Knowing Our Numbers Ex 1.2 Class 6 NCERT Solutions

Understanding Word Problems with Large Numbers

Exercise 1.2 is designed to test your ability to use the four basic mathematical operations (addition, subtraction, multiplication, and division) with large numbers in the context of word problems. The real skill here isn't just calculation, but understanding the story of the problem.

First, you need to read the problem carefully, maybe even two or three times. Imagine the situation in your head. Is someone gaining something (addition)? Is something being taken away or are you finding a difference (subtraction)? Are you finding the total of many equal groups (multiplication)? Or are you sharing a large amount into smaller, equal parts (division)? Look for keywords! Words like 'total', 'altogether', and 'sum' often mean addition. 'Left', 'difference', 'how much more' usually mean subtraction. 'Product' or 'times' point to multiplication, while 'each', 'share', and 'per' often signal division. Mastering this translation from English to math is the key to success.

A Step-by-Step Method to Solve Word Problems

1. Step 1: Read and Understand — Read the entire problem carefully. Identify what information is given and what question you need to answer. Don't rush this step!
2. Step 2: Identify Key Information — Note down all the numbers given in the problem. Figure out what each number represents (e.g., number of books, price of a TV).
3. Step 3: Choose the Correct Operation — Based on the question and keywords (like 'in all', 'left over', 'how many in each'), decide whether you need to add (+), subtract (-), multiply (×), or divide (÷).
4. Step 4: Perform the Calculation — Carefully perform the chosen operation. When working with large numbers, write them down neatly, aligning the place values correctly to avoid mistakes.
5. Step 5: Write the Final Answer — State your answer clearly with a concluding sentence. Don't forget to include the correct units (e.g., rupees, metres, books).

Worked Examples from Real Life

• Problem: A factory produces 12,500 toy cars every day. How many toy cars will it produce in the month of June (which has 30 days)? Solution: Step 1: Information Given - Cars produced in 1 day = 12,500 - Number of days = 30 (for June) Step 2: Operation to Use We need to find the total cars for 30 days, so we need to multiply. Step 3: Calculation 12500 × 30 ------- 00000 (12500 × 0) 37500x (12500 × 3) ------- 375000 ------- Step 4: Final Answer The factory will produce 375,000 toy cars in the month of June.
• Problem: A school library has 9,875 books. The school decided to buy 2,500 new books. Out of the new total, 1,250 books were found to be old and were removed. How many books are left in the library? Solution: This is a two-step problem. Step 1: Find the total books after buying new ones (Addition). 9,875 (old books) + 2,500 (new books) ------- 12,375 (total books) Step 2: Find the final number of books after removing old ones (Subtraction). 12,375 (total books) - 1,250 (removed books) ------- 11,125 (books left) Step 3: Final Answer There are 11,125 books left in the library.

Check Your Answer's Logic!

After you get an answer, always ask yourself: "Does this make sense?" For example, if you are dividing 100 sweets among 10 friends, and your answer is 1000, you know you've made a mistake! The answer should be smaller, not larger. This simple check can help you catch multiplication/division errors.

Also, in exams, always write proper statements for each step. Don't just write the numbers and the final answer. For example:

• 'Number of tickets sold on day 1 = 1,094'
• 'Total tickets sold = ...'

This shows the examiner you understand the process and can earn you partial marks even if your final calculation has a small error.

Practice Questions with Solutions

• Q: A famous cricketer has scored 15,030 runs so far. He wants to achieve a career target of 22,000 runs. How many more runs does he need to score? A: Step 1: Identify the given information. Total runs scored so far = 15,030. Target runs = 22,000. Step 2: Determine the operation. To find 'how many more', we need to find the difference between the target and the current score. This means we must subtract. Step 3: Perform the calculation. 22,000 - 15,030 -------- 6,970 -------- Final answer: The cricketer needs to score 6,970 more runs.
• Q: A merchant had ₹80,592 with her. She placed an order for purchasing 40 mobile phones at ₹1,200 each. How much money will remain with her after the purchase? A: Step 1: Calculate the total cost of the mobile phones. This is a multiplication problem. Cost of 1 phone = ₹1,200. Number of phones = 40. Total Cost = 1200 × 40 = 48,000. Step 2: Calculate the money remaining. This is a subtraction problem. Initial money = ₹80,592. Money spent = ₹48,000. Money remaining = 80,592 - 48,000 = 32,592. Final answer: ₹32,592 will remain with the merchant after the purchase.
• Q: To stitch a shirt, 2 m 15 cm cloth is needed. Out of 40 m cloth, how many shirts can be stitched and how much cloth will remain? A: Step 1: Convert all measurements to a single unit. It's easiest to use centimeters (cm). 1 m = 100 cm. So, 2 m 15 cm = (2 × 100) + 15 = 215 cm. Total cloth = 40 m = 40 × 100 = 4000 cm. Step 2: Find the number of shirts. We need to see how many times 215 cm fits into 4000 cm. This is a division problem. 4000 ÷ 215. When you calculate, 4000 ÷ 215 gives a quotient of 18 and a remainder of 130. Step 3: Interpret the result. The quotient (18) is the number of shirts that can be stitched. The remainder (130) is the amount of cloth left over in cm. Final answer: 18 shirts can be stitched, and 130 cm (or 1 m 30 cm) of cloth will remain.
• Q: A newspaper vendor delivers 250 newspapers every day. How many newspapers does he deliver in the months of January and February combined in a non-leap year? A: Step 1: Find the total number of days. Number of days in January = 31. Number of days in February (non-leap year) = 28. Total days = 31 + 28 = 59 days. Step 2: Calculate the total number of newspapers delivered. This is a multiplication problem. Newspapers per day = 250. Total days = 59. Total newspapers = 250 × 59. 250 x 59 ----- 2250 (250 × 9) 1250x (250 × 5) ----- 14750 ----- Final answer: The vendor delivers 14,750 newspapers in January and February combined.

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