What is the simplest form of 36:48?
Understand the Problem
The question is asking for the simplest form of the ratio 36:48, which involves finding the greatest common divisor (GCD) of the two numbers and dividing both by that GCD to simplify the ratio.
Answer
The simplest form of the ratio $36:48$ is $3:4$.
Answer for screen readers
The simplest form of the ratio $36:48$ is $3:4$.
Steps to Solve
- Find the GCD of 36 and 48
To simplify the ratio, we first need to find the greatest common divisor (GCD) of the two numbers. The GCD is the largest number that divides both of them without leaving a remainder.
The factors of 36 are:
- 1, 2, 3, 4, 6, 9, 12, 18, 36
The factors of 48 are:
- 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
The common factors are:
- 1, 2, 3, 4, 6, 12
The greatest of these is 12. Thus, the GCD is 12.
- Divide both numbers by the GCD
Now we can simplify the ratio (36:48) by dividing both numbers by the GCD:
$$ \frac{36}{12} : \frac{48}{12} $$
This gives us:
$$ 3 : 4 $$
- Write the simplified ratio
So, the simplest form of the ratio (36:48) is (3:4).
The simplest form of the ratio $36:48$ is $3:4$.
More Information
Simplifying ratios is useful in many areas, such as cooking, scaling models, and even in financial calculations. Understanding how to find the GCD helps improve one’s mathematical reasoning and can be applied to various problems.
Tips
- Incorrect GCD calculation: Many might confuse smaller factors if they're not listed, leading to an incorrect GCD. Always list out factors carefully.
- Misapplying the simplification: Some might divide incorrectly, leading to wrong ratios. It's essential to divide both sides by the same GCD.
