Ratio and proportion worksheet for Grade 6 - Free Printable

Let's solve each question step by step with clear explanations.

---

III. GIVE SHORT ANSWERS (10 Marks)

---

11. Write the simplest form of the ratio of 8 hours to 3 days

Step 1: Convert both quantities to the same unit.
We know:
1 day = 24 hours
So, 3 days = 3 × 24 = 72 hours

Now, the ratio is:
8 hours : 72 hours

Step 2: Simplify the ratio:
Divide both sides by 8:
8 ÷ 8 = 1
72 ÷ 8 = 9

So, the simplest form is:
1 : 9

✔ Ans: 1 : 9

---

12. Complete the table

| 12 | 20 | ___ | 4 | 8 |
|----|----|-----|---|---|
| ___ | 5 | 6 | 1 | 2 |

This appears to be a proportion table where each column has two numbers in proportion.

Let’s look at the pattern:

- First column: 12 and ? → Let’s find the relationship
- Second column: 20 and 5 → 20 / 5 = 4 → So, top number is 4 times bottom number.
- Third column: ? and 6 → So if same rule applies, top should be 4×6 = 24
- Fourth column: 4 and 1 → 4 / 1 = 4 → same ratio
- Fifth column: 8 and 2 → 8 / 2 = 4 → consistent!

So the ratio is: Top : Bottom = 4 : 1, or Top = 4 × Bottom

Now fill in missing values:

- Third column: Top = 4 × 6 = 24
- First column: Top = 12, so Bottom = 12 ÷ 4 = 3

✔ Completed table:

| 12 | 20 | 24 | 4 | 8 |
|----|----|----|---|---|
| 3 | 5 | 6 | 1 | 2 |

✔ Ans: 24 and 3

---

13. Find the value of ‘x’ if 2, 3, 10, x are in proportion.

If four numbers are in proportion:
a : b = c : d ⇒ a/b = c/d

So:
2 : 3 = 10 : x
⇒ 2/3 = 10/x

Cross-multiply:
2x = 3 × 10 = 30
x = 30 ÷ 2 = 15

✔ Ans: 15

---

14. Divide 30 chocolates between Rosy and Fathima in the ratio 2:3

Total parts = 2 + 3 = 5

Each part = 30 ÷ 5 = 6 chocolates

- Rosy’s share = 2 × 6 = 12
- Fathima’s share = 3 × 6 = 18

✔ Ans: Rosy’s share = 12, Fathima’s share = 18

---

15. If a car covers 80 km in 2 hours, then find the distance covered in 5 hours using Unitary method

Unitary method:
Find distance covered in 1 hour, then multiply by 5.

Distance in 1 hour = 80 km ÷ 2 = 40 km/hour

Distance in 5 hours = 40 × 5 = 200 km

✔ Ans: 200 km

---

IV. GIVE DETAILED ANSWERS (10 Marks)

---

16. Out of 60 students, 40 are boys. Find the simplest form of ratio of:

Total students = 60
Boys = 40
Girls = 60 - 40 = 20

(a) Number of boys to number of girls
= 40 : 20
Simplify: divide both by 20 → 2 : 1

✔ Ans: 2 : 1

(b) Number of boys to total students
= 40 : 60
Divide by 20 → 2 : 3

✔ Ans: 2 : 3

(c) Number of girls to total students
= 20 : 60
Divide by 20 → 1 : 3

✔ Ans: 1 : 3

---

17. A line segment 45 cm long is to be divided into two parts in the ratio 4:5. Find the length of each part.

Total parts = 4 + 5 = 9

Each part = 45 ÷ 9 = 5 cm

- First part (4 parts) = 4 × 5 = 20 cm
- Second part (5 parts) = 5 × 5 = 25 cm

✔ Ans: First part = 20 cm, Second part = 25 cm

---

✔ Final Answers Summary:

11. 1 : 9
12. 24, 3
13. 15
14. Rosy: 12, Fathima: 18
15. 200 km
16.
a. 2 : 1
b. 2 : 3
c. 1 : 3
17. First part: 20 cm, Second part: 25 cm

Let me know if you'd like these answers formatted for printing or submission!