simplify 35:49
Understand the Problem
The question asks to simplify the ratio 35:49. This involves finding the greatest common divisor of the two numbers and dividing both numbers by it to get their simplest form.
Answer
The simplified ratio of 35:49 is $5:7$.
Answer for screen readers
The simplified ratio of 35:49 is $5:7$.
Steps to Solve
- Identify the numbers in the ratio
We have the ratio 35:49. The two numbers are 35 and 49.
- Find the greatest common divisor (GCD)
We need to determine the GCD of 35 and 49 to simplify the ratio. The GCD is the largest number that divides both.
- The factors of 35 are: 1, 5, 7, 35
- The factors of 49 are: 1, 7, 49
From the factors, we see that the GCD is 7.
- Divide both numbers by the GCD
Now we divide both numbers in the ratio by the GCD.
$$ \frac{35}{7} = 5 $$
$$ \frac{49}{7} = 7 $$
- Write the simplified ratio
After dividing both numbers by their GCD, the simplified ratio is expressed as:
$$ 5:7 $$
The simplified ratio of 35:49 is $5:7$.
More Information
Simplifying ratios is an important skill in mathematics as it helps in comparing quantities in their most basic form. This practice is useful in various real-life scenarios like cooking and budgeting.
Tips
A common mistake when simplifying ratios is failing to find the correct GCD or overlooking to divide both terms of the ratio by the GCD, which leads to incorrect simplification.
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