GCSE Maths Practice: estimation

Question 9 of 10

Practise estimating multi-step expressions by rounding each number before calculation.

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\( \begin{array}{l} \textbf{Estimate:} \\ (298.4 \times 19.7) \div 100.2 \end{array} \)

Choose one option:

Round each value to an easy number before multiplying and dividing. Show every rounded step in your working.

Understanding Multi-Step Estimation

Estimation questions often combine multiplication and division in one expression. They test your ability to simplify numbers quickly while keeping results sensible. The goal is not to find an exact answer but to show accurate reasoning using rounded values. In this example, the expression (298.4 × 19.7) ÷ 100.2 involves two operations and three numbers, so careful rounding is key.

Step-by-Step Method

  1. Identify each number: Look for values that can be rounded to the nearest whole number or to one significant figure.
  2. Round sensibly: 298.4 → 300, 19.7 → 20, 100.2 → 100. Choose values that make the arithmetic straightforward.
  3. Handle the numerator first: Multiply 300 × 20 = 6000.
  4. Then divide: 6000 ÷ 100 = 60.
  5. Check if the estimate is reasonable: The result should be close to what a calculator would produce.

Worked Examples

Example 1: (298.4 × 19.7) ÷ 100.2 → 60 (as shown).

Example 2: (452 × 9.8) ÷ 49.5 → Round to 450, 10, 50 ⇒ (4500 ÷ 50) = 90.

Example 3: (72.6 × 3.9) ÷ 8.1 → Round to 70, 4, 8 ⇒ (280 ÷ 8) = 35.

Common Mistakes

  • Rounding inconsistently — e.g., rounding one value up and another too far down, skewing the estimate.
  • Doing division before multiplication, when brackets require multiplication first.
  • Dropping zeros or misplacing decimal points after rounding.
  • Failing to check if the answer is of the right order of magnitude.

Real-Life Applications

Multi-step estimation appears in finance, engineering, and everyday decision-making. For example, when comparing fuel costs or calculating rough budgets, you often multiply and divide rounded figures. A builder might estimate total material cost by multiplying approximate quantities and dividing by packaging sizes. Estimation ensures quick mental results without relying on technology.

FAQs

Q1: How do I decide how much to round?
A: Use 1 significant figure for quick checks, or 2 if the question involves several operations.

Q2: Should I round before or after calculating?
A: Always round before for estimation, otherwise you defeat the purpose of simplifying.

Q3: Why might my estimate differ from a calculator answer?
A: Because rounding changes the values slightly — but the aim is closeness, not precision.

Study Tip

In exams, write down the rounded numbers before performing operations. Examiners look for your method and reasoning steps, not exact arithmetic. Use arrows or brackets to show the order of operations clearly.

Summary

Multi-step estimation helps you evaluate complex calculations quickly. By rounding all numbers first and performing operations in order, you gain confidence in judging whether results are realistic. Practise this method with various operations to strengthen number sense and mental agility.