Comparison of -5/9 and -3/4

Values:
-5/9 and -3/4 are both negative rational numbers. The first fraction, -5/9, can be expressed as -0.555... when rounded to three decimal places. The second fraction, -3/4, can be expressed as -0.75 when rounded to two decimal places.

Numerical Comparison:
-5/9 is closer to zero than -3/4 because -0.555... is greater than -0.75. This indicates that -5/9 is a larger number in the negative rational spectrum compared to -3/4.

Common Denominator:
To compare the two fractions directly, we can find a common denominator. The least common multiple of 9 and 4 is 36. Therefore, when both fractions are expressed with a denominator of 36, we get -20/36 and -27/36.

Decimal Equivalents:
-20/36 simplifies to -5/9, which we already know is approximately -0.555... -27/36 simplifies to -3/4, which is exactly -0.75. This confirms our earlier comparison that -5/9 is greater than -3/4.

Conclusion:
In conclusion, -5/9 is greater than -3/4 when comparing their decimal equivalents and common denominators. This comparison highlights the importance of understanding fractions and decimals in order to accurately compare rational numbers.