Compare the fraction 3/5 to 1/2
The Correct Answer and Explanation is :
To compare the fractions ( \frac{3}{5} ) and ( \frac{1}{2} ), we need to determine which fraction is larger.
Step 1: Finding a common denominator
The first step in comparing fractions is to find a common denominator. To do this, we look for the least common denominator (LCD), which is the smallest number that both denominators (5 and 2) can divide into evenly.
The least common denominator of 5 and 2 is 10, because 10 is the smallest multiple that both 5 and 2 divide into without leaving a remainder.
Step 2: Converting the fractions
Next, we convert both fractions so they have the same denominator of 10.
For ( \frac{3}{5} ), we multiply both the numerator and denominator by 2 to get:
[
\frac{3}{5} = \frac{3 \times 2}{5 \times 2} = \frac{6}{10}
]
For ( \frac{1}{2} ), we multiply both the numerator and denominator by 5 to get:
[
\frac{1}{2} = \frac{1 \times 5}{2 \times 5} = \frac{5}{10}
]
Step 3: Comparing the fractions
Now that both fractions have the same denominator (10), we can compare their numerators directly. We have:
[
\frac{6}{10} \quad \text{and} \quad \frac{5}{10}
]
Since 6 is greater than 5, it follows that ( \frac{6}{10} ) is larger than ( \frac{5}{10} ). Therefore, ( \frac{3}{5} > \frac{1}{2} ).
Conclusion:
Thus, ( \frac{3}{5} ) is greater than ( \frac{1}{2} ).
Explanation:
The key idea behind comparing fractions is to find a common denominator, which allows you to compare the fractions directly. Once we expressed both fractions with the same denominator, we could easily compare the numerators to determine which fraction is larger. The larger the numerator, the larger the fraction. In this case, ( \frac{3}{5} ) is larger than ( \frac{1}{2} ) because 6 (the numerator of ( \frac{3}{5} )) is greater than 5 (the numerator of ( \frac{1}{2} )).