Fractions, Decimals, and Percents Word Problems Worksheet | PDF ... - Free Printable

Let's solve each problem step by step, explaining the reasoning and calculations clearly.

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Section A – Non-calculator

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#### 1) Which is the biggest number in each set? Circle your answer.

a) 0.25 or $\frac{3}{7}$

- Convert $\frac{3}{7}$ to a decimal:
$$
\frac{3}{7} \approx 0.4286
$$
- Compare:
$0.25 < 0.4286$

✔ Answer: $\frac{3}{7}$

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b) $\frac{2}{3}$ or 66%

- Convert $\frac{2}{3}$ to decimal:
$$
\frac{2}{3} \approx 0.666...
$$
- Convert 66% to decimal:
$$
66\% = 0.66
$$
- Compare:
$0.666... > 0.66$

✔ Answer: $\frac{2}{3}$

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c) 95%, $\frac{17}{200}$, or 0.099

- Convert all to decimals:
- 95% = 0.95
- $\frac{17}{200} = 0.085$
- 0.099 = 0.099

Compare:
$0.085 < 0.099 < 0.95$

✔ Answer: 95%

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#### 2) Which of the following numbers have the same value as...

a) $\frac{7}{10}$

Convert $\frac{7}{10}$ to decimal and percent:
- $\frac{7}{10} = 0.7$
- $0.7 = 70\%$
- Also: $\frac{70}{100} = 0.7$

So, the equivalent values are:
- 0.7
- 70%
- $\frac{70}{100}$

✔ Answers: 0.7, 70%, $\frac{70}{100}$

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b) 9.5%

Convert 9.5% to decimal and fraction:
- 9.5% = 0.095
- $\frac{9.5}{100} = \frac{95}{1000} = \frac{19}{200}$

So, the equivalents are:
- 0.095
- $\frac{19}{200}$

✔ Answers: 0.095, $\frac{19}{200}$

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#### 3) Compare test scores: Miriam, Nina, Elio

- Miriam: $\frac{2}{3}$ correct
Convert to decimal:
$\frac{2}{3} \approx 0.666... = 66.6...\%$

- Nina: 18 out of 25
$$
\frac{18}{25} = \frac{72}{100} = 72\%
$$

- Elio: 68%

Now order from lowest to highest:
- Miriam: ~66.6%
- Elio: 68%
- Nina: 72%

✔ Order: Miriam < Elio < Nina

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#### 4) Student loan spending on rent

Let’s assume each student gets $100 (for simplicity; since we’re comparing proportions, actual amount doesn’t matter).

Oscar: spends 73% on rent → $73

Ivy: saves $\frac{1}{4}$, so spends $1 - \frac{1}{4} = \frac{3}{4}$ on rent
→ $\frac{3}{4} \times 100 = \$75$

Lewis: spends rent : keeps = 4:1
So total parts = 5 → spends $ \frac{4}{5} $ on rent
→ $ \frac{4}{5} \times 100 = \$80 $

Compare:
- Oscar: $73
- Ivy: $75
- Lewis: $80

✔ Lewis spends the most on rent.

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Section B – Calculator

> A father gives pocket money to his three children:
- Abdi: 60¢ per week
- Batul: $6 every other week (i.e., every 2 weeks)
- Careem: $20 every month (every 4 weeks)

We’ll compute monthly totals first.

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#### i) How much does Abdi get as a fraction of the total pocket money given each month?

- Abdi: 60¢ per week → 60 × 4 = $2.40 per month
- Batul: $6 every 2 weeks → in 4 weeks (1 month), he gets $6 × 2 = $12
- Careem: $20 per month

Total monthly pocket money:
$$
2.40 + 12 + 20 = 34.40
$$

Abdi’s share as a fraction:
$$
\frac{2.40}{34.40} = \frac{240}{3440} = \frac{24}{344} = \frac{6}{86} = \frac{3}{43}
$$

✔ Answer: $\frac{3}{43}$

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#### ii) After a year, Batul’s allowance is increased to match Careem’s monthly amount ($20). What percentage has Batul's pocket money increased by?

- Original: $12 per month
- New: $20 per month

Increase = $20 - $12 = $8

Percentage increase:
$$
\frac{8}{12} \times 100\% = \frac{2}{3} \times 100\% \approx 66.67\%
$$

✔ Answer: 66.67% increase

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#### iii) After Batul's increase, the children receive 0.0208 of the amount their father earns each month. How much does their father earn each month?

Total monthly pocket money after increase:
- Abdi: $2.40
- Batul: $20
- Careem: $20
- Total = $2.40 + $20 + $20 = $42.40

This is 0.0208 of father’s monthly earnings.

Let $ x $ be father’s monthly income:
$$
0.0208x = 42.40
$$

Solve for $ x $:
$$
x = \frac{42.40}{0.0208}
$$

Calculate:
$$
x = \frac{42.40}{0.0208} = \frac{4240}{2.08} = \frac{424000}{208} = 2038.4615...
$$

Round to nearest cent: $2038.46

✔ Answer: Father earns $2038.46 per month

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✔ Final Answers Summary:

#### Section A
1) a) $\frac{3}{7}$ b) $\frac{2}{3}$ c) 95%
2) a) 0.7, 70%, $\frac{70}{100}$ b) 0.095, $\frac{19}{200}$
3) Order: Miriam (66.7%) < Elio (68%) < Nina (72%)
4) Lewis spends the most on rent ($80 vs $75 vs $73)

#### Section B
i) $\frac{3}{43}$
ii) 66.67%
iii) $2038.46

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