Operations on decimals Revision Notes for Edexcel GCSE Maths

Operations on decimals

Adding and subtracting decimals

When working with decimal addition and subtraction, the most important rule is to align the decimal points correctly. This ensures that digits with the same place value are lined up properly.

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Critical Rule for Addition and Subtraction

Always align the decimal points vertically before performing any calculations. This ensures digits with the same place value are properly lined up, which is essential for accurate results.

Method:

Line up the digits with the same place value
Align the decimal points vertically
Include a decimal point in your answer, directly below the others

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Helpful Tip: Using Placeholder Zeros

Write zeros to make both numbers have the same number of decimal places if needed. For example, write $1.6$ as $1.60$ when adding to $0.75$ - this makes alignment much clearer and reduces errors.

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Worked Example: Adding and Subtracting Decimals

Example 1: $0.75 + 1.6$

Rewrite as: $0.75 + 1.60$ (adding zero for clarity)
Align decimal points vertically
Add: $0.75 + 1.60 = 2.35$

Example 2: $3.5 - 0.21$

Rewrite as: $3.50 - 0.21$ (adding zero for clarity)
Align decimal points vertically
Subtract: $3.50 - 0.21 = 3.29$

Multiplying decimals

Multiplication with decimals requires a different approach. You can ignore the decimal points initially and work with whole numbers, then place the decimal point correctly at the end.

Method:

Multiply the numbers as if they were whole numbers (ignore decimal points)
Count the total number of decimal places in both original numbers
Place the decimal point in your answer so it has the same total number of decimal places

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Worked Example: Multiplying Decimals

Example 1: $8.69 × 12$

Step 1: Multiply as whole numbers: $869 × 12 = 10428$
Step 2: Count decimal places: $8.69$ has 2 decimal places, $12$ has 0
Step 3: Total decimal places = 2, so answer is $104.28$

Example 2: $8.5 × 0.04$

Step 1: Multiply as whole numbers: $85 × 4 = 340$
Step 2: Count decimal places: $8.5$ has 1, $0.04$ has 2
Step 3: Total decimal places = 3, so answer is $0.340 = 0.34$

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Estimation Check for Decimal Placement

You can estimate first to check your decimal point placement. For $8.69 × 12$ , estimate $9 × 12 = 108$ , so $104.28$ looks reasonable. This quick check can help you catch decimal point errors.

Dividing decimals

Division involving decimals can be tricky, but there's a useful technique to make it easier by converting to whole number division.

Method:

Multiply both numbers by 10, 100, or 1000 to make the divisor (second number) a whole number
Divide using the new whole numbers

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Key Insight: Equivalent Division

Multiplying both numbers by the same amount doesn't change the answer, but makes the calculation much simpler. This is because $\frac{a × k}{b × k} = \frac{a}{b}$ for any value $k$ .

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Worked Example: Dividing Decimals

Example 1: $55.8 ÷ 3$

Since 3 is already a whole number, divide directly: $55.8 ÷ 3 = 18.6$

Example 2: $40.6 ÷ 1.4$

Multiply both numbers by 10: $(40.6 × 10) ÷ (1.4 × 10) = 406 ÷ 14$
Now divide: $406 ÷ 14 = 29$

Exam tips

Working with decimals in exams requires careful attention to detail and systematic approaches. Here are essential strategies to maximise your success:

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Essential Exam Strategies

Always line up decimal points when adding or subtracting
Count decimal places carefully when multiplying
Use estimation to check if your answer makes sense
Show your working clearly - partial marks are often available
Double-check decimal point placement - this is a common source of errors

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Key Points to Remember:

Alignment is key for addition and subtraction - always line up the decimal points
Count the decimal places in multiplication - add up the total from both numbers
Make the divisor whole when dividing by converting both numbers
Estimation helps you spot mistakes in decimal point placement
Practice makes perfect - decimal operations require careful attention to detail

Operations on decimals (Edexcel GCSE Maths): Revision Notes