Grade 5 word problems worksheet on fraction mixed operations with real-life scenarios and an accompanying illustration.

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 confusing. Let's read carefully.

She planned to spend $ \frac{3}{4} $ hour per applicant, but actually spent $ \frac{1}{2} $ hour per applicant.

But the question asks: *"How much more time did she spend..."* — but she spent less time per applicant.

So we need to check if it’s asking about extra time, or maybe there's a typo?

Let’s re-read:

> "Instead of $ \frac{3}{4} $ of an hour, Bilen spent $ \frac{1}{2} $ of an hour to meet each applicant."

So she spent less time per applicant than planned.

But the question says: *“How much more time did she spend…”*

That can't be right unless we misread.

Wait — perhaps the wording is reversed?

Let’s suppose the problem meant:
- She planned $ \frac{1}{2} $ hour per applicant,
- But actually spent $ \frac{3}{4} $ hour per applicant.

But the original says: “Instead of $ \frac{3}{4} $, she spent $ \frac{1}{2} $” → so she spent less.

But then the question says “how much more time did she spend”? That contradicts.

So likely, the question has a typo, or we're misunderstanding.

But let’s assume the problem means:

> Instead of spending $ \frac{3}{4} $ of an hour per applicant, she actually spent $ \frac{1}{2} $ hour per applicant.

Then she spent less time.

But the question asks: "How much more time did she spend?" — which implies she spent more.

So either:
- The fractions are reversed, or
- The question should say “how much less time”

But let's double-check the original:

> "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?"

This is logically inconsistent — she spent less time, not more.

Unless... wait! Could it be that she spent $ \frac{1}{2} $ hour per applicant instead of $ \frac{3}{4} $, and the question is asking how much less time?

But it says "more".

Alternatively, maybe the planned time was $ \frac{1}{2} $, and actual was $ \frac{3}{4} $?

But the text says: “Instead of $ \frac{3}{4} $, she spent $ \frac{1}{2} $” → so $ \frac{1}{2} $ is actual, $ \frac{3}{4} $ is planned.

So she spent less.

Therefore, the question must have a mistake.

But let’s suppose the intended meaning is:

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

Then we can compute how much more time she spent.

But the text clearly says: “Instead of $ \frac{3}{4} $, she spent $ \frac{1}{2} $”.

So she spent less.

Let’s proceed with the numbers as given, and calculate the difference, and see what makes sense.

We’ll assume the question meant to ask:
"How much less time did she spend?"

But since it says "more", let’s try to interpret it correctly.

Wait — maybe the total time was more?

No — per applicant, $ \frac{1}{2} < \frac{3}{4} $, so total time is less.

So unless there are more applicants, it’s impossible.

Wait — could it be that she spent $ \frac{1}{2} $ hour per applicant instead of $ \frac{3}{4} $, so she saved time?

But again, the question says “how much more time did she spend?”

This is a contradiction.

Perhaps the fractions are reversed?

Let’s look at the third problem — it mentions “$ \frac{1}{4} $ of an hour” and “$ \frac{1}{2} $”, so maybe it's consistent.

Alternatively, perhaps the planned time was $ \frac{1}{2} $, and actual was $ \frac{3}{4} $, but the sentence says “instead of $ \frac{3}{4} $, she spent $ \frac{1}{2} $” — that would mean she didn’t spend $ \frac{3}{4} $, but only $ \frac{1}{2} $.

So she saved time.

Given that, I suspect the question has a typo, and it should say:
"How much less time did she spend?"

But since it says "more", let’s consider another possibility.

Wait — could it be that she met more applicants?

No — the problem doesn’t say that.

Alternatively, maybe the planned time was $ \frac{1}{2} $, and actual was $ \frac{3}{4} $, but the sentence is miswritten.

But the sentence says: “Instead of $ \frac{3}{4} $, she spent $ \frac{1}{2} $” — so she did not spend $ \frac{3}{4} $, she spent $ \frac{1}{2} $.

So she spent less.

So unless the question is wrong, we can’t answer “more”.

But let’s suppose the intended meaning is:

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

Then the difference per applicant is:

$$
\frac{3}{4} - \frac{1}{2} = \frac{3}{4} - \frac{2}{4} = \frac{1}{4} \text{ hour more per applicant}
$$

For 6 applicants:

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

But that contradicts the text.

Alternatively, maybe the planned time was $ \frac{3}{4} $, actual was $ \frac{1}{2} $, so she spent less time.

Difference per applicant:

$$
\frac{3}{4} - \frac{1}{2} = \frac{1}{4} \text{ hour less per applicant}
$$

Total less time:

$$
6 \times \frac{1}{4} = \frac{6}{4} = 1\frac{1}{2} \text{ hours less}
$$

So she spent 1.5 hours less, not more.

Thus, the question “how much more time” is incorrect.

But perhaps the problem meant to say:

> "Instead of $ \frac{1}{2} $ of an hour, Bilen spent $ \frac{3}{4} $ of an hour..."

Then it would make sense.

Given that, and since the third problem uses $ \frac{1}{4} $ and $ \frac{1}{2} $, it’s possible the second problem has a typo.

But let’s assume the problem is correct as written, and the question is:
"How much more time did she spend?" — but she spent less.

So unless we reinterpret, we can’t answer.

But wait — perhaps she spent $ \frac{1}{2} $ hour per applicant, but planned $ \frac{3}{4} $, so she saved time.

So the answer to “how much more” is 0, or negative?

That doesn’t make sense.

Alternatively, maybe the number of applicants changed?

But no — it says “all the applicants” — same 6.

So I think the only logical conclusion is that the question has a typo, and it should be:

> "How much less time did she spend meeting all the applicants?"

Then we can solve it.

Let’s go with that.

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Revised Problem 2:

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

So per applicant, she saved:

$$
\frac{3}{4} - \frac{1}{2} = \frac{3}{4} - \frac{2}{4} = \frac{1}{4} \text{ hour}
$$

For 6 applicants:

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

✔ So she spent 1.5 hours less.

But the question says "more", so unless it’s a typo, we can’t answer.

But let’s move on to Problem 3 — maybe that will clarify.

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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?

#### Step-by-step:

- Total applicants = 6
- Hired = 2
- Rejected = 6 - 2 = 4

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

Total time for rejected applicants:
$$
4 \times \frac{1}{4} = 1 \text{ hour}
$$

Total time for hired applicants:
$$
2 \times \frac{1}{2} = 1 \text{ hour}
$$

Total time:
$$
1 + 1 = 2 \text{ hours}
$$

✔ Answer: 2 hours

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Final Answers:

1. $ 4\frac{1}{2} $ hours
2. There is likely a typo in the question. Based on the given numbers, Bilen spent $ 1\frac{1}{2} $ hours less, not more.
If the question meant to ask “how much less time,” then answer is $ 1\frac{1}{2} $ hours.
If it truly asks “how much more,” then the answer is 0 (she didn’t spend more), or the problem is flawed.

3. 2 hours

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✔ Final Answer Summary:

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

Let me know if you'd like me to revise Problem 2 based on a corrected version.