Is 1/5 equivalent to 2/10?
Understand the Problem
The question is asking if the fraction one-fifth (1/5) has the same value as two-tenths (2/10). To determine this, we will compare the two fractions to see if they are equal.
Answer
Yes, $\frac{1}{5} = \frac{2}{10}$.
Answer for screen readers
Yes, $\frac{1}{5}$ has the same value as $\frac{2}{10}$.
Steps to Solve
- Understanding Fractions
We need to compare the two fractions: $\frac{1}{5}$ and $\frac{2}{10}$. The goal is to see if they are equivalent.
- Finding a Common Denominator
The denominators in our fractions are 5 and 10. The smallest common denominator is 10. We will convert $\frac{1}{5}$ to have a denominator of 10.
- Converting $\frac{1}{5}$ to $\frac{10}$
To convert $\frac{1}{5}$: Multiply the numerator and the denominator of $\frac{1}{5}$ by 2.
$$ \frac{1 \times 2}{5 \times 2} = \frac{2}{10} $$
- Comparing the Fractions
Now, both fractions can be compared as they have the same denominator:
- $\frac{1}{5} = \frac{2}{10}$
- $\frac{2}{10}$ is already given.
Since both are equal, we conclude that they represent the same value.
Yes, $\frac{1}{5}$ has the same value as $\frac{2}{10}$.
More Information
This fraction comparison shows how multiplying the numerator and denominator by the same number can create equivalent fractions. Understanding fractions helps in many aspects of math, including simplifying and adding fractions.
Tips
- A common mistake is not multiplying both the numerator and denominator by the same number, which results in incorrect conversions.
- Confusing the relationship between the numerators and denominators without converting them can also lead to errors.
