Fraction Operation: Challenge Question (Cambridge IGCSE ® Complete Mathematics Extended Sixth Edition,
2023)
Solution:
10 ml from B added into A. For A:
Total volume = 110 ml.
Concentration of juice = Amount (Volume) of juice to total volume = 10/110 = 1/11
Concentration of water = Amount (Volume) of water to total volume = 100/110 = 10/11
10 ml is then taken from A. In this portion:
Amount (Vol) of juice = (1/11) x 10 ml = 10/11 ml
Amount (Vol) of water = (10/11) x 10 = 100/11 ml
This is added into B. For B:
Total volume = 100 ml
Amount (Vol) of juice = (10/11) + 90 = (10 + 990)/11 = 1000/11 ml
Concentration of juice = Amt (Vol) of juice to total Vol = (1000/11)/100 = 1000/1100 = 10/11
Amount (Vol) of water = 100/11 ml
Concentration of water = Amt (Vol) of water to total Vol = (100/11)/100 = 100/1100 = 1/11
Is there more juice in the water? Look at concentration of juice in A = 1/11
Is there more water in the juice? Look at concentration of water in B = 1/11
Answer: Both have the same concentration so amount of juice in the water = amount of water in the juice
The shell of a newly hatched crab is 1 cm across. As it grows, it gets new shells that are each one-third
bigger than the previous one. The shell of a fully grown crab is approximately 10 cm across. How many
shells does a crab have during its lifetime?