The fraction 2/8 equals which single fraction piece?
The Correct Answer and Explanation is :
The fraction ( \frac{2}{8} ) simplifies to ( \frac{1}{4} ).
Explanation:
To simplify a fraction, you divide both the numerator (the top number) and the denominator (the bottom number) by their greatest common divisor (GCD). In the case of ( \frac{2}{8} ), we first need to identify the GCD of 2 and 8.
- Finding the GCD: The GCD is the largest number that divides both the numerator and denominator without leaving a remainder. The factors of 2 are 1 and 2, while the factors of 8 are 1, 2, 4, and 8. The largest common factor is 2.
- Dividing by the GCD: Now, we divide both the numerator and denominator of ( \frac{2}{8} ) by their GCD:
- Numerator: ( 2 \div 2 = 1 )
- Denominator: ( 8 \div 2 = 4 ) Therefore, ( \frac{2}{8} ) simplifies to ( \frac{1}{4} ).
Understanding Fractions:
Fractions represent a part of a whole. In the context of ( \frac{2}{8} ), it means that we have 2 parts out of a total of 8 equal parts. When we simplify it to ( \frac{1}{4} ), we are saying that those 2 parts can be expressed as 1 part out of 4 equal parts.
Visualizing the Fractions:
To visualize this, imagine a pizza divided into 8 equal slices. If you take 2 slices, you have ( \frac{2}{8} ) of the pizza. If we were to cut the pizza into 4 equal slices instead, each of those larger slices would consist of 2 of the smaller slices. Hence, taking 2 of the original smaller slices corresponds to taking 1 of the larger slices, confirming that ( \frac{2}{8} = \frac{1}{4} ).
This process of simplifying fractions is essential in mathematics, as it helps make calculations easier and results clearer.