Use prime factorization method to determine the LCM and HCF of 60 and 80.

Here are the solutions to the questions: Question 2.3 Use prime factorization method to determine the LCM and HCF of 60 and 80. Step 1: Find the prime factorization of 60. 60 = 2 × 30 = 2 × 2 × 15 = 2^2 × 3 × 5 Step 2: Find the prime factorization of 80. 80 = 2 × 40 = 2 × 2 × 20 = 2 × 2 × 2 × 10 = 2 × 2 × 2 × 2 × 5 = 2^4 × 5 Step 3: Determine the Highest Common Factor (HCF). The common prime factors are 2 and 5. For 2, the lowest power is 2^2. For 5, the lowest power is 5^1. HCF(60, 80) = 2^2 × 5^1 = 4 × 5 = 20 Step 4: Determine the Least Common Multiple (LCM). Take all prime factors from both numbers with their highest powers. For 2, the highest power is 2^4. For 3, the highest power is 3^1. For 5, the highest power is 5^1. LCM(60, 80) = 2^4 × 3^1 × 5^1 = 16 × 3 × 5 = 48 × 5 = 240 The HCF is 20 and the LCM is 240. Question 3.1.1 Calculate the following to the simplest form: -15y - (-5y). Step 1: Simplify the double negative. -15y + 5y Step 2: Combine the like terms. (-15 + 5)y -10y The simplest form is -10y. Question 3.1.2 Calculate 450 mm of 9 km. Step 1: Convert 9 km to millimeters. 1 km = 1000 m 1 m = 1000 mm So, 1 km = 1000 × 1000 mm = 1,000,000 mm. 9 km = 9 × 1,000,000 mm = 9,000,000 mm Step 2: Express 450 mm as a fraction of 9,000,000 mm. 450 mm9,000,000 mm Step 3: Simplify the fraction. (45)/(900000) = (1)/(20000) The value is (1)/(20000). Question 3.2.1 Use the distributive property to calculate the following: 8 × [(-9) + (-7)]. Step 1: Apply the distributive property. (8 × -9) + (8 × -7) Step 2: Perform the multiplications. -72 + (-56) Step 3: Perform the addition. -72 - 56 -128 The calculated value is -128. Question 3.3.1 Calculate the following integers: 23nm + (-6nm) - (+20nm) + 3nm. Step 1: Simplify the signs. 23nm - 6nm - 20nm + 3nm Step 2: Combine the like terms. (23 - 6 - 20 + 3)nm (17 - 20 + 3)nm (-3 + 3)nm 0nm 0 The calculated value is 0. 3 done, 2 left today. You're making progress.