How are 18:3 and 6:1 equivalent ratios
The Correct Answer and Explanation is :
To determine how the ratios 18:3 and 6:1 are equivalent, we need to simplify both ratios to see if they reduce to the same value.
Step 1: Simplifying the ratios
- For 18:3:
- To simplify this ratio, divide both terms by their greatest common divisor (GCD). The GCD of 18 and 3 is 3.
- Dividing both numbers by 3:
[
\frac{18}{3} : \frac{3}{3} = 6 : 1
]
- For 6:1:
- This ratio is already in its simplest form.
Now, we can see that both ratios simplify to 6:1.
Step 2: Understanding Equivalent Ratios
Equivalent ratios represent the same relationship between two quantities. When we say two ratios are equivalent, we mean that they express the same proportion.
In this case, both 18:3 and 6:1 can be interpreted in various contexts. For example, if you have 18 apples and 3 oranges, the ratio of apples to oranges is 18:3. When simplified, it shows that for every 6 apples, there is 1 orange, thus forming the ratio of 6:1.
Step 3: Applications of Equivalent Ratios
Understanding equivalent ratios is crucial in various fields, such as cooking, finance, and science. For instance, when adjusting a recipe, if you need to maintain the flavor balance, knowing that you can use either 18 cups of flour to 3 cups of sugar or 6 cups of flour to 1 cup of sugar allows flexibility in measurement without altering the recipe’s integrity.
In conclusion, 18:3 and 6:1 are equivalent ratios as they represent the same proportional relationship between two quantities, illustrating how simplification can reveal underlying connections between different numerical expressions.