Which is bigger, 2/5 or 3/7?
Understand the Problem
The question is asking to compare two fractions: 2/5 and 3/7 to determine which one is larger.
Answer
$ \frac{3}{7} $
Answer for screen readers
The larger fraction is $ \frac{3}{7} $.
Steps to Solve
- Find a Common Denominator
To compare the fractions, we first need a common denominator. The denominators are 5 and 7. The least common multiple (LCM) of 5 and 7 is 35.
- Convert Each Fraction
Now we will convert each fraction to have that common denominator of 35.
For $ \frac{2}{5} $: $$ \frac{2}{5} = \frac{2 \times 7}{5 \times 7} = \frac{14}{35} $$
For $ \frac{3}{7} $: $$ \frac{3}{7} = \frac{3 \times 5}{7 \times 5} = \frac{15}{35} $$
- Compare the Two Converted Fractions
Now we can compare the two fractions:
- $ \frac{14}{35} $ (which is $\frac{2}{5}$)
- $ \frac{15}{35} $ (which is $\frac{3}{7}$)
Since $ 14 < 15 $, we can conclude that $ \frac{14}{35} < \frac{15}{35} $.
- Determine Which Fraction is Larger
From the comparison, we find that:
$$ \frac{2}{5} < \frac{3}{7} $$
Therefore, $ \frac{3}{7} $ is the larger fraction.
The larger fraction is $ \frac{3}{7} $.
More Information
When comparing fractions, finding a common denominator makes it easier to see which fraction is larger. This method can be applied to any two fractions to determine their relative size.
Tips
- A common mistake is forgetting to convert both fractions to the common denominator before comparing them. This can lead to incorrect conclusions about which fraction is larger.
- Another mistake is miscalculating the multiplication when finding equivalent fractions. It's important to double-check the math.
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