Is 3/8 smaller than 3/4?
Understand the Problem
The question is asking for a comparison between the fractions 3/8 and 3/4 to determine which one is smaller.
Answer
$\frac{3}{8} < \frac{3}{4}$
Answer for screen readers
The fraction $\frac{3}{8}$ is smaller than $\frac{3}{4}$.
Steps to Solve
- Find a common denominator
To compare the fractions $\frac{3}{8}$ and $\frac{3}{4}$, we need a common denominator. The least common multiple (LCM) of 8 and 4 is 8.
- Convert $\frac{3}{4}$ to have a denominator of 8
Now, we convert $\frac{3}{4}$ to an equivalent fraction with a denominator of 8. We do this by multiplying both the numerator and denominator by 2:
$$ \frac{3}{4} = \frac{3 \cdot 2}{4 \cdot 2} = \frac{6}{8} $$
- Compare the fractions
Now that both fractions have the same denominator, we can compare them directly:
$$ \frac{3}{8} \text{ and } \frac{6}{8} $$
Since 3 is less than 6, it follows that:
$$ \frac{3}{8} < \frac{6}{8} $$
This means that:
$$ \frac{3}{8} < \frac{3}{4} $$
The fraction $\frac{3}{8}$ is smaller than $\frac{3}{4}$.
More Information
When comparing fractions, having a common denominator allows for an easy visual comparison. Since we multiplied to find equivalent fractions, we can directly see that $\frac{3}{8}$ represents a smaller part of a whole compared to $\frac{3}{4}$.
Tips
- Not finding a common denominator: Always remember to compare fractions with the same denominator.
- Forgetting to convert correctly: Make sure to multiply both the numerator and denominator when converting a fraction.
