GCSE Maths Practice: estimation

Question 2 of 10

Estimate a price per item by rounding total cost and item count to friendly numbers, then dividing.

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\( \begin{array}{l}\textbf{Estimate: unit price}\\ \text{£47.80 for }9~\text{items}\end{array} \)

Choose one option:

Use balanced rounding (some up, some down) to keep estimates neutral, then add units to your final statement.

Estimating Unit Price (Cost per Item)

When you see a total cost and a number of items, estimating the price per item helps you decide quickly if an offer is reasonable. The idea is to replace awkward numbers with friendlier ones (usually to one significant figure), then divide. This gives a fast, sensible benchmark you can compare against an exact calculation.

Method

  1. Round the total cost to a simple nearby value.
  2. Round the item count to a simple nearby value.
  3. Divide the rounded cost by the rounded count.
  4. Interpret the result (a little high or low) based on your rounding direction.

Why It Works

Rounding preserves the scale of the numbers while removing fussy detail. Dividing the rounded pair gives the correct order of magnitude and a stable check against calculator errors or misleading labels.

Worked Examples (different numbers)

  • Total £62.40 for 8 items → £60 ÷ 8 = £7.50 each (exact £7.80).
  • Total £19.50 for 3 items → £20 ÷ 4 (balanced) ≈ £5 each (exact £6.50 if you instead use £19.5 ÷ 3).
  • Total £121 for 11 items → £120 ÷ 10 = £12 each (exact ≈ £11.00).

Upper–Lower Range Check

Bracket the answer by rounding one value up and the other down. If the total is rounded down and the count up, you get a lower bound; reversing gives an upper bound. The true unit price should sit between them.

Common Pitfalls

  • Rounding only one value and not the other.
  • Rounding too aggressively (e.g., to the nearest hundred when tens would do).
  • Forgetting the units and reporting a bare number.

Real-Life Uses

Use unit-price estimation when comparing multipacks, bulk items, or different sizes on supermarket shelves, and when planning budgets for class resources or catering.

FAQ

  • How close should the estimate be? Within about 5–10% is fine for quick decisions.
  • Should I always round up prices? Not necessarily; balance rounding to avoid a biased estimate.
  • What if one number is already neat? Leave it and round only the awkward one.

Study Tip

Say the rounded division aloud (e.g., “about £50 over about 10 items is about £5 each”). Verbalising cements the sense of scale and reduces mistakes under time pressure.