5. Divide 36 in the ratio: a) \( 1: 2 \) b) \( 1: 3 \) c) \( 5: 4 \)

To divide the number **36** into different ratios, you can follow these general steps: 1. **Add the parts of the ratio to find the total number of parts.** 2. **Divide the total number by the total number of parts to find the value of one part.** 3. **Multiply the value of one part by each part of the ratio to find the individual shares.** Let's apply these steps to each ratio provided. --- ### a) **Ratio \( 1 : 2 \)** 1. **Total Parts:** \( 1 + 2 = 3 \) parts 2. **Value of One Part:** \( \frac{36}{3} = 12 \) 3. **Individual Shares:** - First share: \( 1 \times 12 = 12 \) - Second share: \( 2 \times 12 = 24 \) **Result:** \( 36 \) is divided into **12** and **24**. --- ### b) **Ratio \( 1 : 3 \)** 1. **Total Parts:** \( 1 + 3 = 4 \) parts 2. **Value of One Part:** \( \frac{36}{4} = 9 \) 3. **Individual Shares:** - First share: \( 1 \times 9 = 9 \) - Second share: \( 3 \times 9 = 27 \) **Result:** \( 36 \) is divided into **9** and **27**. --- ### c) **Ratio \( 5 : 4 \)** 1. **Total Parts:** \( 5 + 4 = 9 \) parts 2. **Value of One Part:** \( \frac{36}{9} = 4 \) 3. **Individual Shares:** - First share: \( 5 \times 4 = 20 \) - Second share: \( 4 \times 4 = 16 \) **Result:** \( 36 \) is divided into **20** and **16**. --- ### **Summary of Results:** - **a)** \( 1 : 2 \) → **12** and **24** - **b)** \( 1 : 3 \) → **9** and **27** - **c)** \( 5 : 4 \) → **20** and **16**