GCSE Maths Practice: decimals

Question 2 of 10

This Higher-level decimals problem tests accuracy when adding multiple decimals with differing decimal places. Proper alignment and column addition are crucial for success.

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\( \begin{array}{l}\textbf{Calculate } 0.625 + 1.25 + 0.375.\end{array} \)

Choose one option:

Estimate first: 0.6 + 1.3 + 0.4 ≈ 2.3, so an answer near 2.25 is realistic. Estimation prevents misplaced decimals.

This Higher-tier GCSE question focuses on accurate addition of several decimals with differing decimal places. Such tasks build essential fluency for calculations involving averages, measurements, and percentage problems.

Concept Overview

When adding multiple decimals, every value must align by its decimal point. Trailing zeros should be added where necessary to equalise the number of digits after the decimal. This preserves correct place value and prevents digit-shift errors.

Step-by-Step Breakdown

  1. Align decimals: Write 0.625, 1.250, and 0.375 vertically.
  2. Add hundredths and thousandths: 5 + 0 + 5 = 10, carry 1.
  3. Continue column addition: 2 + 5 + 7 = 14, carry 1; 6 + 2 + 3 + 1 = 12, carry 1.
  4. Write down the decimal point directly below the others.
  5. Result: 2.250 → 2.25 after removing trailing zero.

Why This Is Higher Level

Although the arithmetic is familiar, accuracy under time pressure and awareness of place value distinguish higher-grade responses. Multi-decimal problems also connect directly to fractions and recurring decimals, which appear in advanced GCSE papers.

Fractions Connection

Each decimal can be expressed as a fraction:

  • 0.625 = \(\frac{5}{8}\)
  • 1.25 = \(1\frac{1}{4} = \frac{5}{4}\)
  • 0.375 = \(\frac{3}{8}\)

Add them using a common denominator of 8: \(\frac{5}{8} + \frac{10}{8} + \frac{3}{8} = \frac{18}{8} = 2.25.\) This cross-check confirms the accuracy of the decimal addition.

Common Mistakes

  • Misaligning decimals so tenths add to hundredths, producing errors.
  • Failing to pad shorter decimals with zeros (e.g., writing 1.25 instead of 1.250).
  • Forgetting that adding numbers less than 1 can still exceed 1 when several are combined.
  • Truncating instead of rounding — never drop digits without checking if rounding is needed.

Worked Comparison Example

Example: 0.75 + 1.4 + 0.08 = ?

Write as 0.750 + 1.400 + 0.080 → add vertically → 2.230 → 2.23.

Different decimal lengths demand consistency before summation.

Checking by Estimation

Estimate: 0.6 + 1.3 + 0.4 ≈ 2.3. The final result 2.25 fits this check, confirming reasonable accuracy.

Extension Thinking

Students targeting Grade 8–9 can extend this by reversing the operation: subtracting 0.625 or dividing the total by 3 to find the mean (2.25 ÷ 3 = 0.75). These steps reinforce fluency with decimal reasoning across multiple contexts.

FAQ

Q1: Why add zeros to equalise decimals?
A1: Equal digits after the decimal ensure each column represents the same place value (tenths with tenths, etc.).

Q2: Can I check with a calculator?
A2: Yes, but you must still align manually in exams to show method marks and catch entry errors.

Q3: Why does 0.625 + 1.25 + 0.375 not give a repeating decimal?
A3: Because all three terminate at thousandths — their denominators are powers of 2 or 5 (8 and 4).

Study Tip

Practise adding decimals of varied lengths (e.g., 1.2 + 0.35 + 0.007). Always line up the decimal point first, then pad with zeros to avoid misalignment. Write intermediate carries clearly — neat column work prevents arithmetic slips.

Fluency with multi-decimal addition is foundational for compound measures, currency calculations, and proportional reasoning across GCSE Maths.