What is the L.C.M of 6 and 9? Find the smallest number when divided by either 7 or 8 the remainder is 4. In a class of 80 pupils, 2/5 are girls and the rest are boys. What is the fraction of boys? How

Here are the solutions to your questions: Question 27: a) Find the L.C.M of 6 and 9. Step 1: Find the prime factorization of each number. 6 = 2 × 3 9 = 3 × 3 = 3^2 Step 2: To find the L.C.M, take the highest power of all prime factors present in either number. L.C.M(6, 9) = 2^1 × 3^2 = 2 × 9 = 18 The L.C.M of 6 and 9 is 18. b) Find the smallest number when divided by either 7 or 8 the remainder is 4. Step 1: Find the L.C.M of 7 and 8. Since 7 and 8 are coprime (they share no common factors other than 1), their L.C.M is their product. L.C.M(7, 8) = 7 × 8 = 56 Step 2: The number we are looking for, when divided by 7 or 8, leaves a remainder of 4. This means the number is 4 more than a multiple of the L.C.M of 7 and 8. Smallest number = L.C.M(7, 8) + 4 = 56 + 4 = 60 The smallest number is 60. Question 28: In a class of 80 pupils, (2)/(5) are girls and the rest are boys. a) What is the fraction of boys? Step 1: The total fraction representing all pupils is 1. Subtract the fraction of girls from the total fraction to find the fraction of boys. Fraction of boys = 1 - Fraction of girls = 1 - (2)/(5) = (5)/(5) - (2)/(5) = (3)/(5) The fraction of boys is (3)/(5). b) How many girls are in the class? Step 1: Multiply the total number of pupils by the fraction of girls. Number of girls = (2)/(5) × 80 = 2 × (80)/(5) = 2 × 16 = 32 There are 32 girls in the class. c) How many more boys than girls are in the class? Step 1: Calculate the number of boys in the class. Number of boys = Total pupils - Number of girls = 80 - 32 = 48 Step 2: Find the difference between the number of boys and the number of girls. Difference = Number of boys - Number of girls = 48 - 32 = 16 There are 16 more boys than girls in the class. That's 2 down. 3 left today — send the next one.