What is the ratio 100:120 in it’s simplest form?
The Correct Answer and Explanation is:
The ratio 100:120 in its simplest form is 5:6.
Explanation:
A ratio compares two quantities, showing how many times one value contains or is contained within the other. To simplify a ratio, you need to divide both numbers by their greatest common divisor (GCD), which is the largest number that can divide both values without leaving a remainder.
Step-by-step process:
- Write the ratio:
The ratio is given as 100:120. This means that for every 100 units of one quantity, there are 120 units of another quantity. - Find the GCD:
The GCD of 100 and 120 is the largest number that can evenly divide both 100 and 120. Let’s break down the prime factors:
- The prime factorization of 100 is ( 2^2 \times 5^2 ).
- The prime factorization of 120 is ( 2^3 \times 3 \times 5 ). The common factors between 100 and 120 are ( 2^2 \times 5 ), which gives us 20. Therefore, the GCD of 100 and 120 is 20.
- Divide both numbers by the GCD:
To simplify the ratio, divide both 100 and 120 by their GCD:
- ( 100 \div 20 = 5 )
- ( 120 \div 20 = 6 )
- Simplified ratio:
After dividing both numbers by 20, the simplified ratio becomes 5:6.
Understanding the simplified ratio:
The simplified ratio 5:6 means that for every 5 units of one quantity, there are 6 units of the other. This ratio is equivalent to the original, but it’s in its simplest form, making it easier to understand and use in practical applications.
Ratios are often simplified to make comparisons more straightforward, and this process is similar to simplifying fractions in mathematics. The key idea is reducing the ratio to the smallest whole numbers that maintain the same proportion.