which two choices are equivalent to the fraction below 2/6
a. 1/2
b. 1/3
c. 4/12
d. 3/8
The correct answer and explanation is:
The fraction given is 2/6. To find equivalent fractions, the fraction must be simplified or compared to other fractions by cross-multiplying or finding a common denominator.
First, simplify 2/6 by dividing both numerator and denominator by their greatest common divisor, which is 2:
2 ÷ 2 = 1
6 ÷ 2 = 3
So, 2/6 simplifies to 1/3.
Now check the options:
a. 1/2
b. 1/3
c. 4/12
d. 3/8
Next, check if each fraction is equivalent to 2/6 by cross-multiplying:
For 1/2:
2 × 1 = 2
6 × 2 = 12
Since 2 ≠ 12, 2/6 ≠ 1/2.
For 1/3:
2 × 3 = 6
6 × 1 = 6
Since both products are equal, 2/6 = 1/3.
For 4/12:
2 × 12 = 24
6 × 4 = 24
Since both products are equal, 2/6 = 4/12.
For 3/8:
2 × 8 = 16
6 × 3 = 18
Since 16 ≠ 18, 2/6 ≠ 3/8.
Therefore, the two fractions equivalent to 2/6 are 1/3 and 4/12.
Equivalent fractions represent the same portion of a whole even though their numerators and denominators differ. Simplifying fractions helps to see this clearly by reducing the fraction to its simplest form. The fraction 2/6 simplifies to 1/3, so any fraction equal to 1/3 will be equivalent to 2/6. Another way to identify equivalent fractions is by multiplying or dividing both numerator and denominator of the fraction by the same nonzero number. For example, multiplying numerator and denominator of 1/3 by 4 gives 4/12, showing both fractions represent the same value. Checking equivalence through cross multiplication is a quick way to verify if two fractions are equal by comparing the products of numerator and denominator diagonally. This method avoids converting fractions to decimals or finding common denominators directly.