Express each of the following ratios in simplest form 40:5
The Correct Answer and Explanation is :
The correct answer is: 8:1
To express the ratio (40:5) in its simplest form, we need to divide both terms of the ratio by their greatest common divisor (GCD).
Step 1: Find the GCD
The GCD of two numbers is the largest number that divides both of them without leaving a remainder. For the numbers 40 and 5, we can identify the factors of each:
- Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
- Factors of 5: 1, 5
The common factors are 1 and 5, with 5 being the greatest. Therefore, the GCD of 40 and 5 is 5.
Step 2: Divide Both Terms by the GCD
Now, we divide both parts of the ratio by the GCD:
[
\frac{40}{5} : \frac{5}{5}
]
This simplifies to:
[
8 : 1
]
Conclusion
The ratio (40:5) in its simplest form is (8:1).
Explanation of Ratios
Ratios are a way to compare two or more quantities, showing their relative sizes. They can be expressed in several forms, including fractions, decimals, or the “a:b” format, as we see here.
Simplifying a ratio is important because it allows for easier interpretation and comparison. For example, if we have a recipe that uses ingredients in a ratio of 40:5, simplifying it to 8:1 means that for every 8 parts of one ingredient, there is 1 part of another.
Ratios are commonly used in various fields, including cooking, finance, and engineering. In cooking, for instance, understanding the ratio of ingredients can help scale recipes up or down. In finance, ratios like debt-to-equity or price-to-earnings help investors assess the health and value of a company.
Overall, simplifying ratios helps clarify relationships between quantities, making it easier to understand their proportions and effects in practical situations.