1. **Problem:** Calculate $\frac{3}{2} + \frac{1}{4}$ correctly. 2. **Formula:** To add fractions, find a common denominator, then add the numerators. 3. **Work:** The denominators are 2 and 4. The least common denominator (LCD) is 4. 4. Convert $\frac{3}{2}$ to $\frac{6}{4}$ by multiplying numerator and denominator by 2. 5. Now add: $$\frac{6}{4} + \frac{1}{4} = \frac{6+1}{4} = \frac{7}{4}$$ 6. **Answer:** $\frac{7}{4}$ or $1 \frac{3}{4}$. 1. **Problem:** Calculate $2^4 \times 2^3$ and $\sqrt{144}$. 2. **Formula:** For powers with the same base, add exponents: $a^m \times a^n = a^{m+n}$. 3. **Work:** $$2^4 \times 2^3 = 2^{4+3} = 2^7 = 128$$ 4. Calculate square root: $$\sqrt{144} = 12$$ 5. **Answer:** $128$ and $12$. 1. **Problem:** Find next two terms of the sequence: 2, 4, 8, 16, 32, ... 2. **Pattern:** Each term is multiplied by 2 to get the next. 3. **Work:** Next terms: $32 \times 2 = 64$, $64 \times 2 = 128$. 4. **Answer:** Next two terms are 64 and 128. 1. **Problem:** Calculate area and perimeter of rectangle with length 12 cm and width 8 cm. 2. **Formula:** Area $= \text{length} \times \text{width}$, Perimeter $= 2(\text{length} + \text{width})$. 3. **Work:** Area: $$12 \times 8 = 96 \text{ cm}^2$$ 4. Perimeter: $$2(12 + 8) = 2 \times 20 = 40 \text{ cm}$$ 5. **Answer:** Area = 96 cm$^2$, Perimeter = 40 cm. 1. **Problem:** In a class of 30 students, 18 like math, 12 like science, 7 like both. 2. **Formula:** Only math = math - both, Only science = science - both. 3. **Work:** Only math: $$18 - 7 = 11$$ 4. Only science: $$12 - 7 = 5$$ 5. **Answer:** 11 students only like math, 5 only like science.