Question

Here are three practice problems using negatives, decimals, and mixed numbers:

1) -23 3/4 + 15.6
2) 8.25 + -12 1/2
3) -7 2/3 + -4.75

Tell me if you want answers or step-by-step solutions.


step by step

Answer 1

Great — here are step-by-step solutions for each problem.

1) -23 3/4 + 15.6
- Convert the mixed number to a decimal: 3/4 = 0.75, so -23 3/4 = -23.75.
- Write with aligned decimals: -23.75 + 15.60.
- Because signs are different, subtract the smaller absolute value from the larger: 23.75 − 15.60 = 8.15.
- Keep the sign of the larger absolute value (23.75 is larger), so the result is -8.15.

Answer: -8.15

2) 8.25 + -12 1/2
- Convert the mixed number: 1/2 = 0.5, so -12 1/2 = -12.5.
- Write aligned: 8.25 + (-12.50).
- Signs differ, subtract: 12.50 − 8.25 = 4.25.
- Keep sign of larger absolute value (12.50), so result = -4.25.

Answer: -4.25

3) -7 2/3 + -4.75
(Using exact fractions)
- Convert to improper fractions:
-7 2/3 = -23/3 (because 7*3+2 = 23),
-4.75 = -4 3/4 = -19/4 (because 4*4+3 = 19).
- Add: -23/3 + -19/4 = -(23/3 + 19/4).
- Find common denominator 12: 23/3 = 92/12, 19/4 = 57/12. Sum = 149/12.
- So result = -149/12. Convert to a mixed number: 149/12 = 12 5/12, so the sum = -12 5/12.
(Decimal form ≈ -12.416666...)

Answer: -149/12 = -12 5/12 (≈ -12.416666...)