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

Let's solve the problems step by step.

---

Section A: Non-calculator

#### 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:
\[
0.25 < 0.4286
\]
- The bigger number is \( \frac{3}{7} \).

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

- Convert \( \frac{2}{3} \) to a decimal:
\[
\frac{2}{3} \approx 0.6667
\]
- Convert \( 66\% \) to a decimal:
\[
66\% = 0.66
\]
- Compare:
\[
0.6667 > 0.66
\]
- The bigger number is \( \frac{2}{3} \).

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

- Convert \( 95\% \) to a decimal:
\[
95\% = 0.95
\]
- Convert \( \frac{17}{200} \) to a decimal:
\[
\frac{17}{200} = 0.085
\]
- Compare:
\[
0.95 > 0.099 > 0.085
\]
- The bigger number is \( 95\% \).

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

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

- Convert \( \frac{7}{10} \) to a decimal:
\[
\frac{7}{10} = 0.7
\]
- Match with the given options:
- \( 77\% = 0.77 \)
- \( 0.7 \)
- \( 0.07 \)
- \( 70\% = 0.7 \)
- \( \frac{70}{100} = 0.7 \)
- \( 7\% = 0.07 \)
- The numbers that match are:
\[
0.7, \quad 70\%, \quad \frac{70}{100}
\]

b) \( 9.5\% \)

- Convert \( 9.5\% \) to a decimal:
\[
9.5\% = 0.095
\]
- Match with the given options:
- \( 0.0095 \)
- \( 0.95 \)
- \( 0.095 \)
- \( \frac{95}{100} = 0.95 \)
- \( \frac{9.5}{10} = 0.95 \)
- \( \frac{19}{200} = 0.095 \)
- The numbers that match are:
\[
0.095, \quad \frac{19}{200}
\]

#### 3) Miriam, Nina, and Elio all sat the same test. Miriam answered approximately \( \frac{2}{3} \) correct. Nina got a score of 18 out of 25. Elio scored 68%. Compare their test results by putting them in order of lowest to highest score. Show how you get your answer.

- Miriam's score:
\[
\frac{2}{3} \approx 0.6667 \quad (\text{or } 66.67\%)
\]

- Nina's score:
\[
\frac{18}{25} = 0.72 \quad (\text{or } 72\%)
\]

- Elio's score:
\[
68\% = 0.68
\]

- Compare the scores:
\[
0.6667 < 0.68 < 0.72
\]

- Order from lowest to highest:
\[
\text{Miriam (66.67\%)}, \quad \text{Elio (68\%)}, \quad \text{Nina (72\%)}
\]

#### 4) Oscar, Ivy, and Lewis all receive the same student loan payments. From one student loan payment, Oscar spends 73% of theirs on rent. Ivy saves \( \frac{1}{4} \) and spends the rest on rent. The amount Lewis spends of his rent : the amount he keeps is = 4:1. Which student spends the most on rent? Show how you get your answer.

- Oscar:
\[
\text{Spends } 73\% \text{ on rent.}
\]

- Ivy:
\[
\text{Saves } \frac{1}{4} = 25\% \text{ and spends the rest on rent.}
\]
\[
\text{Rent spending} = 100\% - 25\% = 75\%
\]

- Lewis:
\[
\text{Rent spending : keeping ratio} = 4:1
\]
\[
\text{Total parts} = 4 + 1 = 5
\]
\[
\text{Rent spending} = \frac{4}{5} \times 100\% = 80\%
\]

- Compare the percentages:
\[
73\% < 75\% < 80\%
\]

- Conclusion: Lewis spends the most on rent.

---

Section B: Calculator

#### A father gives pocket money to his three children. Abdi gets 60¢ each week. Batul gets $6 every other week and Careem gets $20 every month (every 4 weeks).

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

- Abdi's monthly income:
\[
60 \text{¢/week} \times 4 \text{ weeks/month} = 240 \text{¢/month} = 2.40 \text{\$/month}
\]

- Batul's monthly income:
\[
6 \text{\$/every other week} \times 2 \text{ payments/month} = 12 \text{\$/month}
\]

- Careem's monthly income:
\[
20 \text{\$/month}
\]

- Total monthly income:
\[
2.40 + 12 + 20 = 34.40 \text{\$/month}
\]

- Abdi's fraction of the total:
\[
\frac{\text{Abdi's income}}{\text{Total income}} = \frac{2.40}{34.40} = \frac{240}{3440} = \frac{3}{43}
\]

##### ii) What percentage has Batul's pocket money increased by?

- Batul's new monthly income:
\[
\text{Same as Careem's} = 20 \text{\$/month}
\]

- Increase in Batul's income:
\[
\text{Increase} = 20 - 12 = 8 \text{\$/month}
\]

- Percentage increase:
\[
\text{Percentage increase} = \left( \frac{\text{Increase}}{\text{Original income}} \right) \times 100 = \left( \frac{8}{12} \right) \times 100 = \frac{2}{3} \times 100 \approx 66.67\%
\]

##### 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 income after Batul's increase:
\[
2.40 + 20 + 20 = 42.40 \text{\$/month}
\]

- Father's monthly earnings:
\[
\text{Father's earnings} = \frac{\text{Total income}}{0.0208} = \frac{42.40}{0.0208} = 2040 \text{\$/month}
\]

---

Final Answers:

1. Biggest numbers:
- a) \( \frac{3}{7} \)
- b) \( \frac{2}{3} \)
- c) \( 95\% \)

2. Numbers with the same value:
- a) \( 0.7, \, 70\%, \, \frac{70}{100} \)
- b) \( 0.095, \, \frac{19}{200} \)

3. Order of scores:
\[
\boxed{\text{Miriam, Elio, Nina}}
\]

4. Student who spends the most on rent:
\[
\boxed{\text{Lewis}}
\]

5. Section B answers:
- i) \( \boxed{\frac{3}{43}} \)
- ii) \( \boxed{66.67\%} \)
- iii) \( \boxed{2040} \)