Are 600: 450 and 60: 45 equivalent ratios? Let’s find out!
To determine equivalent ratios, we simplify each ratio by dividing both numbers by their greatest common divisor (GCD). For 600: 450, the GCD is 150, resulting in 4:3. For 60: 45, the GCD is 15, also resulting in 4:3.
How it works:
For 600: 450
1. Find the greatest common divisor (GCD) of 600 and 450.
2. Factors of 600: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, 300, 600
3. Factors of 450: 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450
4. The greatest common divisor (GCD) is 150.
5. Divide both numbers by the GCD: 600 ÷ 150 = 4, 450 ÷ 150 = 3
6. Simplified ratio: 4:3
For 60: 45
1. Find the greatest common divisor (GCD) of 60 and 45.
2. Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
3. Factors of 45: 1, 3, 5, 9, 15, 45
4. The greatest common divisor (GCD) is 15.
5. Divide both numbers by the GCD: 60 ÷ 15 = 4, 45 ÷ 15 = 3
6. Simplified ratio: 4:3
Since both ratios simplify to 4:3, they are indeed equivalent. This means that the relationship between the numbers in each ratio is the same. Equivalent ratios are essential in math, and now you know how to identify them!
