Equivalent Fractions Word Problems Worksheets - Free Printable

Let's solve each of the fractions – mixed operations word problems step by step.

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Problem 1:

Of the 95 children in 6th grade, $ \frac{2}{5} $ went to holiday parties. How many students went to holiday parties in all?

Step-by-step solution:

We need to find $ \frac{2}{5} $ of 95.

$$
\frac{2}{5} \times 95 = \frac{2 \times 95}{5} = \frac{190}{5} = 38
$$

✔ Answer: 38 students went to holiday parties.

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Problem 2:

Amy has 72 sweets in a bag. She keeps $ \frac{1}{3} $ of them for herself and shares the rest with friends. How many sweets will she give to her friends?

Step-by-step solution:

First, find how many sweets Amy keeps:
$$
\frac{1}{3} \times 72 = 24
$$

So, she keeps 24 sweets.

Now, subtract that from total to find how many she gives away:
$$
72 - 24 = 48
$$

✔ Answer: Amy gives 48 sweets to her friends.

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Problem 3:

A train arrives at the station with 150 passengers on board. $ \frac{2}{5} $ of the passengers get off the train in Seattle, and then 35 passengers board the train. How many passengers are on the train when it leaves the station?

Step-by-step solution:

First, calculate how many passengers get off:
$$
\frac{2}{5} \times 150 = \frac{2 \times 150}{5} = \frac{300}{5} = 60
$$

So, 60 passengers get off.

Remaining passengers:
$$
150 - 60 = 90
$$

Then, 35 new passengers board:
$$
90 + 35 = 125
$$

✔ Answer: 125 passengers are on the train when it leaves the station.

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Problem 4:

30 people watched the soccer game last night. Tickets cost $2.75 each. Half of these fans bought a program at $1.50 each. How much money was collected?

Step-by-step solution:

First, calculate revenue from tickets:
$$
30 \times 2.75 = 82.50
$$

Now, half of the fans bought a program:
$$
\frac{1}{2} \times 30 = 15 \text{ fans}
$$

Revenue from programs:
$$
15 \times 1.50 = 22.50
$$

Total money collected:
$$
82.50 + 22.50 = 105.00
$$

✔ Answer: $105.00 was collected.

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✔ Final Answers:

1. 38 students
2. 48 sweets
3. 125 passengers
4. $105.00

Let me know if you'd like this explained visually or with diagrams!