which fraction is greater 3/4 or 7/8
The Correct Answer and Explanation is:
To determine which fraction is greater between 3/4 and 7/8, we need to compare them.
First, convert both fractions to have a common denominator:
- The denominators are 4 and 8.
- The least common denominator (LCD) of 4 and 8 is 8.
Now convert 3/4 to an equivalent fraction with a denominator of 8:3/4=(3×2)/(4×2)=6/83/4 = (3 \times 2)/(4 \times 2) = 6/83/4=(3×2)/(4×2)=6/8
So we are comparing 6/8 and 7/8.
Since both have the same denominator, we just compare the numerators:
- 6 is less than 7
Therefore, 6/8 < 7/8, which means 3/4 < 7/8.
Final Answer:
7/8 is greater than 3/4.
Explanation
Fractions represent parts of a whole. When comparing two fractions, the easiest method is to make their denominators the same. A denominator tells us how many equal parts the whole is divided into, and the numerator tells us how many parts we have.
In this example, we are comparing 3/4 and 7/8. Since the denominators are different, we find the least common denominator, which is the smallest number that both denominators divide into evenly. The least common denominator of 4 and 8 is 8.
We then convert both fractions so they have the same denominator. We multiply both the numerator and denominator of 3/4 by 2 to get 6/8. This does not change the value of the fraction; it only changes its form. The fraction 7/8 already has 8 as its denominator, so it remains the same.
Now that both fractions have a common denominator, we can compare the numerators directly. 6/8 has a numerator of 6, and 7/8 has a numerator of 7. Since 7 is greater than 6, 7/8 is the larger fraction.
Another way to think about it is in terms of portions of a pie. If a pie is cut into 8 slices, having 6 slices (6/8) is less than having 7 slices (7/8). Similarly, 3/4 of a pie is the same as 6 out of 8 slices, which is slightly less than 7 out of 8 slices.
So, when comparing 3/4 and 7/8, the fraction 7/8 is clearly the greater one.
