GCSE Maths Practice: estimation

Question 5 of 10

Estimate the total distance from two running sessions by rounding each distance to the nearest ten before adding.

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\( \begin{array}{l}\textbf{Estimate: total distance run}\cr68.7~\text{km}+27.5~\text{km}\end{array} \)

Choose one option:

Rounding each value to the same place value makes addition faster and checks reasonableness in everyday maths.

Estimating Totals in Everyday Life: Fitness Example

Estimation isn’t only for exams — it helps in real-world planning. Runners, cyclists, and even delivery drivers often add distances mentally to plan routes or set goals. Here we practise estimating a total distance run over two sessions.

Scenario: Total Weekly Running Distance

A runner jogged 68.7 km in one week and 27.5 km the next. Instead of using a calculator, they estimate the total distance. Round to easy numbers: 70 km and 30 km. Adding gives about 100 km in total — a quick, realistic mental estimate before checking the precise total (96.2 km).

Why Estimation Matters

Estimation helps athletes and planners monitor progress without technology. It gives a rough sense of effort or performance while training or budgeting time. For GCSE Maths students, it reinforces number sense and the ability to judge reasonableness of results.

Method: Rounding and Adding

  1. Round each number to a convenient value (nearest ten for large numbers).
  2. Add the rounded figures mentally using basic number facts.
  3. Adjust slightly if you know one rounding was up and one was down.

Worked Examples

  • Example 1: 68.7 + 27.5 → 70 + 30 = 100 (exact 96.2).
  • Example 2: 45.8 + 14.2 → 50 + 10 = 60 (actual 60.0 — perfect estimate).
  • Example 3: 189.4 + 112.9 → 190 + 110 = 300 (actual 302.3).

Checking Reasonableness

After estimating, compare it to the exact total. If your estimate and the real answer differ by less than 10%, your mental calculation was accurate enough for planning purposes.

Common Mistakes

  • Mixing units — ensure both distances are in the same unit (e.g., kilometres, not km and miles).
  • Rounding one number up and the other down in a way that over-cancels.
  • Forgetting to include the unit in the final answer (e.g., saying 100 instead of 100 km).

Real-Life Applications

Estimation appears in fitness tracking, travel planning, and budgeting time. For instance, a delivery driver might add 68.7 km and 27.5 km to check if they can complete the route with one tank of fuel. Estimation allows decisions without relying on technology.

FAQs

  • Q: When should I use estimation instead of exact addition?
    A: When you only need a quick sense of scale, not a precise answer.
  • Q: Is it better to round to tens or hundreds?
    A: Use tens for small numbers (under 1,000) and hundreds for large values.
  • Q: How can I make estimates more accurate?
    A: Round one number up and the other down to balance over- and underestimation.

Study Tip

Always check that your estimate is close to the real answer by reasoning about scale. For example, adding 70 and 30 gives 100, so the true sum must be slightly below that.

Summary

Rounding 68.7 km to 70 and 27.5 km to 30 simplifies the addition to 100. Estimation helps athletes, planners, and students make confident, quick judgments without a calculator — a vital real-life maths skill.