Addition of Decimals
Addition of decimals works just like addition of whole numbers, with one critical rule: line up the decimal points. Once the decimal points are aligned vertically, you add column by column from right to left, carrying over when the sum in any column reaches 10 or more.
We use decimal addition every day without even thinking about it: adding prices while shopping at the market, combining measurements when sewing or cooking, or totalling the distance walked in a day. The challenge for students is remembering to align the decimal points and handle numbers with different numbers of decimal places.
In Class 5, you will add decimals with the same number of decimal places, add decimals with different decimal places, add whole numbers to decimals, add three or more decimals, and solve word problems involving money, weight, distance, and time.
What is Addition of Decimals - Class 5 Maths (Decimals)?
Adding decimals means finding the total (sum) of two or more decimal numbers by placing them in columns with the decimal points aligned.
Golden Rule: Always line up the decimal points vertically before adding.
Addition of Decimals Formula
Steps to add decimals (the AEAD method):
- Align: Write the numbers one below the other with decimal points in a straight vertical line.
- Equalise: If numbers have different decimal places, add trailing zeros to the shorter number so all have the same number of decimal places.
- Add: Add from the rightmost column to the left, just like whole-number addition. Carry over when a column sum is 10 or more.
- Decimal: Place the decimal point in the answer directly below the decimal points above.
Align → Equalise → Add → Decimal point
Estimation tip: Before adding, round each number to the nearest whole and add mentally. This gives a rough answer to check against your exact calculation.
Types and Properties
Types of decimal addition problems:
- Same number of decimal places: e.g., 3.45 + 2.31 = 5.76. Straightforward — just align and add.
- Different decimal places: e.g., 4.5 + 3.25 → write as 4.50 + 3.25 = 7.75. Must add trailing zero.
- Whole number + Decimal: e.g., 8 + 2.75 → write as 8.00 + 2.75 = 10.75. Write the whole number with .00.
- Adding three or more decimals: Line up all decimal points in one column, add all digits in each column.
- Addition with carrying: When column sums exceed 9, carry to the next column. Example: 7.86 + 5.47 involves carrying.
- Word problems: Finding total cost, total distance, total weight, combined scores, etc.
Solved Examples
Example 1: Example 1: Same Decimal Places
Problem: Add 12.34 + 5.62.
Solution:
Step 1: Align decimal points:
12.34
+ 5.62
------
17.96
Step 2: Add each column: Hundredths: 4+2=6. Tenths: 3+6=9. Ones: 2+5=7. Tens: 1+0=1.
Estimation check: 12 + 6 = 18. Our answer 17.96 is close. Correct!
Answer: 12.34 + 5.62 = 17.96
Example 2: Example 2: Different Decimal Places
Problem: Add 6.5 + 3.875.
Solution:
Step 1: Equalise: 6.5 has 1 decimal place, 3.875 has 3. Write 6.5 as 6.500.
6.500
+ 3.875
------
10.375
Step 2: Thousandths: 0+5=5. Hundredths: 0+7=7. Tenths: 5+8=13 (write 3, carry 1). Ones: 6+3+1=10 (write 0, carry 1). Tens: 0+0+1=1.
Answer: 6.5 + 3.875 = 10.375
Example 3: Example 3: Whole Number + Decimal
Problem: Add 15 + 4.73.
Solution:
Step 1: Write 15 as 15.00 (a whole number has zero decimal places, so add .00).
15.00
+ 4.73
------
19.73
Step 2: Hundredths: 0+3=3. Tenths: 0+7=7. Ones: 5+4=9. Tens: 1.
Answer: 15 + 4.73 = 19.73
Example 4: Example 4: Addition with Multiple Carries
Problem: Add 7.86 + 5.47.
Solution:
7.86
+ 5.47
-----
13.33
Column by column:
- Hundredths: 6 + 7 = 13. Write 3, carry 1.
- Tenths: 8 + 4 + 1 (carry) = 13. Write 3, carry 1.
- Ones: 7 + 5 + 1 (carry) = 13. Write 3, carry 1.
- Tens: 0 + 0 + 1 (carry) = 1.
Estimation check: 8 + 5 = 13. Our answer 13.33 is close. Correct!
Answer: 7.86 + 5.47 = 13.33
Example 5: Example 5: Adding Three Decimals
Problem: Add 2.4 + 3.15 + 0.625.
Solution:
Step 1: Equalise to 3 decimal places: 2.400 + 3.150 + 0.625
2.400
3.150
+ 0.625
------
6.175
Column by column: Thousandths: 0+0+5=5. Hundredths: 0+5+2=7. Tenths: 4+1+6=11 (write 1, carry 1). Ones: 2+3+0+1=6.
Answer: 2.4 + 3.15 + 0.625 = 6.175
Example 6: Example 6: Word Problem (Shopping Bill)
Problem: Meera buys a notebook for Rs.45.50 and a pen for Rs.12.75. How much does she pay in total?
Solution:
Identify: Total cost = sum of both prices.
45.50
+ 12.75
------
58.25
Check: 45 + 13 = 58. Our answer Rs.58.25 is close. Reasonable.
Answer: Meera pays Rs.58.25 in total.
Example 7: Example 7: Word Problem (Distance)
Problem: Arjun walks 1.75 km to school and then 0.8 km to the library. What is the total distance walked?
Solution:
Step 1: Equalise: 1.75 + 0.80
1.75
+ 0.80
-----
2.55
Interpretation: Arjun walks 2.55 km in total, which is about 2 km and 550 metres.
Answer: Arjun walks 2.55 km in total.
Example 8: Example 8: Word Problem (Weight of Fruits)
Problem: A fruit seller weighs three bags: apples (2.5 kg), bananas (1.25 kg), and oranges (3.125 kg). Find the total weight.
Solution:
Step 1: Equalise to 3 decimal places: 2.500 + 1.250 + 3.125
2.500
1.250
+ 3.125
------
6.875
Estimation: 3 + 1 + 3 = 7 kg. Our answer 6.875 is close. Correct!
Answer: Total weight = 6.875 kg
Example 9: Example 9: Word Problem (Cricket Run Rate)
Problem: In a cricket match, India's run rate in the first 10 overs was 4.5 runs per over, and in the next 10 overs it was 6.75 runs per over. What is the sum of the two run rates?
Solution:
Step 1: Equalise: 4.50 + 6.75
4.50
+ 6.75
-----
11.25
Note: The sum of run rates (11.25) is not the average. The average run rate = 11.25 ÷ 2 = 5.625 per over.
Answer: Sum of run rates = 11.25
Example 10: Example 10: Adding Multiple Items (Shopping)
Problem: Priya buys a tiffin box for Rs.235.60, a water bottle for Rs.189.95, and a school bag for Rs.575.00. What is the total cost?
Solution:
235.60
189.95
+ 575.00
-------
1000.55
Column work: Hundredths: 0+5+0=5. Tenths: 6+9+0=15 (write 5, carry 1). Ones: 5+9+5+1=20 (write 0, carry 2). Tens: 3+8+7+2=20 (write 0, carry 2). Hundreds: 2+1+5+2=10 (write 0, carry 1). Thousands: 1.
Answer: Total cost = Rs.1000.55
Real-World Applications
Real-life uses of decimal addition:
- Shopping: Adding prices of multiple items to find the total bill at a grocery store or stationery shop.
- Measurement: Adding lengths of wood pieces for a shelf, weights of ingredients for cooking, or volumes of liquids when mixing.
- Travel: Calculating total distance covered in multiple legs of a journey (home to school, school to tuition, etc.).
- Banking: Adding multiple deposits or credits to find the total account balance.
- Sports: Adding scores from multiple rounds, adding timings for relay races, or combining distances in multi-event competitions.
- Health: Adding nutritional values (calories, protein in grams) from different food items.
Key Points to Remember
- Always align the decimal points vertically before adding. This is the most important rule.
- Add trailing zeros to equalise the number of decimal places. This does not change the value.
- Add column by column from right to left, carrying over when any column sum is 10 or more.
- The decimal point in the answer is placed directly below the decimal points in the numbers above.
- Adding a whole number and a decimal: write the whole number with .00 (e.g., 5 becomes 5.00).
- The sum of two positive decimals is always greater than each individual number.
- Estimation check: Round each decimal to the nearest whole number and add mentally. Your exact answer should be close to this estimate.
- Verify by subtracting one number from the sum — you should get the other number.
Practice Problems
- Add 23.46 + 8.37.
- Add 5.6 + 12.345.
- Add 9 + 3.58. (Remember to write 9 as 9.00.)
- Add 4.25 + 3.8 + 1.125.
- Ria buys a pencil for Rs.8.50, an eraser for Rs.5.25, and a sharpener for Rs.3.75. What is the total cost?
- Neha jogs 2.35 km on Monday and 3.7 km on Tuesday. What is the total distance jogged?
- A container has 4.5 litres of water. Dev pours in 2.75 litres more. How much water is in the container now?
- Find the sum: 0.005 + 0.05 + 0.5. Express your answer as a decimal.
Frequently Asked Questions
Q1. How do I add two decimal numbers?
Write the numbers one below the other with decimal points aligned vertically. Add trailing zeros so both have the same number of decimal places. Then add column by column from right to left, carrying when needed. Place the decimal point directly below in the answer.
Q2. Why do we need to line up the decimal points?
Aligning decimal points ensures that tenths are added to tenths, hundredths to hundredths, and so on. Without proper alignment, you would add digits of different place values and get a wrong answer.
Q3. Can I add a whole number and a decimal?
Yes. Write the whole number with a decimal point and trailing zeros. For example, 7 + 3.45: write 7 as 7.00, then add 7.00 + 3.45 = 10.45.
Q4. What if the numbers have different numbers of decimal places?
Add trailing zeros to the shorter decimal until both have the same number of decimal places. For example, to add 4.5 and 3.125: write 4.5 as 4.500, then add 4.500 + 3.125 = 7.625.
Q5. Does adding trailing zeros change the number?
No. 4.5 = 4.50 = 4.500. Trailing zeros after the decimal do not change the value. They only help with alignment during addition and subtraction.
Q6. How do I check my decimal addition answer?
Two methods: (1) Estimate by rounding each number to the nearest whole and adding mentally. If your exact answer is close, it is likely correct. (2) Subtract one addend from the sum — you should get the other addend.
Q7. Is decimal addition related to fraction addition?
Yes, they give the same result but use different methods. In decimal addition, you align decimal points. In fraction addition, you find a common denominator. For example, 0.5 + 0.25 = 0.75, and 1/2 + 1/4 = 3/4 = 0.75.
Q8. Can carrying happen in decimal addition just like whole numbers?
Yes. Carrying works exactly as in whole-number addition. If the sum in any column is 10 or more, write the ones digit in that column and carry the tens digit to the next column on the left.
Q9. Is this topic in the NCERT Class 5 syllabus?
Yes. Addition of decimals is a key topic in the NCERT/CBSE Class 5 Maths curriculum under the Decimals chapter. Students learn the column method with alignment and apply it to word problems.
Related Topics
- Subtraction of Decimals
- Decimals (Grade 5)
- Addition of Decimals
- Comparing and Ordering Decimals
- Multiplication of Decimals
- Division of Decimals
- Converting Fractions to Decimals (Grade 5)
- Converting Decimals to Fractions
- Decimal Word Problems (Grade 5)
- Decimal Place Value (Grade 5)
- Rounding Decimals
- Multiplying Decimals by 10, 100 and 1000
- Dividing Decimals by 10, 100 and 1000
