Question

Which set of mixed numbers has a difference less than 1? A. 1^ 2/9, 1^ 1/9B. 3^ 4/7, 2^ 1/7C. 2^ 4/5, 1^ 1/3D. 2^ 7/9 , 1^ 1/3​

Answer 1

The set of mixed numbers with a difference less than 1 is 12/9 and 11/9 (Option A). This is because their difference, 1/9, is less than 1, whereas the differences in the other options are all greater than 1.

Step-by-step explanation:

To determine which set of mixed numbers has a difference less than 1, we subtract the smaller mixed number from the larger one in each set. Here are the calculations for each option:

• For A. 12/9 and 11/9, the difference is 12/9 - 11/9 = 1/9, which is less than 1.
• For B. 34/7 and 21/7, the difference is 34/7 - 21/7 = 13/7, which is greater than 1.
• For C. 24/5 and 11/3, the difference is 24/5 - 11/3, which needs to be calculated using a common denominator. Converting to denominators of 15, we get 212/15 - 15/15 = 17/15, which is greater than 1.
• For D. 27/9 and 11/3, the difference can be calculated by finding a common denominator, but regardless, it will be greater than 1 since the whole number part itself provides a difference of 1.

Option A is the only set with a difference less than 1.