A fraction of the remainder

A fraction of the remainder refers to the amount left after an earlier action. Your child needs to identify that new amount before applying the next fraction. This page extends the MOE Primary 4 fraction-of-a-set idea to a sequence of actions. The syllabus names fraction as part of a set; the remainder problems here apply that idea when the collection being considered changes during the story.

• Read the actions in order and name the original collection, the first part used and the amount remaining after that action.
• Calculate the first remainder before finding a stated fraction of it, so the next division uses the correct collection.
• Keep the fraction of the original whole separate from a fraction of what remains; their denominators may refer to different collections.
• Use equal groups of the remainder to find the second part, then subtract again if the question asks what is left at the end.
• Label the amounts used at each stage, enabling your child to explain how those separate parts and the final remainder account for the original total.

If two parts are used in sequence and nothing is added, the first part, second part and final remainder must sum to the original amount. Your child should check with the actual quantities used at each stage, rather than adding fractions that refer to different wholes.

Intermediate questions restore a remaining amount after a fixed sum is spent or find the amount left after successive uses of a known total. Challenge questions include successive shares, a difference between two purchases, a fixed extra expense and a final amount expressed as a fraction of the original whole. Ask your child to name the amount each fraction refers to before calculating: the starting quantity and a later remainder are different wholes. Keep those stages in order when working backwards, checking each restored amount against the next stage. When that chain is difficult to follow, revisit the written solution after an attempt and identify the point where the whole changes. The free model-kit question gives written working that restores the money available before buying paint, then uses that remainder to recover the earlier purchase.

Why can the same fraction give two different amounts in one story? The amount depends on the collection to which the fraction refers. One half of the original set and one half of a smaller remainder are different counts. Ask your child to name the whole for each fraction before comparing the resulting quantities.

Can my child add the first and second fractions to find the total used? Only fractions of the same whole can be combined directly in that way. When the second fraction is of the remainder, your child must first relate it to the original whole or calculate the actual amounts. Adding the two stated fractions without checking their wholes does not describe the total used.

What should my child write beside an intermediate answer? A short label naming its stage is enough, such as the amount left after the first action or the amount used next. These labels keep the quantities distinct when the story has several steps. They also make it possible to check the final total against the original collection.