Is 3/4 Bigger Than 2/3

To compare fractions, we need to find a common denominator. The least common multiple (LCM) of 4 and 3 is 12. So, we’ll convert both fractions to have a denominator of 12.

³⁄₄ = (3 × 3) / (4 × 3) = ⁹⁄₁₂ ²⁄₃ = (2 × 4) / (3 × 4) = ⁸⁄₁₂

Now we can compare the two fractions:

⁹⁄₁₂ > ⁸⁄₁₂

Since 9 is greater than 8, we can conclude that ³⁄₄ is indeed bigger than ²⁄₃.

To put it simply, if you had a pizza that was cut into 4 slices and you ate 3 of them, you’d have eaten more of the pizza than if it were cut into 3 slices and you ate 2 of them.

Here’s a simple way to visualize it:

³⁄₄ = ████████████╗ (9 out of 12 parts) ²⁄₃ = ███████████ (8 out of 12 parts)

As you can see, ³⁄₄ covers more area than ²⁄₃, making it the larger fraction.

Key Takeaway

When comparing fractions, finding a common denominator can help you determine which one is larger. In this case, ³⁄₄ is bigger than ²⁄₃ because ⁹⁄₁₂ is greater than ⁸⁄₁₂.

Step-by-Step Solution

1. Find the least common multiple (LCM): Determine the smallest number that both denominators (4 and 3) can divide into evenly. In this case, the LCM is 12.
2. Convert fractions to have the same denominator: Multiply the numerator and denominator of each fraction by the necessary factor to get a denominator of 12.
3. Compare the fractions: Now that both fractions have the same denominator, compare the numerators (9 and 8) to determine which fraction is larger.

Pro-Con Analysis

Pros of using a common denominator: - Easy to compare fractions - Simple to visualize the difference - Works for any two fractions

Cons of using a common denominator: - May require additional calculations - Can be confusing if the LCM is large

By following these steps and understanding the concept of comparing fractions, you’ll be able to determine which fraction is larger in any given situation.

In conclusion, comparing fractions with different denominators can be achieved by finding a common denominator, converting the fractions, and then comparing the numerators. By following these steps and practicing with different fractions, you’ll become proficient in comparing fractions and understanding their relative sizes.