A ratio is a comparison of two or more quantities of the same kind, expressed as a fraction or with a colon. It shows how much of one quantity there is compared to another.

Here are the answers to your questions: 1. A ratio is a comparison of two or more quantities of the same kind, expressed as a fraction or with a colon. It shows how much of one quantity there is compared to another. 2. If the ratio of boys to girls is 3:2 and there are 30 students total: Step 1: Find the total number of parts in the ratio. Total parts = 3 (boys) + 2 (girls) = 5 parts Step 2: Determine the value of one part. Value per part = Total studentsTotal parts = (30)/(5) = 6 students/part Step 3: Calculate the number of boys. Number of boys = Boys' ratio part × Value per part = 3 × 6 = 18 There are 18 boys. 3. A rate is a ratio that compares two quantities with different units. It describes how one quantity changes in relation to another. 4. To find the hourly rate of pay: Step 1: Divide the total earnings by the total hours worked. Hourly rate = Total earningsTotal hours = GHC6008 hours = GHC75/hour The hourly rate of pay is GHC75 per hour. 5. A proportion is a statement that two ratios are equal. Real-life example: If 1 cup of flour is needed for 12 cookies, then 2 cups of flour are needed for 24 cookies. This can be written as the proportion (1)/(12) = (2)/(24). 6. (Question 6 is not visible in the image.) 7. In a school with 1,200 students, the ratio of male to female students is 5:7: Step 1: Find the total number of parts in the ratio. Total parts = 5 (male) + 7 (female) = 12 parts Step 2: Determine the value of one part. Value per part = Total studentsTotal parts = (1200)/(12) = 100 students/part Step 3: Calculate the number of female students. Number of female students = Female ratio part × Value per part = 7 × 100 = 700 There are 700 female students in the school. 8. A map has a scale of 1 cm : 5 km. If two towns are 8 cm apart on the map: Step 1: Use the scale to find the actual distance. Actual distance = Map distance × Scale factor Actual distance = 8 cm × 5 km1 cm = 40 km The actual distance between the towns is 40 km. 9. If 6 workers can complete a job in 15 days: Step 1: Calculate the total "worker-days" required for the job. Total worker-days = 6 workers × 15 days = 90 worker-days Step 2: If 9 workers are doing the job, divide the total worker-days by the new number of workers. Days needed = Total worker-daysNumber of workers = 90 worker-days9 workers = 10 days It would take 10 days for 9 workers to complete the same job. 10. Three friends share a profit in the ratio 2:3:5. The total profit is GHC5,000: Step 1: Find the total number of parts in the ratio. Total parts = 2 + 3 + 5 = 10 parts Step 2: Determine the value of one part. Value per part = Total profitTotal parts = GHC500010 = GHC500/part Step 3: Calculate how much each friend receives. Friend 1: 2 × GHC500 = GHC1000 Friend 2: 3 × GHC500 = GHC1500 Friend 3: 5 × GHC500 = GHC2500 The friends receive GHC1000, GHC1500, and GHC2500 respectively. 11. A car uses 8 litres of fuel to travel 120 km: Step 1: Calculate the fuel efficiency in km per litre. Fuel efficiency = 120 km8 litres = 15 km/litre Step 2: To travel 300 km, divide the distance by the fuel efficiency. Litres needed = 300 km15 km/litre = 20 litres 20 litres of fuel are needed to travel 300 km. 12. A farmer has animals in the ratio of cows to goats to sheep of 3:4:5. There are 60 animals in total: Step 1: Find the total number of parts in the ratio. Total parts = 3 (cows) + 4 (goats) + 5 (sheep) = 12 parts Step 2: Determine the value of one part. Value per part = Total animalsTotal parts = (60)/(12) = 5 animals/part Step 3: Calculate the number of each type of animal. Cows: 3 × 5 = 15 cows Goats: 4 × 5 = 20 goats Sheep: 5 × 5 = 25 sheep Reasoning: The total number of animals (60) is divided by the sum of the ratio parts (12) to find the value of one part (5 animals). This value is then multiplied by each individual ratio part to determine the count for each animal type, ensuring the proportions are maintained. The farmer has 15 cows, 20 goats, and 25 sheep. 13. Two quantities are in the ratio 5:8. The difference between them is 45: Step 1: Let the two quantities be 5x and 8x. Step 2: Set up an equation based on their difference. 8x - 5x = 45 Step 3: Solve for x. 3x = 45 x = (45)/(3) = 15 Step 4: Find the two quantities. First quantity: 5x = 5 × 15 = 75 Second quantity: 8x = 8 × 15 = 120 Reasoning: By representing the quantities as multiples of a common factor x, the difference between them can be expressed in terms of x. Solving for x allows us to find the actual values of the quantities while maintaining their given ratio. The two quantities are 75 and 120. Drop the next question.