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
- 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 $\frac{3}{6}$:
$$ \frac{3}{6} = 0.5 $$
- Check if the decimals are equal
Now we will compare the two decimal values that we calculated.
Since both decimals are equal:
$$ 0.5 = 0.5 $$
- 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:
$$ 6 = 6 $$
- 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.