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NCERT Solutions Ganita Prakash Chapter 3 Figure it Out — Digits and Operations

Book page 66 & 67 Updated on2026-09-05

Q1.
Write an example for each of the below scenarios whenever possible: 5-digit + 5-digit to give a 5-digit sum more than 90,250; 5-digit + 3-digit to give a 6-digit sum; 4-digit + 4-digit to give a 6-digit sum; 5-digit + 5-digit to give a 6-digit sum; 5-digit + 5-digit to give 18,500; 5-digit − 5-digit to give a difference less than 56,503; 5-digit − 3-digit to give a 4-digit difference; 5-digit − 4-digit to give a 4-digit difference; 5-digit − 5-digit to give a 3-digit difference; 5-digit − 5-digit to give 91,500. Could you find examples for all the cases? If not, think and discuss what could be the reason.
Answer
ScenarioExamplePossible?
5-digit + 5-digit → 5-digit sum more than 90,25045,000 + 45,500 = 90,500Yes
5-digit + 3-digit → 6-digit sum99,999 + 999 = 1,00,998Yes
4-digit + 4-digit → 6-digit sumlargest possible is 9999 + 9999 = 19,998No
5-digit + 5-digit → 6-digit sum60,000 + 40,000 = 1,00,000Yes
5-digit + 5-digit → 18,500smallest possible is 10,000 + 10,000 = 20,000No
5-digit − 5-digit → difference less than 56,50380,000 − 50,000 = 30,000Yes
5-digit − 3-digit → 4-digit difference10,000 − 999 = 9,001Yes
5-digit − 4-digit → 4-digit difference12,000 − 2,500 = 9,500Yes
5-digit − 5-digit → 3-digit difference50,999 − 50,000 = 999Yes
5-digit − 5-digit → 91,500largest possible is 99,999 − 10,000 = 89,999No

Three of the ten cases are impossible. Here is the reason for each:

  • 4-digit + 4-digit = 6-digit: even the two biggest 4-digit numbers give 9999 + 9999 = 19,998, which has only 5 digits. To reach 1,00,000 you would need much larger numbers.
  • 5-digit + 5-digit = 18,500: the smallest 5-digit number is 10,000, so the smallest possible sum is 20,000 — already bigger than 18,500.
  • 5-digit − 5-digit = 91,500: the biggest difference two 5-digit numbers can have is 99,999 − 10,000 = 89,999, which is less than 91,500.
Math Talk: make your own such questions and let your friends decide. Two good ones — “4-digit + 4-digit to give 2,900” (possible: 1,900 + 1,000 = 2,900) and “5-digit + 5-digit to give a 7-digit sum” (impossible: the biggest sum is 99,999 + 99,999 = 1,99,998, only 6 digits).
Q2.
Always, Sometimes, Never? Below are some statements. Think, explore and find out if each of the statement is ‘Always true’, ‘Only sometimes true’ or ‘Never true’. Why do you think so? a. 5-digit number + 5-digit number gives a 5-digit number b. 4-digit number + 2-digit number gives a 4-digit number c. 4-digit number + 2-digit number gives a 6-digit number d. 5-digit number – 5-digit number gives a 5-digit number e. 5-digit number – 2-digit number gives a 3-digit number
Answer
StatementVerdictReason with an example
a. 5-digit + 5-digit = 5-digitOnly sometimes true10,000 + 10,000 = 20,000 ✓ but 60,000 + 50,000 = 1,10,000 ✗
b. 4-digit + 2-digit = 4-digitOnly sometimes true1,000 + 10 = 1,010 ✓ but 9,999 + 99 = 10,098 ✗
c. 4-digit + 2-digit = 6-digitNever truethe biggest possible sum is 9,999 + 99 = 10,098 — only 5 digits
d. 5-digit − 5-digit = 5-digitOnly sometimes true99,999 − 10,000 = 89,999 ✓ but 12,000 − 10,000 = 2,000 ✗
e. 5-digit − 2-digit = 3-digitNever truethe smallest possible answer is 10,000 − 99 = 9,901 — still 4 digits
How to decide quickly: test the two extreme cases. If the smallest possible answer and the largest possible answer are both outside what the statement asks for, the statement is never true. If one example works and another does not, it is only sometimes true.
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