Final answer:
To find the missing values in pairs of equivalent fractions like 2/3 and 5/6, and 3/4 and 7/8, we establish a common denominator and adjust the numerators. The complete pairs are 2/3 and 4/6, and 3/4 and 6/8.
Step-by-step explanation:
When finding the missing value in each pair of equivalent fractions, we use the concept of a common denominator. To make fractions equivalent, we need to find a number that both denominators can multiply into, which becomes the common denominator. Then, adjust the numerators accordingly to maintain the value of the fractions.
Let's look at the pairs of fractions you provided: 2/3 and 5/6, 3/4 and 7/8. To find the missing values, we can cross-multiply and solve for the unknown. For example, to make 2/3 equivalent to something over 6, we multiply both the numerator and denominator of 2/3 by 2. This gives us 4/6, which is equivalent to 2/3. Now, it's clear that the missing numerator for 5/6 to be equivalent to 2/3 is 5.
Similarly, to make 3/4 equivalent to something over 8, we multiply both the numerator and denominator of 3/4 by 2. This gives us 6/8, which is equivalent to 3/4. So, the missing numerator for 7/8 to be equivalent to 3/4 is 7.
In conclusion, using the common denominator approach, the complete pairs of equivalent fractions are 2/3 and 4/6, 3/4 and 6/8.