CBSE Class 6 Maths: Decimals Exercise 8.4 (NCERT Solutions)

The Big Idea: How to Add and Subtract Decimals

Adding and subtracting decimals might seem tricky, but there's one golden rule that makes it easy: Always line up the decimal points! When you write the numbers one below the other, make sure the decimal points form a perfectly straight vertical line. Why is this so important? Because it ensures you are adding or subtracting the correct place values. You add tenths to tenths, hundredths to hundredths, and ones to ones. Imagine you have rupees and paise. You would add rupees to rupees and paise to paise, right? It's the same idea! If a number doesn't seem to have enough decimal places (like adding 2.5 to 3.42), you can add a zero at the end (2.5 becomes 2.50). This doesn't change the number's value but makes the columns line up perfectly. This process is called making 'like decimals', and it's your secret weapon for getting the right answer every time.

Step-by-Step Guide: Adding and Subtracting Decimals

1. Step 1: Align the Numbers — Write the numbers you want to add or subtract in a column. The most crucial part is to make sure the decimal points are directly under each other. If you have a whole number like 25, write it as 25. to see its decimal point.
2. Step 2: Pad with Zeros (Make Like Decimals) — Look at the numbers. Do they have the same number of digits after the decimal point? If not, add zeros to the end of the shorter ones until they match. For example, to add 14.5 and 2.673, you would write 14.5 as 14.500.
3. Step 3: Add or Subtract — Now, just ignore the decimal points for a moment and add or subtract the numbers as if they were whole numbers. Start from the rightmost column and move left. Remember to borrow if you're subtracting and a top digit is smaller than the bottom one.
4. Step 4: Place the Decimal Point — Once you have your answer, bring the decimal point straight down into your answer line. It should be in the same column as the decimal points of the numbers you were working with. That's it!

Worked Examples: Solving Real-Life Problems

• Problem 1: Finding Change Ravi bought a notebook for ₹ 45.75. He gave the shopkeeper a ₹ 100 note. How much money did he get back? Solution: We need to subtract the cost of the notebook from the money Ravi gave. Step 1: Write ₹ 100 as a decimal: 100.00. Step 2: Align the decimal points and subtract: 100.00 - 45.75 ---------- Step 3: Perform subtraction, borrowing where needed. 9 9 9 10 1 0 0 . 0 0 - 4 5 . 7 5 ---------- 5 4 . 2 5 Final Answer: Ravi got back ₹ 54.25.
• Problem 2: Calculating Total Distance Sunita travelled 15 km 268 m by bus, 7 km 7 m by car and 500 m on foot in order to reach her school. How far is her school from her residence? Solution: First, we must convert all distances to a single unit, kilometres (km). Step 1: Convert all measurements to km. Distance by bus = 15 km 268 m = 15.268 km Distance by car = 7 km 7 m = 7.007 km Distance on foot = 500 m = 0.500 km Step 2: Add all the distances together. Align the decimal points. 15.268 7.007 + 0.500 ---------- 22.775 Final Answer: Sunita's school is 22.775 km from her residence.

The Golden Rule & Common Mistakes

• Don't Forget to Align! The most common mistake is not lining up the decimal points. Always write the numbers vertically with the points in a straight column before you start.
• Whole Numbers are Decimals too! To subtract 9.85 from 20, you must treat 20 as 20.00. Adding the decimal point and zeros is key.
• Borrowing Works the Same Way: When subtracting, if a digit on top is smaller than the digit below it, you borrow from the digit to its left, just like you've always done. The decimal point doesn't change the borrowing rule.
• Units Must Match: In word problems, make sure all quantities are in the same unit (like all in 'kg' or all in 'km') before you add or subtract.

Practice Questions with Solutions

• Q: Find the sum of 27.076 + 0.55 + 0.004. A: Step 1: Arrange the numbers vertically, aligning the decimal points. Add zeros to make them 'like decimals'. 27.076 0.550 + 0.004 ---------- Step 2: Add the numbers column by column from right to left. 6+0+4 = 10 (write 0, carry 1) 1+7+5+0 = 13 (write 3, carry 1) 1+0+5+0 = 6 7+0+0 = 7 2 = 2 Step 3: Place the decimal point in the answer directly below the others. Final answer: 27.630
• Q: Subtract 2.58 kg from 8.5 kg. A: Step 1: Write the numbers so the decimal points align. Write 8.5 as 8.50 to make it a 'like decimal' with 2.58. 8.50 kg - 2.58 kg ---------- Step 2: Perform the subtraction, borrowing where necessary. In the hundredths place, we can't subtract 8 from 0, so we borrow from the 5. 4 10 8.5 0 - 2.5 8 ---------- 5.9 2 Final answer: 5.92 kg
• Q: Aarav had a rope of length 10.5 m. He cut off a piece of 4.78 m. What is the length of the remaining rope? A: Step 1: We need to subtract the length of the cut piece from the total length. Write 10.5 as 10.50. 10.50 m - 4.78 m ---------- Step 2: Align the decimal points and subtract. You will need to borrow. 9 14 10 1 0 . 5 0 - 4 . 7 8 ---------- 5 . 7 2 Final answer: The length of the remaining rope is 5.72 m.
• Q: Tina bought fruits weighing 5 kg 300 g and vegetables weighing 3 kg 250 g. What is the total weight of items she bought? A: Step 1: Convert both weights to a single unit, kilograms (kg). Remember 1000g = 1kg. Weight of fruits = 5 kg 300 g = 5.300 kg Weight of vegetables = 3 kg 250 g = 3.250 kg Step 2: Add the two weights, keeping the decimal points aligned. 5.300 kg + 3.250 kg ---------- 8.550 kg Final answer: The total weight is 8.550 kg.

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