Which fraction is equivalent to $\frac{2}{6}$?
A. $\frac{3}{7}$, because $\frac{2}{6}=\frac{2+1}{6+1}=\frac{3}{7}$
B. $\frac{3}{9}$, because $\frac{2}{6}=\frac{1}{3}$ and $\frac{1}{3}=\frac{3}{9}$
C. $\frac{3}{12}$, because $\frac{2}{6}=\frac{1}{3}$ and $\frac{1}{3}=\frac{3}{12}$
D. $\frac{3}{8}$, because $\frac{2}{6}=\frac{1}{2}=\frac{2+1}{6+2}=\frac{3}{8}$
Answer (2)
Simplify the given fraction: 6 2 = 3 1 .
Check each option to see if it is equivalent to 3 1 .
9 3 simplifies to 3 1 .
Therefore, the equivalent fraction is 9 3 .
Explanation
Problem Analysis We need to determine which fraction is equivalent to 6 2 . To do this, we will simplify 6 2 and then compare it to the given options.
Simplifying the Fraction First, let's simplify the fraction 6 2 . Both the numerator and the denominator are divisible by 2. Dividing both by 2, we get: 6 2 = 6 ÷ 2 2 ÷ 2 = 3 1
Checking the Options Now, let's examine each option to see if it is equivalent to 3 1 .
Analyzing Option 1 Option 1: 7 3 . This is not equal to 3 1 . The reasoning provided, 6 2 = 6 + 1 2 + 1 = 7 3 , is incorrect because you cannot simply add the same number to the numerator and denominator to find an equivalent fraction.
Analyzing Option 2 Option 2: 9 3 . We can simplify this fraction by dividing both the numerator and the denominator by 3: 9 3 = 9 ÷ 3 3 ÷ 3 = 3 1 Since 9 3 = 3 1 , this option is correct.
Analyzing Option 3 Option 3: 12 3 . We can simplify this fraction by dividing both the numerator and the denominator by 3: 12 3 = 12 ÷ 3 3 ÷ 3 = 4 1 Since 12 3 = 4 1 and 4 1 = 3 1 , this option is incorrect.
Analyzing Option 4 Option 4: 8 3 . This fraction is not equal to 3 1 . The reasoning provided is also incorrect.
Final Answer Therefore, the fraction equivalent to 6 2 is 9 3 .
Examples
Fractions are used in everyday life, such as when cooking, measuring ingredients, or splitting a bill with friends. For example, if you want to make half of a recipe that calls for 6 2 cup of flour, you need to find an equivalent fraction that is easier to work with. In this case, you would simplify 6 2 to 3 1 , so you know you need 3 1 cup of flour.
The fraction equivalent to 6 2 is 9 3 , as both simplify to 3 1 . Therefore, the correct answer is option B. This shows how fractions can represent the same value even if they look different initially.
;
