Question 1: Find the HCF of 48 and 180, then use it to simplify the ratio 48:180.

Answer: HCF=12; 48/12=4, 180/12=15; ratio=4:15

Question 2: A recipe calls for 36 grams of sugar and 48 grams of flour. Simplify the ratio of sugar to flour using the HCF method.

Answer: HCF=12; 36/12=3, 48/12=4; ratio=3:4

Question 3: Calculate the HCF of 84, 126, and 210, and then simplify the ratio 84:126:210.

Answer: HCF=42; 84/42=2, 126/42=3, 210/42=5; ratio=2:3:5

Question 4: A class has 24 boys and 36 girls. Use the HCF method to find the largest equal group size that divides both groups, and state the number of groups for each gender.

Answer: HCF=12; boys=24/12=2 groups, girls=36/12=3 groups

Question 5: Simplify the ratio 54:90 using the HCF method. Show all steps.

Answer: HCF=18; 54/18=3, 90/18=5; ratio=3:5

Question 6: A mixture contains 60 grams of salt and 90 grams of water. Simplify their ratio using the HCF method.

Answer: HCF=30; salt=60/30=2, water=90/30=3; ratio=2:3

Question 7: Find the HCF of 128, 224, and 352, then simplify the ratio 128:224:352.

Answer: HCF=32; 128/32=4, 224/32=7, 352/32=11; ratio=4:7:11

Question 8: A school has 120 boys and 150 girls. Use the HCF method to determine the largest possible number of equal-sized groups for each gender, and specify the group counts.

Answer: HCF=30; boys=120/30=4 groups, girls=150/30=5 groups

Question 9: Simplify the ratio 72:108:144 by finding the HCF and dividing each term.

Answer: HCF=36; 72/36=2, 108/36=3, 144/36=4; ratio=2:3:4

Question 10: Identify the common errors students might make when simplifying ratios using the HCF method, and explain how to avoid them.

Answer: Common errors include dividing numerator and denominator by incorrect HCF, missing the step of finding the HCF first, or simplifying only part of the ratio. To avoid these, ensure accurate HCF calculation and divide all terms equally.