Adding, Subtracting, Multiplying and Dividing Decimals

Grade: 6–7 | Topic: Arithmetic

What You Will Learn

By the end of this page, you will be able to add, subtract, multiply, and divide decimal numbers confidently. Each operation has its own rule — and once you understand why the rule works, you will never mix them up again.

Theory

Adding and Subtracting Decimals

The rule: Line up the decimal points vertically. Then add or subtract as with whole numbers.

You can add zeros to the right of a decimal to make both numbers the same length — this does not change the value.

$3.75 + 2.4 = 3.75 + 2.40 = 6.15$

Why line up the decimal points? Because it ensures you are adding tenths to tenths, hundredths to hundredths — the place values match up correctly.

Multiplying Decimals

The rule:

1. Ignore the decimal points and multiply the numbers as if they were whole numbers
2. Count the total number of decimal places in both original numbers
3. Place the decimal point that many places from the right in your answer

$2.3 \times 1.4: \quad 23 \times 14 = 322, \quad \text{2 decimal places} \implies 3.22$

Why count decimal places? Multiplying by a decimal is the same as multiplying by a fraction: $2.3 \times 1.4 = \frac{23}{10} \times \frac{14}{10} = \frac{322}{100} = 3.22$.

Dividing Decimals

The rule: If the divisor (the number you are dividing by) has decimal places, multiply both the dividend and divisor by a power of 10 to make the divisor a whole number.

$\frac{6.4}{0.8} = \frac{6.4 \times 10}{0.8 \times 10} = \frac{64}{8} = 8$

If only the dividend has decimal places (divisor is already a whole number), simply place the decimal point directly above its position in the dividend and divide normally.

Worked Examples

Example 1: Adding Decimals with Different Lengths

Problem: Calculate $14.6 + 3.045 + 0.72$.

Step 1: Line up decimal points and pad with zeros. $14.600 + 3.045 + 0.720$

Step 2: Add column by column from right to left. $14.600 + 3.045 + 0.720 = 18.365$

Answer: 18.365

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Example 2: Subtracting Decimals

Problem: Calculate $20 - 4.37$.

Step 1: Write 20 as 20.00 to match decimal places. $20.00 - 4.37$

Step 2: Subtract, borrowing where needed. $20.00 - 4.37 = 15.63$

Answer: 15.63

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Example 3: Multiplying Decimals

Problem: Calculate $4.6 \times 0.35$.

Step 1: Ignore decimals and multiply $46 \times 35$. $46 \times 35 = 1610$

Step 2: Count total decimal places: $4.6$ has 1, $0.35$ has 2 — total of 3.

Step 3: Place decimal point 3 places from the right of 1610. $1610 \implies 1.610 = 1.61$

Answer: 1.61

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Example 4: Dividing a Decimal by a Decimal

Problem: Calculate $7.56 \div 0.12$.

Step 1: The divisor is $0.12$ — it has 2 decimal places. Multiply both by 100. $\frac{7.56}{0.12} = \frac{756}{12}$

Step 2: Divide normally. $756 \div 12 = 63$

Answer: 63

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Example 5: Real-World Problem

Problem: A roll of ribbon is 8.4 metres long. Maria cuts pieces that are each 0.6 metres. How many pieces does she get?

Step 1: Divide $8.4 \div 0.6$.

Step 2: Multiply both by 10: $\frac{84}{6} = 14$.

Answer: Maria gets 14 pieces.

Common Mistakes

Mistake 1: Not Lining Up Decimal Points When Adding

❌ $3.5 + 1.24$ written as $3.5 + 1.24$, then adding $35 + 124 = 159$ to get $1.59$.

✅ Line up: $3.50 + 1.24 = 4.74$. The decimal goes between the ones and tenths — it stays in the same column.

Mistake 2: Adding Decimal Places Instead of Counting Them When Multiplying

❌ $0.3 \times 0.4 = 1.2$ (student adds 1 place to get 1 decimal place).

✅ $0.3 \times 0.4$: $3 \times 4 = 12$, count 2 decimal places total, answer = $0.12$.

Mistake 3: Forgetting to Adjust the Dividend When Converting the Divisor

❌ $2.4 \div 0.3$: multiply divisor by 10 to get $2.4 \div 3 = 0.8$.

✅ Multiply both by 10: $24 \div 3 = 8$.

Practice Problems

Try these on your own before checking the answers:

1. $5.38 + 12.6 + 0.047$
2. $30 - 8.65$
3. $3.7 \times 0.08$
4. $9.45 \div 0.05$
5. Petrol costs $1.85 per litre. If a car takes 42.5 litres, what is the total cost?

Click to see answers

1. $5.380 + 12.600 + 0.047 = \mathbf{18.027}$
2. $30.00 - 8.65 = \mathbf{21.35}$
3. $37 \times 8 = 296$, 3 decimal places total = $\mathbf{0.296}$
4. $945 \div 5 = \mathbf{189}$
5. $185 \times 425 = 78{,}625$, 4 decimal places = $78.6250$. Total cost = $78.63 (rounded to cents).

Summary

• Adding/Subtracting: Line up decimal points, pad with zeros, then operate normally.
• Multiplying: Multiply as whole numbers, then count total decimal places and insert the decimal point.
• Dividing: Make the divisor a whole number by multiplying both numbers by the same power of 10.
• Never move just one number — always apply the same change to both parts of a division.

Related Topics

• Fractions — Complete Guide
• Converting Between Fractions and Decimals
• Converting Between Fractions, Decimals, and Percentages

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