Are 2/3 and 4/6 equivalent?
Understand the Problem
The question is asking whether the fractions 2/3 and 4/6 are equivalent, meaning they represent the same value. To determine this, we can simplify or compare the two fractions.
Answer
Yes, the fractions $ \frac{2}{3} $ and $ \frac{4}{6} $ are equivalent.
Answer for screen readers
Yes, the fractions $ \frac{2}{3} $ and $ \frac{4}{6} $ are equivalent.
Steps to Solve
- Simplifying the second fraction
First, we simplify the fraction $ \frac{4}{6} $. We can do this by finding the greatest common divisor (GCD) of the numerator and the denominator, which is 2.
So, we divide both the numerator and denominator by 2:
$$ \frac{4 \div 2}{6 \div 2} = \frac{2}{3} $$
- Comparing the simplified fractions
Now we can compare the simplified fraction $ \frac{2}{3} $ with the first fraction $ \frac{2}{3} $.
Since both fractions are now the same, we see that:
$$ \frac{2}{3} = \frac{2}{3} $$
- Conclusion about equivalence
Since the two fractions simplify to the same value, we can conclude that:
$$ \frac{2}{3} \text{ and } \frac{4}{6} \text{ are equivalent.} $$
Yes, the fractions $ \frac{2}{3} $ and $ \frac{4}{6} $ are equivalent.
More Information
Both fractions represent the same part of a whole and are equal. It's important to recognize that finding common denominators or simplifying fractions can help identify equivalences.
Tips
- A common mistake is assuming that two fractions are equivalent just because they look similar. Always simplify or find a common denominator to verify equivalence.
