In Math 9, my partner and I completed an in-class exercise and ordered five rational numbers from least to greatest. Four of these numbers were represented as fractions, one as a decimal. We first assessed if the fractions had a common denominator. It turned out that 24 was the lowest common denominator for -3/4, 5/6, 7/8, and -1/3. Then, we multiplied numerators of these fractions with the factors that made the denominators 24. The results were:
- -3/4 = -18/24
- 5/6 = 20/24
- 7/8 = 21/24
- -1/3 = -8/24
In other words, the order for these four rational numbers was -3/4, -1/3, 5/6, 7/8.
However, there was still one rational number left to order: -0.6. We knew that -0.6 is equivalent to -6/10. However, 24 was not a common denominator for 10. To solve this problem, the easiest was to multiply the two denominators together:
- -0.6 = -144/240
- -3/4 = -180/240
- 5/6 = 200/240
- 7/8 = 210/240
- -1/3 = -80/240
The final order for the five rational numbers from least to greatest was -3/4, -0.6, -1/3, 5/6, 7/8.
We found that changing all rational numbers to a common denominator was the easiest method. Although 240 was not the lowest common denominator for 10 and 24, we chose to use it because it was easy to multiply the fractions by 10.