Patterns & Reasoning

Problem

Choose round up or round down in context

A school has 423 boys and 418 girls. Every student is to receive 2 notebooks. The store only sells notebooks in packs of 10. We must find the fewest notebooks the school can buy so that there are enough for everyone.
OperationsBase-ten numbers
Your answer
How to solve
Strategy Identify Subproblems — This is a multi-step problem: first work out how many notebooks are actually needed (count students, then multiply by 2), then decide how many packs of 10 cover that amount. Because the store sells only whole packs of 10, the real question is which way to estimate — since we must have ENOUGH notebooks, we round UP to the next multiple of 10. Tracking the units (students, notebooks, packs) keeps each step honest.
1STEP 1

Count all the students

Add the boys and girls to find the total number of students who will receive notebooks.

423 + 418 = 841
2STEP 2

Find how many notebooks are needed

Each of the 841 students gets 2 notebooks, so multiply the number of students by 2 to get the total notebooks needed.

841 × 2 = 1682
3STEP 3

Decide whether to round up or down

Packs come in tens and 1680 would leave 2 students short, so round up to 1690.

1682 → 1690
4STEP 4

Check it in packs

1690 is exactly 169 packs of ten, more than the 1682 that are needed.

1690 ÷ 10 = 169 packs
Answer
1690 notebooks
About 840 students each needing 2 notebooks is roughly 1700 notebooks, and 1690 is just above 1682, the exact need. The answer is a multiple of 10 (a whole number of packs) and is only 8 more than required — the smallest possible overshoot, so it is reasonable.
Takeaway

When you must have enough, round UP to the next full pack — a leftover few still needs one more whole pack.

  • Count all the students
  • Find how many notebooks are needed
  • Decide whether to round up or down
  • Check it in packs
Where next?
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▶ Practice — 12 problems