microscope work. Scale = distance on image : length of the real object For example, if the scale is \( 1: 1000 \) then 1 cm represents 1000 cm . Simplify the following scales to their simplest form. a. \( 5 \mathrm{~cm}: 1 \mathrm{~m} \) b. \( 15 \mathrm{~mm}: 6000 \mathrm{~km} \) c. \( \frac{1}{2} \mathrm{~cm}: 10 \mathrm{~km} \) The scale on a plan is \( 1: 500 \). How long is the real object if the following is measured? a. 3 cm on the plan is b. 15 mm on the plan is _ \( 1,5 \mathrm{~cm} \) on the plan is_ in reality \( = \) c. \( \quad \mathrm{cm} \) in reality \( = \) _ The ratio of boys to girls in a class is \( 3: 4 \). If there are 16 girls: a. How many boys are there in the class? b. How many children are there in the class? c. What fraction of the class are girls? The springbok rugby squad consists of 22 players, If 10 players are over \( 25 y \) old: a. What is the ratio of over 25 's to under 25 's? b. Write the ratio in its simplest form.

Certainly! Let's tackle each of your questions step-by-step. --- ### **1. Simplify the Following Scales to Their Simplest Form** **a. \( 5\,\text{cm} : 1\,\text{m} \)** 1. **Convert to the Same Unit:** - \( 1\,\text{m} = 100\,\text{cm} \) - So, \( 5\,\text{cm} : 100\,\text{cm} \) 2. **Simplify the Ratio:** - Divide both sides by 5: - \( \frac{5}{5} : \frac{100}{5} = 1 : 20 \) **Simplest Form:** \( 1 : 20 \) --- **b. \( 15\,\text{mm} : 6000\,\text{km} \)** 1. **Convert to the Same Unit (millimeters):** - \( 1\,\text{km} = 1,000,000\,\text{mm} \) - \( 6000\,\text{km} = 6000 \times 1,000,000\,\text{mm} = 6,000,000,000\,\text{mm} \) - So, \( 15\,\text{mm} : 6,000,000,000\,\text{mm} \) 2. **Simplify the Ratio:** - Divide both sides by 15: - \( \frac{15}{15} : \frac{6,000,000,000}{15} = 1 : 400,000,000 \) **Simplest Form:** \( 1 : 400,000,000 \) --- **c. \( \frac{1}{2}\,\text{cm} : 10\,\text{km} \)** 1. **Convert to the Same Unit (centimeters):** - \( 1\,\text{km} = 100,000\,\text{cm} \) - \( 10\,\text{km} = 10 \times 100,000\,\text{cm} = 1,000,000\,\text{cm} \) - So, \( 0.5\,\text{cm} : 1,000,000\,\text{cm} \) 2. **Simplify the Ratio:** - Divide both sides by 0.5: - \( \frac{0.5}{0.5} : \frac{1,000,000}{0.5} = 1 : 2,000,000 \) **Simplest Form:** \( 1 : 2,000,000 \) --- ### **2. Real Object Length Based on Plan Scale \( 1 : 500 \)** **Scale Interpretation:** \( 1\,\text{cm} \) on the plan represents \( 500\,\text{cm} \) (or \( 5\,\text{m} \)) in reality. **a. \( 3\,\text{cm} \) on the Plan** 1. **Calculate Real Length:** - \( 3\,\text{cm} \times 500 = 1,500\,\text{cm} \) 2. **Convert to Meters:** - \( 1,500\,\text{cm} = 15\,\text{m} \) **Real Length:** \( 15\,\text{meters} \) --- **b. \( 15\,\text{mm} \) on the Plan** 1. **Convert Millimeters to Centimeters:** - \( 15\,\text{mm} = 1.5\,\text{cm} \) 2. **Calculate Real Length:** - \( 1.5\,\text{cm} \times 500 = 750\,\text{cm} \) 3. **Convert to Meters:** - \( 750\,\text{cm} = 7.5\,\text{meters} \) **Real Length:** \( 7.5\,\text{meters} \) --- **c. \( 1.5\,\text{cm} \) on the Plan** 1. **Calculate Real Length:** - \( 1.5\,\text{cm} \times 500 = 750\,\text{cm} \) 2. **Convert to Meters:** - \( 750\,\text{cm} = 7.5\,\text{meters} \) **Real Length:** \( 7.5\,\text{meters} \) --- ### **3. Ratio of Boys to Girls in a Class** **Given:** - Ratio of boys to girls = \( 3 : 4 \) - Number of girls = 16 **a. Number of Boys** 1. **Determine the Value of One Part:** - \( 4 \) parts (girls) = 16 girls - \( 1 \) part = \( \frac{16}{4} = 4 \) 2. **Calculate Boys:** - \( 3 \) parts = \( 3 \times 4 = 12 \) boys **Number of Boys:** \( 12 \) --- **b. Total Number of Children** 1. **Total Parts in Ratio:** - \( 3 + 4 = 7 \) parts 2. **Total Children:** - \( 7 \) parts × \( 4 \) = \( 28 \) children **Total Children:** \( 28 \) --- **c. Fraction of the Class That Are Girls** 1. **Girls' Portion:** - \( 4 \) parts out of \( 7 \) 2. **Fraction:** - \( \frac{4}{7} \) **Fraction of Girls:** \( \frac{4}{7} \) --- ### **4. Ratio in the Springbok Rugby Squad** **Given:** - Total players = 22 - Players over 25 years old = 10 **a. Ratio of Over 25's to Under 25's** 1. **Determine Under 25's:** - \( 22 - 10 = 12 \) players 2. **Ratio:** - \( 10 : 12 \) **Ratio:** \( 10 : 12 \) --- **b. Simplify the Ratio** 1. **Find the Greatest Common Divisor (GCD) of 10 and 12:** - GCD = 2 2. **Divide Both Terms by GCD:** - \( \frac{10}{2} : \frac{12}{2} = 5 : 6 \) **Simplest Form of the Ratio:** \( 5 : 6 \) --- I hope this provides a clear and comprehensive explanation for each of your questions!