Is 1/2 equivalent to 3/6?

Understand the Problem

The question is asking whether the fraction 1/2 is equivalent to the fraction 3/6. To determine this, we can compare the two fractions and see if they represent the same value.

Answer

Yes, $\frac{1}{2} = \frac{3}{6}$.
Answer for screen readers

Yes, the fraction $\frac{1}{2}$ is equivalent to the fraction $\frac{3}{6}$.

Steps to Solve

  1. Convert fractions to decimals (if needed)

To determine if the fractions are equivalent, we can convert both fractions to decimals.

For $\frac{1}{2}$:

$$ \frac{1}{2} = 0.5 $$

For $\frac{3}{6}$:

$$ \frac{3}{6} = 0.5 $$

  1. Check if the decimals are equal

Now we will compare the two decimal values that we calculated.

Since both decimals are equal:

$$ 0.5 = 0.5 $$

  1. Cross-multiplication method

Another method is to use cross-multiplication. For the fractions $\frac{1}{2}$ and $\frac{3}{6}$:

We multiply the numerator of the first fraction by the denominator of the second fraction and vice versa:

  • For $\frac{1}{2}$, we have $1 \times 6 = 6$
  • For $\frac{3}{6}$, we have $3 \times 2 = 6$

Now we can compare:

$$ 1 \times 6 = 3 \times 2 $$ which simplifies to:

$$ 6 = 6 $$

  1. Conclusion on equivalence

Since we found that both fractions yield the same decimal value and the cross-multiplication shows they are equal, we can conclude that:

$$ \frac{1}{2} = \frac{3}{6} $$

Yes, the fraction $\frac{1}{2}$ is equivalent to the fraction $\frac{3}{6}$.

More Information

Both fractions represent the same part of a whole, which is 50%. This means that if you take 1 out of 2 equal parts, it's the same as taking 3 out of 6 equal parts.

Tips

  • A common mistake is incorrectly simplifying fractions or not using the cross-multiplication method correctly. To avoid this, double-check your calculations and ensure you understand each step.
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