simplify 48/60
Understand the Problem
The question is asking to simplify the fraction 48/60 to its lowest terms. To solve this, we will find the greatest common divisor (GCD) of the numerator and denominator and then divide both by this number.
Answer
The simplified fraction is \( \frac{4}{5} \).
Answer for screen readers
The simplified form of the fraction ( \frac{48}{60} ) is ( \frac{4}{5} ).
Steps to Solve
- Find the GCD of 48 and 60
First, we need to determine the greatest common divisor (GCD) of the numerator (48) and the denominator (60).
The GCD is the largest number that divides both 48 and 60 without leaving a remainder. The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48. The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.
The common factors are 1, 2, 3, 4, and 6. The largest of these is 12. Thus, the GCD is 12.
- Divide the numerator and denominator by the GCD
Now, we will simplify the fraction by dividing both the numerator and the denominator by their GCD.
[ \frac{48 \div 12}{60 \div 12} = \frac{4}{5} ]
- Final check for simplicity
Now that we have $\frac{4}{5}$, we check if it can be simplified further. The numerator (4) and the denominator (5) have no common factors besides 1, so this is indeed in its simplest form.
The simplified form of the fraction ( \frac{48}{60} ) is ( \frac{4}{5} ).
More Information
Simplifying fractions is an important skill in mathematics that helps in understanding proportions and ratios. The process of finding the GCD can also be important in number theory and has applications in various fields, including engineering and computer science.
Tips
- Not finding the GCD correctly: Always double-check the factors to ensure that the GCD is accurate.
- Forgetting to simplify: Make sure to divide both the numerator and denominator by the GCD to simplify the fraction properly.
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