Add and subtract fractions with the same denominator and denominators that are multiples of the same number - Reasoning

In a mathematical exercise exploring fractions, students are challenged to consider the different combinations that can be used to add two fractions with the same denominator to achieve a sum. Specifically, the task requires filling in two boxes with fractions that have an eighth as the denominator, in order to sum up to seven-eighths. This exercise not only tests the students' understanding of addition with fractions but also encourages them to think critically and reason out all the possible combinations.

The answer to the question reveals a systematic approach to finding all the combinations. Starting with zero-eighths added to seven-eighths and incrementally increasing the numerator of the first fraction while decreasing the numerator of the second, the students can find all the pairs that sum up to seven-eighths. The possible combinations are 0/8 + 7/8, 1/8 + 6/8, 2/8 + 5/8, 3/8 + 4/8, and their respective reversals. This exercise not only reinforces the concept of equivalent fractions and addition with like denominators but also introduces the idea that there are multiple solutions to a single problem, an important concept in mathematical reasoning.