1. **Write 0.25 as a common fraction in simplest form.** 0.25 means 25 hundredths, so as a fraction it is $\frac{25}{100}$. To simplify, find the greatest common divisor (GCD) of 25 and 100, which is 25. Divide numerator and denominator by 25: $$\frac{25 \div 25}{100 \div 25} = \frac{1}{4}$$ So, 0.25 as a simplest fraction is $\frac{1}{4}$. 2. **Complete the table:** | COMMON FRACTIONS | DECIMAL FRACTIONS | PERCENTAGE | |------------------|-------------------|------------| | 1 | 4.2.1 | 4.2.2 | | 4.2.3 | 4.2.4 | 40% | - Given 40% = 0.40 as decimal and $\frac{2}{5}$ as fraction (since $\frac{2}{5} = 0.4 = 40\%$). - For 4.2.1 (decimal for 1): Since 1 as fraction is $\frac{1}{1}$, decimal is 1.0. - For 4.2.2 (percentage for 1): 1 as decimal is 1.0, so percentage is $1.0 \times 100 = 100\%$. - For 4.2.3 (fraction for 0.4): 0.4 as fraction is $\frac{2}{5}$. - For 4.2.4 (decimal for $\frac{1}{4}$): $\frac{1}{4} = 0.25$. So the completed table is: | COMMON FRACTIONS | DECIMAL FRACTIONS | PERCENTAGE | |------------------|-------------------|------------| | 1 | 1.0 | 100% | | $\frac{2}{5}$ | 0.4 | 40% | 3. **Complete the matchstick table and find the rule:** Shapes and matchsticks: Shape 1: 4 matchsticks Shape 2: 7 matchsticks Shape 3: 10 matchsticks Shape 4: unknown (4.3.1) Observe the pattern: From shape 1 to 2: increase by 3 matchsticks (7 - 4 = 3) From shape 2 to 3: increase by 3 matchsticks (10 - 7 = 3) So each new shape adds 3 matchsticks. Calculate matchsticks for shape 4: $$10 + 3 = 13$$ So 4.3.1 = 13 matchsticks. **Rule (4.3.2):** Number of matchsticks for shape $n$ is: $$\text{Matchsticks} = 4 + 3(n - 1)$$ Explanation: The first shape has 4 matchsticks, and each additional shape adds 3 more. **Final answers:** 4.1: $\frac{1}{4}$ 4.2.1: 1.0 4.2.2: 100% 4.2.3: $\frac{2}{5}$ 4.2.4: 0.4 4.3.1: 13 4.3.2: $\text{Matchsticks} = 4 + 3(n - 1)$