GCSE Maths Practice: estimation

Question 7 of 10

Estimate total fuel cost by rounding distance and rate to easy numbers before multiplying.

‹ ›

\( \begin{array}{l}\textbf{Estimate: total fuel cost}\cr64.6~\text{miles at £12.8 per 10 miles}\end{array} \)

Choose one option:

Before multiplying, round both quantities to convenient numbers to make planning easier and results clearer.

Estimating Fuel Costs for a Journey

Estimation helps when planning trips or managing expenses. Instead of multiplying exact decimals, rounding both numbers gives a quick and reliable total. In this example, multiplication represents estimating the fuel cost for a long journey.

Scenario: Calculating Journey Cost

A driver travels 64.6 miles and their car uses roughly £12.80 of fuel for every 10 miles. To estimate the total cost, round 64.6 to 60 and 12.8 to 10. Multiply: 60 × 10 = £600. The real total is a bit higher (£64.6 × £12.8 ≈ £826), but the estimate gives a clear, simple figure for quick planning.

Why This Is Useful

Drivers and logistics planners estimate before checking precise numbers to:

  • Plan travel budgets,
  • Check if fuel money is sufficient,
  • Compare routes or vehicle efficiency.

GCSE estimation skills mirror these real-world habits — you’re learning mental maths that actually saves time and money.

How to Estimate Multiplications Effectively

  1. Round both numbers to the same level of simplicity (nearest ten or whole number).
  2. Multiply mentally using known number facts (e.g., 6 × 1 = 6, then add zeros).
  3. Check direction: both rounded down → actual answer slightly higher; both rounded up → actual slightly lower.

Worked Examples

  • Example 1: 64.6 × 12.8 → 60 × 10 = 600 (actual ≈ 826).
  • Example 2: 112.5 × 8.4 → 110 × 8 = 880 (actual ≈ 945).
  • Example 3: 24.7 × 9.1 → 25 × 9 = 225 (actual ≈ 224.8 — almost perfect).

Interpreting the Result

Even if an estimate isn’t exact, it should reveal the general size of the answer. In this question, 600 tells you the cost is in the hundreds — not tens or thousands. This sense of scale is crucial for accuracy checking in GCSE exams.

Common Errors

  • Forgetting to round both numbers before multiplying.
  • Rounding too much, such as to the nearest hundred when tens would be enough.
  • Misplacing zeros (writing 6,000 instead of 600).
  • Ignoring the real-life units (pounds, litres, miles, etc.).

Real-World Links

Estimation isn’t just about maths; it’s about decision-making. Car mechanics estimate repair costs, delivery drivers estimate times, and event organisers estimate expenses. Quick estimates make planning faster and prevent surprises later.

FAQ

  • Q: How close should my estimate be to the real value?
    A: Within about 10% is usually accurate enough for everyday use.
  • Q: Why not calculate exactly every time?
    A: Estimation is faster and helps you check whether exact calculations make sense.
  • Q: What if the estimate feels too low?
    A: Recheck your rounding — perhaps one number was rounded down too far.

Study Tip

When rounding two numbers for estimation, aim for ‘friendly’ pairs that keep mental multiplication easy — like 60 and 10 here. Practise this habit regularly for faster reasoning in non-calculator GCSE questions.

Summary

Rounding 64.6 to 60 and 12.8 to 10 makes estimation quick and clear: 60 × 10 = 600. This approach simplifies planning fuel costs, shopping totals, or any real-life multiplication task.