What is bigger ?5/8 or 3/4
The Correct Answer and Explanation is :
To compare the fractions ( \frac{5}{8} ) and ( \frac{3}{4} ), we first need to express them with a common denominator or convert them to decimals.
Method 1: Common Denominator
The denominators of the fractions are 8 and 4. The least common denominator (LCD) of 8 and 4 is 8. We can convert ( \frac{3}{4} ) to have this common denominator:
[
\frac{3}{4} = \frac{3 \times 2}{4 \times 2} = \frac{6}{8}
]
Now we have:
- ( \frac{5}{8} )
- ( \frac{6}{8} )
Now that both fractions have the same denominator, we can compare the numerators. Since 5 is less than 6, we conclude that:
[
\frac{5}{8} < \frac{6}{8}
]
Thus, ( \frac{5}{8} < \frac{3}{4} ).
Method 2: Decimal Conversion
Alternatively, we can convert both fractions to decimals to compare them directly:
- To convert ( \frac{5}{8} ):
[
\frac{5}{8} = 0.625
]
- To convert ( \frac{3}{4} ):
[
\frac{3}{4} = 0.75
]
Now, comparing the decimal values:
- ( 0.625 < 0.75 )
This confirms our earlier conclusion that ( \frac{5}{8} < \frac{3}{4} ).
Conclusion
Both methods indicate that ( \frac{3}{4} ) is greater than ( \frac{5}{8} ). This understanding of comparing fractions through finding a common denominator or converting them to decimals is crucial in mathematics, as it enhances our ability to make comparisons between different numerical values, aiding in a variety of mathematical and real-world applications. Therefore, the answer is that ( \frac{3}{4} ) is larger than ( \frac{5}{8} ).