The ratio $60: 48$ in its simplest form is
Answer (1)
Find the greatest common divisor (GCD) of 60 and 48, which is 12.
Divide both parts of the ratio by the GCD: 12 60 = 5 and 12 48 = 4 .
Express the simplified ratio as 5 : 4 .
The simplest form of the ratio 60 : 48 is 5 : 4 .
Explanation
Understanding the Problem We are given the ratio 60 : 48 and asked to express it in its simplest form. To do this, we need to find the greatest common divisor (GCD) of 60 and 48, and then divide both numbers by their GCD.
Finding the Greatest Common Divisor (GCD) The greatest common divisor (GCD) of two numbers is the largest number that divides both of them without leaving a remainder. We can find the GCD of 60 and 48 using the Euclidean algorithm or by listing the factors of each number. The result of this operation is 12.
Dividing by the GCD Now, we divide both parts of the ratio by the GCD, which is 12: 12 60 = 5 12 48 = 4
Simplifying the Ratio So, the simplified ratio is 5 : 4 .
Final Answer Therefore, the ratio 60 : 48 in its simplest form is 5 : 4 .
Examples
Ratios are used in everyday life, such as when cooking, mixing paint, or calculating distances on a map. For example, if a recipe calls for a ratio of 2 parts water to 1 part juice concentrate, simplifying the ratio helps to easily scale the recipe up or down. In this case, simplifying ratios makes it easier to understand and apply proportions in various practical situations.
