GCSE Maths Practice: estimation

Question 1 of 10

Estimate a division by rounding both numbers before calculating.

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\( \begin{array}{l} \textbf{Estimate:} \\ 198.7 \div 3.9 \end{array} \)

Choose one option:

Round the dividend and divisor sensibly before dividing. Always check that the result makes sense.

Understanding Division Estimation

Estimation by division is one of the most common mental-math skills in GCSE Maths. It involves rounding numbers to convenient values before dividing them. This technique makes calculations faster and helps check if an exact answer is reasonable. In this problem, the division 198.7 ÷ 3.9 is simplified by rounding both numbers to one significant figure before calculating.

Step-by-Step Method

  1. Identify the numerator and denominator: 198.7 (numerator) and 3.9 (denominator).
  2. Round sensibly: 198.7 → 200, 3.9 → 4. Rounding both keeps the ratio realistic.
  3. Perform the division: 200 ÷ 4 = 50.
  4. State the estimate clearly: Always include the word “approximately” or use the ≈ symbol when presenting estimated results.

Worked Examples

Example 1: 198.7 ÷ 3.9 → 200 ÷ 4 = 50.

Example 2: 452 ÷ 9.8 → 450 ÷ 10 = 45.

Example 3: 625 ÷ 12.2 → 600 ÷ 12 = 50.

Common Mistakes

  • Rounding one number too aggressively (e.g., 3.9 → 5), which distorts the estimate.
  • Forgetting which number is divided by which, reversing numerator and denominator.
  • Not checking the reasonableness of the result. For instance, dividing 200 by 4 should give a smaller number than 200, not a larger one.
  • Omitting units when the question is about speed, density, or rate.

Real-Life Applications

Division estimation is widely used in everyday reasoning. Shoppers estimate price per item by dividing total cost by quantity. Drivers calculate average speed by dividing distance by time. Scientists estimate population density or material concentration through quick mental division. This practical skill allows quick decisions without a calculator, saving time in real-world contexts.

FAQs

Q1: Why round both numbers instead of only one?
A: Rounding both maintains a balanced ratio and avoids distorting the proportion.

Q2: How accurate should an estimate be?
A: The goal is to get a result close to the real answer within about 10 %. The reasoning process is more important than exact accuracy.

Q3: What symbol should I use for an estimate?
A: Use the “approximately equal” sign (≈) or state “Estimate ≈ 50.”

Study Tip

In estimation questions, always show how you rounded the numbers. Even if your final answer differs slightly from the expected one, you can earn full method marks for demonstrating logical rounding and division steps. Practise rounding to 1 or 2 significant figures to make mental arithmetic easier.

Summary

Estimating division problems sharpens numerical sense and helps detect calculator errors. By rounding both numbers to convenient values, you can quickly obtain a realistic, easy-to-check result. This method is essential for quick reasoning in exams and everyday problem-solving.