what is the fraction of 24/16 simplest form
The Correct Answer and Explanation is :
To simplify the fraction ( \frac{24}{16} ), we need to find the greatest common divisor (GCD) of the numerator (24) and the denominator (16).
Step 1: Find the GCD
The GCD of two numbers is the largest number that divides both of them without leaving a remainder.
- Factors of 24:
- The factors are: (1, 2, 3, 4, 6, 8, 12, 24).
- Factors of 16:
- The factors are: (1, 2, 4, 8, 16).
The common factors of 24 and 16 are (1, 2, 4). The greatest of these is (4).
Step 2: Divide by the GCD
Now we divide both the numerator and the denominator by the GCD, which is 4:
[
\frac{24 \div 4}{16 \div 4} = \frac{6}{4}
]
Step 3: Simplify Further
Next, we can simplify ( \frac{6}{4} ) further by finding the GCD of 6 and 4:
- Factors of 6:
- The factors are: (1, 2, 3, 6).
- Factors of 4:
- The factors are: (1, 2, 4).
The common factors of 6 and 4 are (1, 2), and the greatest is (2).
Now we simplify ( \frac{6}{4} ) by dividing both the numerator and the denominator by 2:
[
\frac{6 \div 2}{4 \div 2} = \frac{3}{2}
]
Conclusion
Thus, the fraction ( \frac{24}{16} ) simplified to its lowest terms is:
[
\frac{3}{2}
]
This means that for every 2 parts of the whole, there are 3 parts of the given quantity. Simplifying fractions is an essential skill in mathematics, as it helps to express ratios in their most efficient form, making calculations and comparisons easier.