Ratio Simplifying Textbook Exercise - Corbettmaths - Free Printable

Let's solve both questions step by step and explain the process clearly.

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🔷 Question 1: Write the ratio of red squares to green circles in simplest form

We need to:
- Count the number of red squares and green circles in each part.
- Write the ratio as Red : Green.
- Simplify the ratio by dividing both numbers by their greatest common divisor (GCD).

---

#### (a)

```
Red squares: 2
Green circles: 4
```

Ratio:
$$
2 : 4
$$

Simplify by dividing both by 2:
$$
1 : 2
$$

✔ Answer: 1 : 2

---

#### (b)

```
Red squares: 6
Green circles: 2
```

Ratio:
$$
6 : 2
$$

Simplify by dividing both by 2:
$$
3 : 1
$$

✔ Answer: 3 : 1

---

#### (c)

```
Red squares: 6
Green circles: 10
```

Ratio:
$$
6 : 10
$$

Simplify by dividing both by 2:
$$
3 : 5
$$

✔ Answer: 3 : 5

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✔ Question 1 Answers:

- (a) $ 1 : 2 $
- (b) $ 3 : 1 $
- (c) $ 3 : 5 $

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🔷 Question 2: Simplify the following ratios

To simplify a ratio, find the GCD of the two numbers and divide both by it. For decimals, convert to whole numbers first.

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#### (a) 4 : 6

GCD of 4 and 6 is 2
$$
\frac{4}{2} : \frac{6}{2} = 2 : 3
$$

✔ 2 : 3

---

#### (b) 14 : 8

GCD of 14 and 8 is 2
$$
\frac{14}{2} : \frac{8}{2} = 7 : 4
$$

✔ 7 : 4

---

#### (c) 15 : 10

GCD of 15 and 10 is 5
$$
\frac{15}{5} : \frac{10}{5} = 3 : 2
$$

✔ 3 : 2

---

#### (d) 6 : 15

GCD of 6 and 15 is 3
$$
\frac{6}{3} : \frac{15}{3} = 2 : 5
$$

✔ 2 : 5

---

#### (e) 30 : 10

GCD is 10
$$
\frac{30}{10} : \frac{10}{10} = 3 : 1
$$

✔ 3 : 1

---

#### (f) 12 : 16

GCD is 4
$$
\frac{12}{4} : \frac{16}{4} = 3 : 4
$$

✔ 3 : 4

---

#### (g) 6 : 18

GCD is 6
$$
\frac{6}{6} : \frac{18}{6} = 1 : 3
$$

✔ 1 : 3

---

#### (h) 45 : 10

GCD is 5
$$
\frac{45}{5} : \frac{10}{5} = 9 : 2
$$

✔ 9 : 2

---

#### (i) 12 : 28

GCD is 4
$$
\frac{12}{4} : \frac{28}{4} = 3 : 7
$$

✔ 3 : 7

---

#### (j) 24 : 36

GCD is 12
$$
\frac{24}{12} : \frac{36}{12} = 2 : 3
$$

✔ 2 : 3

---

#### (k) 25 : 60

GCD is 5
$$
\frac{25}{5} : \frac{60}{5} = 5 : 12
$$

✔ 5 : 12

---

#### (l) 27 : 63

GCD is 9
$$
\frac{27}{9} : \frac{63}{9} = 3 : 7
$$

✔ 3 : 7

---

#### (m) 48 : 60

GCD is 12
$$
\frac{48}{12} : \frac{60}{12} = 4 : 5
$$

✔ 4 : 5

---

#### (n) 120 : 260

GCD is 20
$$
\frac{120}{20} : \frac{260}{20} = 6 : 13
$$

✔ 6 : 13

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#### (o) 8000 : 75

Find GCD of 8000 and 75.

Break down:
- 8000 = 8 × 1000 = $ 2^6 \times 5^3 $
- 75 = 3 × 5²

Common factor: $ 5^2 = 25 $

So divide both by 25:
$$
\frac{8000}{25} = 320,\quad \frac{75}{25} = 3
$$

✔ 320 : 3

---

#### (p) 33 : 121

Check GCD:
- 33 = 3 × 11
- 121 = 11 × 11

GCD = 11

$$
\frac{33}{11} : \frac{121}{11} = 3 : 11
$$

✔ 3 : 11

---

#### (q) 2.5 : 4.5

Convert to whole numbers by multiplying both by 10:
$$
25 : 45
$$

GCD of 25 and 45 is 5
$$
\frac{25}{5} : \frac{45}{5} = 5 : 9
$$

✔ 5 : 9

---

#### (r) 1.5 : 20

Multiply both by 10 to eliminate decimal:
$$
15 : 200
$$

GCD of 15 and 200 is 5
$$
\frac{15}{5} : \frac{200}{5} = 3 : 40
$$

✔ 3 : 40

---

#### (s) 6 : 1.2

Multiply both by 10:
$$
60 : 12
$$

GCD of 60 and 12 is 12
$$
\frac{60}{12} : \frac{12}{12} = 5 : 1
$$

✔ 5 : 1

---

#### (t) 2.25 : 4.95

Multiply both by 100 to eliminate decimals:
$$
225 : 495
$$

Now simplify:

Find GCD of 225 and 495.

Use Euclidean algorithm:
- 495 ÷ 225 = 2 remainder 45
- 225 ÷ 45 = 5 remainder 0 → GCD = 45

Divide both:
$$
\frac{225}{45} : \frac{495}{45} = 5 : 11
$$

✔ 5 : 11

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✔ Final Answers for Question 2:

| Part | Simplified Ratio |
|------|------------------|
| (a) | 2 : 3 |
| (b) | 7 : 4 |
| (c) | 3 : 2 |
| (d) | 2 : 5 |
| (e) | 3 : 1 |
| (f) | 3 : 4 |
| (g) | 1 : 3 |
| (h) | 9 : 2 |
| (i) | 3 : 7 |
| (j) | 2 : 3 |
| (k) | 5 : 12 |
| (l) | 3 : 7 |
| (m) | 4 : 5 |
| (n) | 6 : 13 |
| (o) | 320 : 3 |
| (p) | 3 : 11 |
| (q) | 5 : 9 |
| (r) | 3 : 40 |
| (s) | 5 : 1 |
| (t) | 5 : 11 |

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📌 Summary of Key Steps:

1. Count shapes carefully in visual problems.
2. Write the ratio as A:B.
3. Simplify by dividing both parts by the GCD.
4. For decimals, multiply both sides by 10, 100, etc., to make them whole numbers first.

Let me know if you'd like this as a printable PDF or want explanations for any specific part!