Express the following in simplest form 49:35
The Correct Answer and Explanation is:
Correct Answer:
7:5
To simplify the ratio 49:35, we follow the same process used to simplify fractions. A ratio is essentially a comparison between two numbers, and we want to express this comparison in its simplest form by dividing both parts of the ratio by their greatest common divisor (GCD).
Step 1: Identify the GCD of 49 and 35
- The number 49 is divisible by 1, 7, and 49
- The number 35 is divisible by 1, 5, 7, and 35
- The greatest common divisor of 49 and 35 is 7
Step 2: Divide both terms of the ratio by the GCD
- 49 ÷ 7 = 7
- 35 ÷ 7 = 5
So, the simplified ratio becomes 7:5.
Why This Simplification Matters
Understanding how to simplify ratios is important because it helps present information in the clearest and most efficient way possible. Simplified ratios are easier to compare and understand, especially in real-life contexts like mixing ingredients, sharing quantities, or calculating rates.
For example, if you had 49 apples and 35 oranges and wanted to know the simplest ratio between them, you could say the ratio is 7:5. That means for every 7 apples, there are 5 oranges. This helps communicate the relationship in a compact and understandable form.
It also shows proportional relationships clearly. If you double both quantities, you’d have 14 apples and 10 oranges, which still keeps the 7:5 ratio. This kind of understanding is essential in mathematics, science, economics, and even everyday tasks like cooking or budgeting.
In conclusion, the simplest form of the ratio 49:35 is 7:5, achieved by dividing both numbers by their greatest common divisor, which is 7.
