3. On Wednesday evening Sonto spent \( \frac{1}{2} \) hour doing homework, 45 minutes doing housework, 1 hour visiting friends and \( 1 \frac{1}{2} \) hours watching television. Write this information as a ratio. 4. In a country there are 48000 people in the defence services. They work in the army, navy and air force in the ratio \( 5: 2: 3 \). How many people are in each servi

Sure, let's solve both problems step by step. --- ### **Problem 3** **Sonto's Evening Activities:** - **Homework:** \( \frac{1}{2} \) hour - **Housework:** 45 minutes - **Visiting Friends:** 1 hour - **Watching Television:** \( 1 \frac{1}{2} \) hours **Objective:** Write the time spent on each activity as a ratio. #### **Step 1: Convert All Times to the Same Unit** It's easiest to convert all times to **minutes** or **hours**. Here, we'll use **hours**. - **Homework:** \( \frac{1}{2} \) hour = 0.5 hours - **Housework:** 45 minutes = 0.75 hours - **Visiting Friends:** 1 hour = 1 hour - **Watching Television:** \( 1 \frac{1}{2} \) hours = 1.5 hours #### **Step 2: Express the Time Spent as a Ratio** Now, we have the times in hours: \[ 0.5 : 0.75 : 1 : 1.5 \] #### **Step 3: Simplify the Ratio to Whole Numbers** To eliminate decimals, find a common multiplier. Multiply each part by **4** to make all terms whole numbers: \[ 0.5 \times 4 = 2 \\ 0.75 \times 4 = 3 \\ 1 \times 4 = 4 \\ 1.5 \times 4 = 6 \] So, the simplified ratio is: \[ 2 : 3 : 4 : 6 \] **Final Answer:** The ratio of time Sonto spent on homework, housework, visiting friends, and watching television is **2 : 3 : 4 : 6**. --- ### **Problem 4** **Given:** - **Total People in Defence Services:** 48,000 - **Ratio of Army : Navy : Air Force = 5 : 2 : 3** **Objective:** Find the number of people in each service. #### **Step 1: Determine the Total Number of Parts in the Ratio** Add the parts of the ratio: \[ 5 (Army) + 2 (Navy) + 3 (Air Force) = 10 \text{ parts} \] #### **Step 2: Find the Value of One Part** Divide the total number of people by the total number of parts: \[ \text{One part} = \frac{48,000}{10} = 4,800 \] #### **Step 3: Calculate the Number of People in Each Service** - **Army:** \( 5 \times 4,800 = 24,000 \) - **Navy:** \( 2 \times 4,800 = 9,600 \) - **Air Force:** \( 3 \times 4,800 = 14,400 \) **Final Answer:** - **Army:** 24,000 people - **Navy:** 9,600 people - **Air Force:** 14,400 people --- If you have any further questions or need additional assistance, feel free to ask!