-1/3, -11/-12, 5/-6, 7/9 in ascending order.. from chapter rational number
The Correct Answer and Explanation is:
To order the rational numbers −13-\frac{1}{3}−31, −1112-\frac{11}{12}−1211, 5−6\frac{5}{-6}−65, and 79\frac{7}{9}97 in ascending order, we first need to express these numbers in a comparable format and analyze their values.
Step 1: Convert the fractions into decimal form
- −13=−0.3333…-\frac{1}{3} = -0.3333\ldots−31=−0.3333… (repeating decimal)
- −1112=−0.9166…-\frac{11}{12} = -0.9166\ldots−1211=−0.9166… (repeating decimal)
- 5−6=−0.8333…\frac{5}{-6} = -0.8333\ldots−65=−0.8333… (repeating decimal)
- 79=0.7777…\frac{7}{9} = 0.7777\ldots97=0.7777… (repeating decimal)
Step 2: Compare the values
We now have the following approximate decimal values for the numbers:
- −13≈−0.3333-\frac{1}{3} \approx -0.3333−31≈−0.3333
- −1112≈−0.9166-\frac{11}{12} \approx -0.9166−1211≈−0.9166
- 5−6≈−0.8333\frac{5}{-6} \approx -0.8333−65≈−0.8333
- 79≈0.7777\frac{7}{9} \approx 0.777797≈0.7777
Step 3: Arrange them in ascending order
We can now compare the decimal values from the smallest to the largest:
- −1112≈−0.9166-\frac{11}{12} \approx -0.9166−1211≈−0.9166
- 5−6≈−0.8333\frac{5}{-6} \approx -0.8333−65≈−0.8333
- −13≈−0.3333-\frac{1}{3} \approx -0.3333−31≈−0.3333
- 79≈0.7777\frac{7}{9} \approx 0.777797≈0.7777
Thus, the rational numbers in ascending order are:−1112, 5−6, −13, 79-\frac{11}{12}, \ \frac{5}{-6}, \ -\frac{1}{3}, \ \frac{7}{9}−1211, −65, −31, 97
Explanation:
In general, when comparing rational numbers, it’s helpful to convert them to decimals or find a common denominator, but comparing their signs (positive or negative) and magnitude also plays a crucial role. Negative fractions with smaller absolute values are greater (closer to zero), while larger negative numbers are less (farther from zero). Similarly, positive fractions are always greater than any negative fraction.
