Here are the solutions and explanations for each problem presented in the image:
1. **9^2 × 4/3 = 108**
- First, calculate 9^2 = 81.
- Then, multiply 81 by 4/3: (81 × 4)/3 = 324/3 = 108.
2. **12 × 27 = 324**
- Multiply 12 by 27 directly to get 324.
3. **(108 + 324) ÷ 9 = 48**
- Add 108 and 324: 108 + 324 = 432.
- Then, divide 432 by 9: 432 ÷ 9 = 48.
4. **21 + 13 + 44 + 19 + 31 = 128**
- Add the numbers sequentially: 21 + 13 = 34, 34 + 44 = 78, 78 + 19 = 97, 97 + 31 = 128.
5. **(7/2 + 1/2) ÷ (1/3) = 12**
- Add the fractions in the numerator: 7/2 + 1/2 = 8/2 = 4.
- Divide 4 by 1/3: 4 ÷ 1/3 = 4 × 3/1 = 12.
6. **√324 ÷ 2 = 9**
- Find the square root of 324: √324 = 18.
- Divide 18 by 2: 18 ÷ 2 = 9.