Which is bigger, 3/5 or 2/3?
Understand the Problem
The question is asking to compare two fractions, 3/5 and 2/3, to determine which one is larger.
Answer
$ \frac{2}{3} $
Answer for screen readers
The larger fraction is $ \frac{2}{3} $.
Steps to Solve
- Find a Common Denominator
To compare the fractions $ \frac{3}{5} $ and $ \frac{2}{3} $, we need to find a common denominator. The denominators here are 5 and 3. The least common multiple (LCM) of 5 and 3 is 15.
- Convert the Fractions
Next, we convert both fractions to have the common denominator of 15.
For $ \frac{3}{5} $, we multiply both the numerator and the denominator by 3: $$ \frac{3 \times 3}{5 \times 3} = \frac{9}{15} $$
For $ \frac{2}{3} $, we multiply both the numerator and the denominator by 5: $$ \frac{2 \times 5}{3 \times 5} = \frac{10}{15} $$
- Compare the New Fractions
Now, we can compare the two fractions, which are now $ \frac{9}{15} $ and $ \frac{10}{15} $. Since both fractions have the same denominator, we only need to compare their numerators.
- Conclusion
Since 10 is greater than 9, we conclude that: $$ \frac{10}{15} > \frac{9}{15} $$ Thus, $ \frac{2}{3} $ is greater than $ \frac{3}{5} $.
The larger fraction is $ \frac{2}{3} $.
More Information
When comparing fractions, converting to a common denominator makes it easier to see which is larger. Understanding this helps in many areas of math, such as solving equations and analyzing inequalities.
Tips
- A common mistake is forgetting to find the common denominator before comparing the fractions. This can lead to incorrect conclusions. Ensure that both fractions are expressed with the same denominator.
