Exercise 1.8/Oefenine 1.8 p) 1) Two numbers are in the ratio 8 . 5 . If the larger number is 56 , lind the smailer number / Tweo nommers is in 'n verhouding 8.5 As die grootter nommer 56 is. Vind die Kleiner nommer b) 2) Nine pens cost R504. How many pens will cost R \( 4032 \% \) / Nege penne kos R504. Hoeveel penne sal R4 032 kos? 5) 3) Devide 3570 in the ratio \( 2 \frac{1}{5}=\frac{3}{5} \) / \( \operatorname{Deel} 3570 \mathrm{in} \mathrm{die} \mathrm{verhouding} 2 \frac{1}{5}: \frac{3}{5} \) 6) Increase 42 in the ratio \( 3 \quad 7 / \) Vermeerder 42 in die verhouding 3.7

Certainly! Let's solve each of the exercises you've provided step by step. --- ### **Exercise 1.8 / Oefening 1.8** #### **a) Problem 1:** **English:** *Two numbers are in the ratio 8:5. If the larger number is 56, find the smaller number.* **Afrikaans:** *Tweë nommers is in die verhouding 8:5. As die groter nommer 56 is, vind die kleiner nommer.* **Solution:** 1. **Understand the Ratio:** The ratio of the two numbers is 8:5. This means for every 8 parts of the larger number, there are 5 parts of the smaller number. 2. **Identify the Parts:** Let each part be represented by \( x \). - Larger number = \( 8x \) - Smaller number = \( 5x \) 3. **Given Value:** The larger number is 56. \( 8x = 56 \) 4. **Find \( x \):** \( x = \frac{56}{8} = 7 \) 5. **Find the Smaller Number:** \( 5x = 5 \times 7 = 35 \) **Answer:** The smaller number is **35**. --- #### **b) Problem 2:** **English:** *Nine pens cost R504. How many pens will cost R4032?* **Afrikaans:** *Nege penne kos R504. Hoeveel penne sal R4 032 kos?* **Solution:** 1. **Find the Cost per Pen:** \( \text{Cost per pen} = \frac{504}{9} = R56 \) per pen. 2. **Find the Number of Pens for R4032:** \( \text{Number of pens} = \frac{4032}{56} = 72 \) **Answer:** **72** pens will cost R4032. --- #### **c) Problem 5:** **English:** *Divide 3570 in the ratio \( 2 \frac{1}{5} : \frac{3}{5} \).* **Afrikaans:** *Deel 3570 in die verhouding \( 2 \frac{1}{5} : \frac{3}{5} \).* **Solution:** 1. **Convert Mixed Numbers to Improper Fractions:** \( 2 \frac{1}{5} = \frac{11}{5} \) \( \frac{3}{5} = \frac{3}{5} \) 2. **Simplify the Ratio:** Multiply both terms by 5 to eliminate the denominators: \( \frac{11}{5} \times 5 : \frac{3}{5} \times 5 = 11 : 3 \) 3. **Total Parts:** \( 11 + 3 = 14 \) parts. 4. **Value of One Part:** \( \frac{3570}{14} = 255 \) 5. **Divide the Amount:** - First part: \( 11 \times 255 = 2805 \) - Second part: \( 3 \times 255 = 765 \) **Answer:** 3570 is divided into **2805** and **765**. --- #### **d) Problem 6:** **English:** *Increase 42 in the ratio 3:7.* **Afrikaans:** *Vermeerder 42 in die verhouding 3:7.* **Solution:** 1. **Interpret the Ratio:** The phrase "increase 42 in the ratio 3:7" implies that 42 corresponds to the first part (3 parts) of the ratio, and we need to find the second part (7 parts). 2. **Set Up the Proportion:** \( \frac{3}{7} = \frac{42}{x} \) 3. **Solve for \( x \):** \( x = \frac{42 \times 7}{3} = 98 \) **Answer:** 42 increased in the ratio 3:7 is **98**. --- Feel free to reach out if you need further clarification on any of these problems!