Question

Select all ratios equivalent to 2:3
3:4
20:30
22:33

Answer 1

To determine which ratios are equivalent to 2:3, we can simplify each ratio and see if it reduces to the same fraction.

1. **2:3** - This is our reference ratio.

2. **3:4** - To check if this is equivalent, we can cross-multiply:
- \(2 \times 4 = 8\)
- \(3 \times 3 = 9\)
Since \(8 \neq 9\), 3:4 is **not** equivalent to 2:3.

3. **20:30** - To check, we can simplify by dividing both parts of the ratio by their greatest common divisor, which is 10:
- \(20 ÷ 10 = 2\)
- \(30 ÷ 10 = 3\)
So, 20:30 simplifies to 2:3, making it **equivalent**.

4. **22:33** - Let's simplify this one by dividing both parts by their greatest common divisor, which is 11:
- \(22 ÷ 11 = 2\)
- \(33 ÷ 11 = 3\)
So, 22:33 simplifies to 2:3, making it **equivalent** as well.

Thus, the ratios equivalent to 2:3 are **20:30** and **22:33**.