CBSE Class 6 Maths: Decimals - Exercise 8.5 (Addition and Subtraction)

Understanding Addition and Subtraction of Decimals

Adding and subtracting decimals is a lot like adding and subtracting whole numbers, but with one very important rule: you must align the decimal points! Think of it like making sure your hundreds are under hundreds, tens under tens, and ones under ones when adding whole numbers. With decimals, we extend this idea to tenths under tenths, hundredths under hundredths, and so on. If numbers have a different number of decimal places, you can add zeros to the end of the shorter decimal without changing its value. For example, 2.5 is the same as 2.50 or 2.500. These trailing zeros are super helpful for lining up your numbers correctly. Once aligned, you can perform the addition or subtraction column by column, just like with whole numbers, and then simply place the decimal point in your answer directly below the decimal points in the numbers you operated on. This careful alignment is the key to getting accurate results every time. Remember, place value is your best friend here!

Step-by-Step: Adding and Subtracting Decimals

1. Step 1: Align the Decimal Points — Write the numbers one below the other, making sure their decimal points are exactly aligned vertically. This ensures that digits with the same place value are in the same column (ones under ones, tenths under tenths, etc.).
2. Step 2: Add Zeros (if needed) — If the numbers have different numbers of digits after the decimal point, add trailing zeros to the number(s) with fewer decimal places until all numbers have the same number of decimal places. This makes the columns complete and prevents errors.
3. Step 3: Perform the Operation — Add or subtract the numbers as you would with whole numbers, starting from the rightmost digit. Remember to carry over digits in addition or borrow in subtraction when necessary.
4. Step 4: Place the Decimal Point — Once you have the result, place the decimal point in your answer directly below the decimal points in the numbers you added or subtracted. The decimal point will always maintain its vertical alignment.

Examples of Decimal Operations

• Example 1: Add 23.54 and 6.8 1. Align decimal points: 23.54 + 6.8 2. Add zeros to equalize decimal places: 23.54 + 6.80 3. Add column by column from right: `` 23.54 + 6.80 ------- 30.34 `` Final answer: 30.34
• Example 2: Subtract 12.35 from 45.7 1. Align decimal points: 45.7 - 12.35 2. Add zeros to equalize decimal places: 45.70 - 12.35 3. Subtract column by column from right (borrowing when needed): `` 6 10 (borrow from 7, then 10 becomes 10+0) 45.70 - 12.35 ------- 33.35 `` Final answer: 33.35
• Example 3: Find the sum of 0.75, 10.42, and 2.005 1. Align decimal points: 0.75 10.42 2.005 2. Add zeros: 0.750 10.420 + 2.005 3. Add: `` 0.750 10.420 + 2.005 ------- 13.175 `` Final answer: 13.175

YoLearn AI Tutor's Exam Tip: Mastering Decimal Operations

To avoid common errors in exams, always double-check your alignment of decimal points before starting any calculation. Many students make mistakes by treating decimals like whole numbers for a moment, leading to incorrect place values. Another critical tip is to practice adding leading or trailing zeros to ensure all numbers have the same number of decimal places before you begin adding or subtracting. This visual aid makes the columns neat and significantly reduces the chance of errors, especially when borrowing or carrying over. Finally, re-read word problems carefully to identify what operation is needed (sum means add, difference means subtract, total means add, etc.). A small mistake in understanding the question can lead to a completely wrong answer.

Practice Questions with Solutions

• Q: Add: 15.3 + 7.85 A: Step 1: Align the decimal points and add a zero to 15.3. `` 15.30 + 7.85 ------ ` Step 2: Add column by column from right to left. ` 15.30 + 7.85 -------- 23.15 `` Final answer: 23.15
• Q: Subtract: 34.6 - 12.08 A: Step 1: Align the decimal points and add a zero to 34.6. `` 34.60 - 12.08 ------- ` Step 2: Subtract column by column from right to left, borrowing as needed. ` 5 10 (borrow from 6, then 10+0) 34.60 - 12.08 -------- 22.52 `` Final answer: 22.52
• Q: Ravi bought a book for ₹35.75 and a pen for ₹15.50. How much money did he spend in total? A: Step 1: To find the total money spent, we need to add the cost of the book and the pen. Cost of book = ₹35.75 Cost of pen = ₹15.50 Step 2: Align the decimal points and add. `` 35.75 + 15.50 -------- 51.25 `` Final answer: Ravi spent ₹51.25 in total.
• Q: The length of a rope is 20.5 meters. If 4.75 meters of rope is cut off, what is the remaining length? A: Step 1: To find the remaining length, we need to subtract the cut length from the original length. Original length = 20.5 m Cut length = 4.75 m Step 2: Align the decimal points and add a zero to 20.5. Then subtract. `` 9 14 10 (borrow from 20, then 5, then 10+0) 20.50 - 4.75 -------- 15.75 `` Final answer: The remaining length of the rope is 15.75 meters.

Frequently Asked Questions