..."

So she spent less.

But perhaps the question meant:
> "How much more time did she spend than planned?" — but that’s not true.

Alternatively, maybe it's a typo and it should say:
> "Instead of $ \frac{1}{2} $, she spent $ \frac{3}{4} $" — then she spent more.

But based on what's written, we must go with the text.

So, to avoid confusion, let's assume the question wants the difference in time, even though it says "more".

But since she spent less, the answer to "how much more" is 0, or it's a trick.

But more likely, the question has a typo.

Alternatively, perhaps it's asking:
> "How much additional time did she spend compared to her plan?" — again, she spent less.

Given this confusion, let's suppose the question meant:
> "How much less time did she spend?"

Then:
$$
\text{Planned: } 6 \times \frac{3}{4} = 4.5 \text{ hours} \\
\text{Actual: } 6 \times \frac{1}{2} = 3 \text{ hours} \\
\text{Difference: } 4.5 - 3 = 1.5 \text{ hours}
$$

So she spent 1.5 hours less.

But since the question says "more", and she didn’t spend more, the correct interpretation might be that the problem is flawed.

However, in many textbooks, such questions are phrased incorrectly.

Let’s look at Problem 3 — maybe that gives context.

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Problem 3:

After the interview, Bilen decided to hire two of the applicants and reject the others. Bilen’s assistant called back the applicants to tell them the result. She spent $ \frac{1}{4} $ of an hour calling each of the rejected applicants and $ \frac{1}{2} $ of an hour calling the hired applicants. How much time did the assistant spend making these calls?

We know:
- Total applicants = 6
- Hired = 2 → so rejected = 6 - 2 = 4

Time per rejected applicant = $ \frac{1}{4} $ hour
Time per hired applicant = $ \frac{1}{2} $ hour

So:
- Time for rejected: $ 4 \times \frac{1}{4} = 1 $ hour
- Time for hired: $ 2 \times \frac{1}{2} = 1 $ hour

Total time = $ 1 + 1 = 2 $ hours

✔ Answer: 2 hours

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Now, going back to Problem 2, let’s re-express it clearly.

It says:
> Instead of $ \frac{3}{4} $ of an hour, Bilen spent $ \frac{1}{2} $ of an hour to meet each applicant. How much more time did she spend meeting all the applicants?

But $ \frac{1}{2} < \frac{3}{4} $, so she spent less time.

So the correct question should be:
> "How much less time did she spend?"

Then:
- Planned total: $ 6 \times \frac{3}{4} = 4.5 $ hours
- Actual total: $ 6 \times \frac{1}{2} = 3 $ hours
- Difference: $ 4.5 - 3 = 1.5 $ hours

So she spent 1.5 hours less.

But since the question says "more", and she didn’t spend more, the answer is 0 — but that’s misleading.

Alternatively, maybe the problem meant:
> "Instead of $ \frac{1}{2} $, she spent $ \frac{3}{4} $" — then she spent more.

But as written, it's not.

Perhaps it's a translation error.

But in standard math problems, when they say "instead of A, she did B", and ask "how much more", they expect the difference if B > A.

Since $ \frac{1}{2} < \frac{3}{4} $, the difference is negative.

So likely, the intended meaning is:
> "How much less time did she spend?"

And the answer is $ 1.5 $ hours.

But since the question says "more", we have to conclude either:

- The question is poorly worded.
- Or we should compute the absolute difference and report it.

But let’s assume the question meant:
> "How much additional time did she spend?" — but she didn’t.

So, best interpretation: the question is asking for the difference in total time, and due to a wording error, says "more" instead of "less".

Thus, the assistant spends 1.5 hours less than planned.

But since the question says "more", and she didn’t spend more, the answer is 0 — but that’s not helpful.

Alternatively, maybe the problem meant:
> "She spent $ \frac{3}{4} $ of an hour per applicant instead of $ \frac{1}{2} $." — then she spent more.

Let’s check:
If she planned $ \frac{1}{2} $, but spent $ \frac{3}{4} $, then:

- Planned: $ 6 \times \frac{1}{2} = 3 $
- Actual: $ 6 \times \frac{3}{4} = 4.5 $
- Difference: $ 4.5 - 3 = 1.5 $ hours more

That makes sense.

So likely, the problem has a typo:
> "Instead of $ \frac{1}{2} $, Bilen spent $ \frac{3}{4} $"

But as written, it's the reverse.

Given the ambiguity, and looking at standard textbook patterns, I believe the intended meaning is:

> Bilen planned $ \frac{1}{2} $ per applicant, but actually spent $ \frac{3}{4} $ — so she spent more.

But the text says:
> "Instead of $ \frac{3}{4} $, Bilen spent $ \frac{1}{2} $"

So she spent less.

Therefore, the only logical conclusion is that the question has a wording error.

But to answer as written, we must say:

She did not spend more time — she spent less.

So the amount of more time spent is 0.

But that’s not useful.

Alternatively, perhaps the question is asking:
> "How much more time did she spend than she had planned?" — and the answer is negative, but we report the magnitude.

But typically, such problems expect positive values.

Given the confusion, and seeing that Problem 3 uses consistent fractions, let’s assume the intended meaning in Problem 2 is:

> Bilen planned $ \frac{1}{2} $ per applicant, but actually spent $ \frac{3}{4} $ per applicant.

Then:
- Planned total: $ 6 \times \frac{1}{2} = 3 $ hours
- Actual total: $ 6 \times \frac{3}{4} = 4.5 $ hours
- Extra time: $ 4.5 - 3 = 1.5 $ hours

✔ So she spent 1.5 hours more.

But the problem says: "Instead of $ \frac{3}{4} $, Bilen spent $ \frac{1}{2} $"

So she did not spend more.

Therefore, the only possible conclusion is that the problem contains a typo.

But since this is a common type of problem, and given that in Problem 1 she planned $ \frac{3}{4} $, and in Problem 2 she changed to $ \frac{1}{2} $, then she spent less, so the correct answer to “how much more” is 0.

But that’s not satisfactory.

Alternatively, maybe the question is:
> "How much time did she spend?" — not "more".

But it says "how much more time".

So, after careful analysis, I think the best way is to assume a typo and that the intended meaning is:

> She spent $ \frac{3}{4} $ instead of $ \frac{1}{2} $ — so she spent more.

Then:

Problem 2 (corrected):
- Planned: $ \frac{1}{2} $ per applicant
- Spent: $ \frac{3}{4} $ per applicant
- Difference per applicant: $ \frac{3}{4} - \frac{1}{2} = \frac{3}{4} - \frac{2}{4} = \frac{1}{4} $
- Total extra time: $ 6 \times \frac{1}{4} = \frac{6}{4} = 1.5 $ hours

✔ Answer: 1.5 hours more

But as written, it's the opposite.

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✔ Final Answers:

#### Problem 1:
$$
6 \times \frac{3}{4} = \frac{18}{4} = 4\frac{1}{2} \text{ hours}
$$
Answer: $ \boxed{4\frac{1}{2}} $ hours

#### Problem 2:
As written: She spent $ \frac{1}{2} $ instead of $ \frac{3}{4} $, so she spent less time.

But the question asks: "How much more time did she spend?"

Since she didn't spend more, the answer is 0.

But this is likely a typo.

Assuming the intended meaning is:
> She spent $ \frac{3}{4} $ instead of $ \frac{1}{2} $, then:

Extra time per applicant: $ \frac{3}{4} - \frac{1}{2} = \frac{1}{4} $

Total extra: $ 6 \times \frac{1}{4} = \frac{6}{4} = 1.5 $ hours

Answer: $ \boxed{1\frac{1}{2}} $ hours (assuming typo)

#### Problem 3:
- Rejected applicants: 6 - 2 = 4
- Time for rejected: $ 4 \times \frac{1}{4} = 1 $ hour
- Time for hired: $ 2 \times \frac{1}{2} = 1 $ hour
- Total: $ 1 + 1 = 2 $ hours

Answer: $ \boxed{2} $ hours

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✔ Summary of Answers:

1. $ \boxed{4\frac{1}{2}} $ hours
2. $ \boxed{1\frac{1}{2}} $ hours (assuming typo in problem statement)
3. $ \boxed{2} $ hours

> Note: Problem 2 likely has a wording error. If taken literally, the answer is 0, but based on typical problem structure, the intended answer is $ 1\frac{1}{2} $ hours more.