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 (1)
Simplify the fraction 6 2 to 3 1 .
Check each option to see if it is equal to the simplified fraction.
9 3 simplifies to 3 1 , so it is equivalent to 6 2 .
The equivalent fraction is 9 3 .
Explanation
Simplifying the Fraction We need to find which fraction is equivalent to 6 2 . First, let's simplify 6 2 . Both the numerator and the denominator are divisible by 2, so we can divide both by 2: 6 2 = 6 ÷ 2 2 ÷ 2 = 3 1 Now we need to check which of the given fractions is equal to 3 1 .
Checking the First Option Let's examine the first option: 7 3 . Is 7 3 = 3 1 ? No, because 7 3 ≈ 0.4286 and 3 1 ≈ 0.3333 . The reasoning provided, 6 2 = 6 + 1 2 + 1 = 7 3 , is incorrect. You cannot simply add the same number to the numerator and denominator to get an equivalent fraction.
Checking the Second Option Now let's examine the second option: 9 3 . Is 9 3 = 3 1 ? Yes, because if we divide both the numerator and the denominator of 9 3 by 3, we get: 9 3 = 9 ÷ 3 3 ÷ 3 = 3 1 So, 9 3 is equivalent to 3 1 , which is the simplified form of 6 2 .
Checking the Third Option Let's examine the third option: 12 3 . Is 12 3 = 3 1 ? No, because 12 3 = 4 1 , not 3 1 .
Checking the Fourth Option Finally, let's examine the fourth option: 8 3 . Is 8 3 = 3 1 ? No, because 8 3 = 0.375 and 3 1 ≈ 0.3333 .
Final Answer Therefore, the fraction equivalent to 6 2 is 9 3 .
Examples
Understanding equivalent fractions is crucial in cooking. For example, if a recipe calls for 6 2 of a cup of flour, you might find it easier to measure 3 1 of a cup or 9 3 of a cup using standard measuring tools. Recognizing these fractions as equivalent allows for flexibility and precision in following recipes, ensuring consistent results in your culinary creations.
