Is 1/2 Greater Than 2/3? Comparing Fractions

Between 1/2 and 2/3, the fraction 2/3 is greater. If we compare 1/2 and 2/3, then 2/3 is the bigger fraction.

To compare 1/2 and 2/3, we first convert them to equivalent fractions with the same denominator. Then compare the numerators. The fraction with the greater numerator will be the larger fraction.

Is 2/3 Greater Than 1/2?

Answer: Yes, 2/3 is greater than 1/2.

Explanation:

The denominators of 1/2 and 2/3 are respectively 2 and 3.

Step 1: Finding Common Denominator.

To compare 1/2 and 2/3, let us convert these fractions to equivalent fractions with common denominator = least common multiple (LCM) of 2 and 3.

We now find the LCM of 2 and 3.

The multiples of 2 are 2, 4, 6, 8, 10, etc. The multiples of 3 are 3, 6, 9, 12, etc.

So the least common multiple of 2 and 3 is 6. That is,

LCM (2, 3) = 6.

Step 2: Convert to Equivalent Fractions with Common Denominator

We now convert 1/2 and 2/3 to equivalent fractions with common denominator 6 = LCM (2, 3).

For 1/2, multiply the numerator and the denominator by 3 to make the denominator 6.

$\dfrac{1}{2} = \dfrac{1 \times 3}{2 \times 3} = \dfrac{3}{6}$.

For 2/3, multiply the numerator and the denominator by 2 to make the denominator 6.

$\dfrac{2}{3} = \dfrac{2 \times 2}{3 \times 2} = \dfrac{4}{6}$.

Step 3: Now compare the numerators.

As 3 < 4, we have that

$\dfrac{3}{6} < \dfrac{4}{6}$.

This implies that

$\dfrac{1}{2} < \dfrac{2}{3}$.

Conclusion: Therefore, the fraction 1/2 is less than 2/3.

More Reading: Is 1/3 Greater Than 3/4?

1/2 or 2/3 Which Fraction is Larger?

We can compare 1/2 and 2/3 by converting them to decimals. Note that

$\dfrac{1}{2}=0.5$ $\dfrac{2}{3}=0.666$

Now compare the decimals 0.666 and 0.5. As 0.666 > 0.5, we conclude that the fraction 2/3 is larger than 1/2.

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