Write the ratio for 220 mins to 4 hours in fraction form ( simplify)
The Correct Answer and Explanation is:
To express the ratio of 220 minutes to 4 hours in fraction form, we begin by converting both quantities to the same unit. Since we have minutes and hours, we’ll first convert 4 hours to minutes.
1 hour = 60 minutes. So,
4 hours = 4 × 60 = 240 minutes.
Now, the ratio of 220 minutes to 240 minutes is: 220240\frac{220}{240}240220
Next, we simplify this fraction by finding the greatest common divisor (GCD) of 220 and 240. To do this, we first find the prime factorizations of the two numbers:
- 220 = 2 × 2 × 5 × 11
- 240 = 2 × 2 × 2 × 2 × 3 × 5
The common factors between 220 and 240 are 2 × 2 × 5, which equals 20. So, the GCD is 20.
Now, divide both the numerator and denominator of the fraction by 20: 220÷20240÷20=1112\frac{220 \div 20}{240 \div 20} = \frac{11}{12}240÷20220÷20=1211
Thus, the simplified ratio of 220 minutes to 4 hours is: 1112\frac{11}{12}1211
Explanation:
A ratio represents the relationship between two quantities. In this case, we are comparing 220 minutes to 4 hours. To compare these two, it’s important to express both quantities in the same unit. We choose minutes, as 220 minutes is already in that unit. Converting 4 hours to minutes ensures consistency, making the comparison more straightforward.
Once the ratio is established as 220240\frac{220}{240}240220, simplifying it requires finding the greatest common divisor (GCD). The GCD of two numbers is the largest number that can divide both numbers exactly. By dividing both the numerator and denominator of the fraction by 20 (the GCD), we simplify the ratio to 1112\frac{11}{12}1211.
This fraction now represents the simplified ratio of 220 minutes to 4 hours. It tells us that for every 12 parts of 240 minutes (4 hours), 11 parts are equivalent to 220 minutes.
