Is 4/10 equivalent to 2/5?
Understand the Problem
The question is asking whether the fraction 4/10 is equivalent to the fraction 2/5. To determine this, we can simplify 4/10 to see if it equals 2/5.
Answer
Yes, $\\frac{4}{10}$ is equivalent to $\\frac{2}{5}$.
Answer for screen readers
Yes, the fraction $\frac{4}{10}$ is equivalent to the fraction $\frac{2}{5}$.
Steps to Solve
- Simplify the fraction $\frac{4}{10}$
To simplify the fraction $\frac{4}{10}$, we need to divide the numerator (4) and the denominator (10) by their greatest common divisor (GCD).
The GCD of 4 and 10 is 2.
So, we calculate:
$$ \frac{4 \div 2}{10 \div 2} = \frac{2}{5} $$
- Compare the simplified fraction to the other fraction
Now we compare the simplified fraction $\frac{2}{5}$ with the other fraction given, which is also $\frac{2}{5}$.
Since both fractions are equal, we can conclude that they are equivalent.
Yes, the fraction $\frac{4}{10}$ is equivalent to the fraction $\frac{2}{5}$.
More Information
Both fractions represent the same value, which is 0.4 when converted to decimal form. This shows that simplifying fractions is an important skill in mathematics, as it helps to recognize equivalencies easily.
Tips
- A common mistake is to forget to reduce the fraction by the correct GCD. Always double-check the GCD for both the numerator and denominator.
- Another mistake is to compare fractions without simplifying them, which may lead to incorrect conclusions.
