Fractions Word Problems (A) Worksheet | Fun and Engaging 5th Grade ... - Free Printable

Let's solve each problem step-by-step with clear explanations.

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Section A – Non-calculator

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#### Problem 1: Cinema Trip

Given:
A father brings $55 to the cinema for himself and his two children.

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##### a. He spends $ \frac{3}{5} $ on tickets. How much money did he spend on tickets?

To find how much he spent on tickets:

$$
\text{Amount spent on tickets} = \frac{3}{5} \times 55
$$

Break it down:
$$
\frac{3}{5} \times 55 = \frac{3 \times 55}{5} = \frac{165}{5} = 33
$$

✔ Answer: He spent $33 on tickets.

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##### b. He spends $15 on snacks. What fraction of the money was spent on snacks?

We know total money = $55, and he spent $15 on snacks.

So, the fraction is:
$$
\frac{15}{55}
$$

Simplify the fraction by dividing numerator and denominator by their GCF (which is 5):
$$
\frac{15 \div 5}{55 \div 5} = \frac{3}{11}
$$

✔ Answer: $ \frac{3}{11} $ of the money was spent on snacks.

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##### c. His wife wanted him to bring $ \frac{2}{11} $ more to the cinema. How much did his wife want him to bring?

"More" means additional amount based on the original $55.

So we calculate:
$$
\frac{2}{11} \times 55 = \frac{2 \times 55}{11} = \frac{110}{11} = 10
$$

So, his wife wanted him to bring $10 more.

✔ Answer: $10 more → total would be $55 + $10 = $65, but the question asks "how much did she want him to bring?" — so just the additional amount.

✔ Answer: $10

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#### Problem 2: USB Port Diagram

##### a. Calculate the perimeter of the USB port. Leave your answer as a mixed fraction.

Dimensions:
- Length = $ \frac{9}{10} $ cm
- Width = $ \frac{3}{4} $ cm

Perimeter of a rectangle:
$$
P = 2 \times (\text{length} + \text{width}) = 2 \left( \frac{9}{10} + \frac{3}{4} \right)
$$

First, add $ \frac{9}{10} + \frac{3}{4} $. Find common denominator: LCM of 10 and 4 is 20.

Convert:
- $ \frac{9}{10} = \frac{18}{20} $
- $ \frac{3}{4} = \frac{15}{20} $

Add:
$$
\frac{18}{20} + \frac{15}{20} = \frac{33}{20}
$$

Now multiply by 2:
$$
2 \times \frac{33}{20} = \frac{66}{20}
$$

Simplify:
$$
\frac{66}{20} = \frac{33}{10} = 3 \frac{3}{10}
$$

✔ Answer: Perimeter = $ 3 \frac{3}{10} $ cm

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##### b. Calculate the shaded area of the front view of the USB cable.

The figure is a large rectangle with a smaller rectangle cut out in the middle.

So:
$$
\text{Shaded Area} = \text{Area of big rectangle} - \text{Area of small rectangle}
$$

Big rectangle:
- Length = $ \frac{9}{10} $ cm
- Width = $ \frac{3}{4} $ cm

$$
\text{Area} = \frac{9}{10} \times \frac{3}{4} = \frac{27}{40} \text{ cm}^2
$$

Small rectangle:
- Length = $ \frac{1}{2} $ cm
- Width = $ \frac{1}{3} $ cm

$$
\text{Area} = \frac{1}{2} \times \frac{1}{3} = \frac{1}{6} \text{ cm}^2
$$

Now subtract:
$$
\frac{27}{40} - \frac{1}{6}
$$

Find common denominator: LCM of 40 and 6 is 120.

Convert:
- $ \frac{27}{40} = \frac{81}{120} $
- $ \frac{1}{6} = \frac{20}{120} $

Subtract:
$$
\frac{81}{120} - \frac{20}{120} = \frac{61}{120}
$$

✔ Answer: Shaded area = $ \frac{61}{120} $ cm²

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Section B – Calculator

> Given: $ \frac{1}{3} $ of our life is spent sleeping.

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#### a) If someone lives until they are 72 years old, how much of their life is spent asleep?

We are told that $ \frac{1}{3} $ of life is spent sleeping, so:

$$
\frac{1}{3} \times 72 = 24 \text{ years}
$$

✔ Answer: 24 years of their life is spent asleep.

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#### b) A newborn baby sleeps:
- 15 hours/day for first month
- 16 hours/day for next two months

We need to find fraction of 3-month life spent asleep.

Assume: 1 month = 4 weeks = 28 days

So:
- First month: 28 days × 15 hours/day = 420 hours
- Next two months: 56 days × 16 hours/day = 896 hours

Total sleep over 3 months:
$$
420 + 896 = 1316 \text{ hours}
$$

Total time in 3 months:
$$
3 \times 28 = 84 \text{ days} = 84 \times 24 = 2016 \text{ hours}
$$

Fraction of time asleep:
$$
\frac{1316}{2016}
$$

Simplify this fraction.

Divide numerator and denominator by 4:
$$
\frac{1316 \div 4}{2016 \div 4} = \frac{329}{504}
$$

Check if further simplification possible.

GCF of 329 and 504?

- 329 ÷ 7 = 47 → 7×47 = 329
- 504 ÷ 7 = 72 → yes!

So divide both by 7:
$$
\frac{329 \div 7}{504 \div 7} = \frac{47}{72}
$$

✔ Answer: $ \frac{47}{72} $ of the baby’s 3-month life is spent asleep.

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#### c) Julian gets $ \frac{2}{7} $ less sleep than recommended 8 hours per day. How much sleep does Julian lose each week compared to recommended?

Recommended: 8 hours/day
Julian gets $ \frac{2}{7} $ less than 8 hours.

So, daily sleep loss:
$$
\frac{2}{7} \times 8 = \frac{16}{7} \text{ hours per day}
$$

Weekly loss (7 days):
$$
7 \times \frac{16}{7} = 16 \text{ hours}
$$

✔ Answer: Julian loses 16 hours of sleep per week compared to recommended.

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✔ Final Answers Summary:

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Section A

1.
a. $33
b. $ \frac{3}{11} $
c. $10

2.
a. $ 3 \frac{3}{10} $ cm
b. $ \frac{61}{120} $ cm²

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Section B

a. 24 years
b. $ \frac{47}{72} $
c. 16 hours

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