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.

To simplify the scale \( 5 \mathrm{~cm}: 1 \mathrm{~m} \), we first convert 1 meter to centimeters, which is 100 cm. So, the scale becomes \( 5 \mathrm{~cm}: 100 \mathrm{~cm} \). Dividing both terms by 5 gives us \( 1: 20 \). For \( 15 \mathrm{~mm}: 6000 \mathrm{~km} \), we convert kilometers to millimeters (6000 km = 6,000,000 mm), resulting in \( 15 \mathrm{~mm}: 6,000,000 \mathrm{~mm} \). Dividing by 15 leads to the simplest form of \( 1: 400,000 \). Similarly, \( \frac{1}{2} \mathrm{~cm}: 10 \mathrm{~km} \) converts to \( 0.5 \mathrm{~cm}: 10,000 \mathrm{~cm} \) (10 km = 1,000,000 cm), simplifying to \( 1: 20,000 \). For the scale \( 1: 500 \), if something measures 3 cm on the plan, the real length is \( 3 \mathrm{~cm} \times 500 = 1500 \mathrm{~cm} \) or \( 15 \mathrm{~m} \). For 15 mm on the plan, it's \( 15 \mathrm{~mm} \times 500 = 7500 \mathrm{~mm} \) or \( 7.5 \mathrm{~m} \). Converting 1.5 cm gives \( 1.5 \mathrm{~cm} \times 500 = 750 \mathrm{~cm} \) or \( 7.5 \mathrm{~m} \). The ratio of boys to girls is 3:4. Given there are 16 girls, the total parts of the ratio are \( 3 + 4 = 7 \). If 4 parts represent 16, then 1 part equals \( \frac{16}{4} = 4 \). So the number of boys is \( 3 \times 4 = 12 \). The total number of children is \( 12 + 16 = 28 \). The fraction of the class that are girls is \( \frac{16}{28} \), which simplifies to \( \frac{4}{7} \). In the springbok rugby squad, with 22 players and 10 over 25 years old, the number of under 25 years old is \( 22 - 10 = 12 \). The ratio of over 25's to under 25's is \( 10:12 \), and simplifying gives us \( 5:6 \).