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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#### 1) A father brings $55 to spend at the cinema for himself and his two children.

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

We need to find $\frac{3}{5}$ of $55.

$$
\frac{3}{5} \times 55 = \frac{3 \times 55}{5} = \frac{165}{5} = 33
$$

✔ Answer: $33

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

Total money = $55
Spent on snacks = $15

Fraction spent on snacks:

$$
\frac{15}{55} = \frac{3}{11} \quad \text{(simplify by dividing numerator and denominator by 5)}
$$

✔ Answer: $\frac{3}{11}$

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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 to the cinema?

He brought $55. She wants him to bring $\frac{2}{11}$ more than that.

So, calculate $\frac{2}{11}$ of $55$:

$$
\frac{2}{11} \times 55 = \frac{2 \times 55}{11} = \frac{110}{11} = 10
$$

So, she wants him to bring an additional $10, meaning total would be:

$$
55 + 10 = 65
$$

But the question says: *"How much did his wife want him to bring?"* — this means the total amount she wanted him to bring.

✔ Answer: $65

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#### 2) The following diagram shows an illustration of a USB port.

##### 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 = $2 \times (\text{length} + \text{width})$

First, add length and width:

$$
\frac{9}{10} + \frac{3}{4}
$$

Find common denominator: LCM of 10 and 4 is 20.

$$
\frac{9}{10} = \frac{18}{20}, \quad \frac{3}{4} = \frac{15}{20}
$$

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

Now multiply by 2:

$$
2 \times \frac{33}{20} = \frac{66}{20} = \frac{33}{10}
$$

Convert to mixed number:

$$
\frac{33}{10} = 3 \frac{3}{10}
$$

✔ Answer: $3 \frac{3}{10}$ cm

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##### b. The diagram below shows the front view of a USB cable. Calculate the shaded area.

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

Inner (unshaded) rectangle:
- Length = $\frac{1}{2}$ cm
- Width = $\frac{1}{3}$ cm

Shaded area = Area of outer rectangle − Area of inner rectangle

Area of outer rectangle:
$$
\frac{9}{10} \times \frac{3}{4} = \frac{27}{40}
$$

Area of inner rectangle:
$$
\frac{1}{2} \times \frac{1}{3} = \frac{1}{6}
$$

Now subtract:

$$
\frac{27}{40} - \frac{1}{6}
$$

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

$$
\frac{27}{40} = \frac{81}{120}, \quad \frac{1}{6} = \frac{20}{120}
$$

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

✔ Answer: $\frac{61}{120}$ 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?

$\frac{1}{3}$ of 72 years:

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

✔ Answer: 24 years

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#### b) A newborn baby spends approximately 15 hours asleep each day for the first month and then 16 hours each day for the next two months. As a fraction, how much of a 3-month year old’s life has been spent asleep (where 1 month = 4 weeks)?

Assume:
- 1 month = 4 weeks
- 1 week = 7 days → so 1 month = $4 \times 7 = 28$ days
- 3 months = $3 \times 28 = 84$ days

Now calculate total sleep time:

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

Total sleep = $420 + 896 = 1316$ hours

Total time in 3 months = $84$ days × $24$ hours/day = $2016$ hours

Fraction of life spent asleep:

$$
\frac{1316}{2016}
$$

Simplify:

Divide numerator and denominator by 4:

$$
\frac{1316 \div 4}{2016 \div 4} = \frac{329}{504}
$$

Check if reducible: GCD of 329 and 504?

Try dividing:
- 329 ÷ 7 = 47
- 504 ÷ 7 = 72

Yes! So:

$$
\frac{329}{504} = \frac{47}{72}
$$

✔ Answer: $\frac{47}{72}$

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#### c) Julian works too hard. He gets $\frac{2}{7}$ less sleep than the recommended amount of 8 hours a day. How much sleep does Julian lose each week compared to what is recommended?

Recommended sleep per day: 8 hours
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: 16 hours

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✔ Final Answers Summary:

#### Section A
1a) $33
1b) $\frac{3}{11}$
1c) $65
2a) $3 \frac{3}{10}$ cm
2b) $\frac{61}{120}$ cm²

#### Section B
a) 24 years
b) $\frac{47}{72}$
c) 16 hours

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