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:
- $95\% = 0.95$
- $\frac{17}{200} = 0.085$
- $0.099$ (already in decimal)

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:
- $\frac{7}{10} = 0.7$
- $0.7 = 70\%$

Now check options:
- 77% → 0.77 ✘
- 0.7 → ✔
- 0.07 → 7% ✘
- 70% → ✔
- $\frac{70}{100} = 0.7$ → ✔
- 7% → 0.07 ✘

✔ Same values: 0.7, 70%, $\frac{70}{100}$

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b) 9.5%

Convert 9.5% to decimal:
- $9.5\% = 0.095$

Check options:
- 0.0095 → 0.95% ✘
- 0.95 → 95% ✘
- 0.095 → ✔
- $\frac{95}{100} = 0.95$ ✘
- $\frac{9.5}{10} = 0.95$ ✘
- $\frac{19}{200}$ → Let’s compute:
$$
\frac{19}{200} = 0.095 \quad \text{(Yes!)} ✔
$$

✔ Same values: 0.095, $\frac{19}{200}$

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#### 3) Miriam, Nina, and Elio test scores

We are given:
- Miriam: $\frac{2}{3}$ correct
- Nina: 18 out of 25
- Elio: 68%

Convert all to decimals:

- Miriam:
$$
\frac{2}{3} \approx 0.6667 \quad (\text{or } 66.67\%)
$$
- Nina:
$$
\frac{18}{25} = 0.72 \quad (\text{or } 72\%)
$$
- Elio:
$$
68\% = 0.68
$$

Now order from lowest to highest:
- Miriam: ~0.6667
- Elio: 0.68
- Nina: 0.72

✔ Order: Miriam < Elio < Nina

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#### 4) Oscar, Ivy, Lewis – who spends most on rent?

Assume each student receives the same loan payment — let’s call it $100 (for simplicity).

Oscar: Spends 73% on rent
→ Rent = $73

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

Lewis: Ratio of rent : kept = 4:1
So total parts = 4 + 1 = 5
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
> - Careem: $20 every month (every 4 weeks)

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

First, calculate monthly amounts:

- Abdi:
60¢ = $0.60 per week
Monthly (4 weeks):
$0.60 × 4 = $2.40

- Batul:
$6 every other week → every 2 weeks
In 4 weeks (1 month), gets:
$6 × 2 = $12

- Careem:
$20 per month

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

Fraction for Abdi:
$$
\frac{2.40}{34.40} = \frac{240}{3440} = \frac{24}{344} = \frac{6}{86} = \frac{3}{43}
$$

✔ Answer: $\frac{3}{43}$

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

Original Batul: $12 per month
New Batul: $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%

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

Total 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 earnings:
$$
0.0208x = 42.40
$$

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

Calculate:
$$
x = \frac{42.40}{0.0208} = \frac{4240}{2.08} = \frac{424000}{208} \quad \text{(multiply numerator and denominator by 100)}
$$

Divide:
$$
424000 ÷ 208 ≈ ?
$$

Do division:
- $208 × 2000 = 416,000$
- Subtract: $424,000 - 416,000 = 8,000$
- $208 × 38 = 7864$
- $8000 - 7864 = 136$

So $2000 + 38 = 2038$, remainder small.

Better:
$$
\frac{424000}{208} = 2038.4615...
$$

But let’s use calculator-style:

$$
42.40 ÷ 0.0208 = ?
$$

Multiply numerator and denominator by 10000:
$$
\frac{424000}{208} = ?
$$

Divide:
- $208 × 2038 = ?$
Try:
- $208 × 2000 = 416,000$
- $208 × 38 = 208×30=6240; 208×8=1664 → 6240+1664=7904$
- Total: $416,000 + 7,904 = 423,904$
- Difference: $424,000 - 423,904 = 96$

So $2038 + \frac{96}{208} ≈ 2038 + 0.46 ≈ 2038.46$

So:
$$
x ≈ \$2038.46
$$

✔ Answer: The father earns approximately \$2038.46 per month.

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✔ Final Answers Summary:

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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 < Elio < Nina
(66.67% < 68% < 72%)

4) Lewis spends the most on rent (80% vs 75% and 73%)

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Section B

i) Abdi gets $\boxed{\frac{3}{43}}$ of total monthly pocket money.

ii) Batul’s pocket money increased by $\boxed{66.67\%}$

iii) Father earns $\boxed{\$2038.46}$ per month.

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