Question

Find the sum of -2 5/10 and -5 4/15. Then, in two or more complete sentences, explain the steps you used to add the mixed numbers.

a) -7 9/30; To add mixed numbers, I first added the whole numbers, which gave me -7. Then, I added the fractions separately. For the fractions, I first found a common denominator, which was 30 in this case. Then, I added the fractions together, resulting in 9/30. Finally, I simplified 9/30 to 3/10, so the sum is -7 3/10.

b) -7 11/30; To add mixed numbers, I first added the whole numbers, which gave me -7. Then, I added the fractions separately. For the fractions, I first found a common denominator, which was 30 in this case. Then, I added the fractions together, resulting in 11/30.

c) -7 13/30; To add mixed numbers, I first added the whole numbers, which gave me -7. Then, I added the fractions separately. For the fractions, I first found a common denominator, which was 30 in this case. Then, I added the fractions together, resulting in 13/30.

d) -7 2/5; To add mixed numbers, I first added the whole numbers, which gave me -7. Then, I added the fractions separately. For the fractions, I first found a common denominator, which was 5 in this case. Then, I added the fractions together, resulting in 2/5.

Answer 1

The sum of -2 5/10 and -5 4/15 is -7 23/30, which is found by adding the whole numbers and fractions separately after converting them to a common denominator. Intuition helps in confirming the logic behind finding common denominators and adding fractions correctly.

Step-by-step explanation:

To find the sum of -2 5/10 and -5 4/15, we need to add the whole numbers and the fractions separately. For whole numbers: -2 + (-5) = -7. To add the fractions, we find a common denominator, which in this case is 30 (because it is the least common multiple of 10 and 15). Convert the fractions to equivalent ones with the common denominator: 5/10 becomes 15/30 and 4/15 becomes 8/30. Now, add the fractions: 15/30 + 8/30 = 23/30.

The mixed number sum is -7 23/30. There are no common factors between 23 and 30, so the fraction cannot be simplified further.

Intuition helps in understanding the need for common denominators and the fact that larger negative numbers indicate a smaller value when adding negative fractions. Understanding that adding fractions requires same denominators, and remembering not to add denominators, plays into our intuitive checks against nonsensical answers like ¼ + ½ = 2/3.