Final answer:
To order the fractions from least to greatest, the list goes -53/7, -46/7, -43/7, 42/7, 51/7, considering both the negative values, which are smaller, and absolute values for comparison.
Step-by-step explanation:
Ordering the given fractions from least to greatest first involves recognizing that negative numbers are smaller than positive numbers and that within the negatives, a larger absolute value means a smaller number. In the given set (-43/7, -46/7, -53/7, 42/7, 51/7), we can arrange them from least to greatest by comparing their absolute values and taking their signs into account.
- -53/7 (since it's the negative with the largest absolute value, it's the smallest)
- -46/7 (next largest absolute value among negatives)
- -43/7 (smallest absolute value among the negatives, but still negative)
- 42/7 (the smallest positive number)
- 51/7 (the largest number overall in this set)
Thus, the numbers in order from least to greatest are: -53/7, -46/7, -43/7, 42/7, 51/7.