Key Ideas
Line up the places: write units under units, tens under tens, and so on. Always start from the units place.
Addition — carrying: if a column adds up to 10 or more, write the units digit and carry the tens digit to the next column on the left.
Subtraction — borrowing: if the upper digit is smaller, borrow 1 from the next place on the left. It becomes 10 in the current place.
Checking a subtraction: Difference + number subtracted = the bigger number. If they match, the answer is correct.
Problem Set 7
QAdd:
(1) 40,722+ 13,819 54,541
(2) 56,427+ 10,648 67,075
(3) 64,027+ 28,409 92,436
(4) 33,216+ 28,540 61,756
- 40,722 + 13,819 = 54,541
- 56,427 + 10,648 = 67,075
- 64,027 + 28,409 = 92,436
- 33,216 + 28,540 = 61,756
Problem Set 8
QAdd:
(1) 42,311+ 65,36,624 65,78,935
(2) 3,17,529+ 8,04,613 11,22,142
(3) 12,42,746+ 4,83,748 17,26,494
(4) 24,12,636+ 23,19,058 47,31,694
(5) 2,654+ 71,209+ 5,03,789 5,77,652
(6) 29+ 726+ 51,36,274 51,37,029
(7) 14,02,649+ 524+ 28,13,749 42,16,922
(8) 23,45,678+ 9,87,654 33,33,332
(9) 22+ 6,047+ 3,84,527 3,90,596
(10) 2,345+ 65,432+ 76,54,369 77,22,146
- 42,311 + 65,36,624 = 65,78,935
- 3,17,529 + 8,04,613 = 11,22,142
- 12,42,746 + 4,83,748 = 17,26,494
- 24,12,636 + 23,19,058 = 47,31,694
- 2,654 + 71,209 + 5,03,789 = 5,77,652
- 29 + 726 + 51,36,274 = 51,37,029
- 14,02,649 + 524 + 28,13,749 = 42,16,922
- 23,45,678 + 9,87,654 = 33,33,332
- 22 + 6,047 + 3,84,527 = 3,90,596
- 2,345 + 65,432 + 76,54,369 = 77,22,146
Problem Set 9
1In a certain election, 13,47,048 women and 14,29,638 men cast their votes. How many votes were polled altogether?
13,47,048+ 14,29,638 27,76,686
Votes polled altogether = women’s votes + men’s votes = 27,76,686 votes.
2What will be the sum of the smallest and the largest six-digit numbers?
The smallest six-digit number is 1,00,000 and the largest six-digit number is 9,99,999.
1,00,000+ 9,99,999 10,99,999
The sum is 10,99,999 (ten lakh ninety-nine thousand nine hundred and ninety-nine).
3If Surekhatai bought a tractor for ₹ 8,07,957 and a thresher for ₹ 32,609, how much money did she spend altogether?
8,07,957+ 32,609 8,40,566
Surekhatai spent ₹ 8,40,566 altogether.
4A textile mill produced 17,24,938 metres of cloth last year and 23,47,056 metres this year. What was the total production for the two years?
17,24,938+ 23,47,056 40,71,994
The total production for the two years was 40,71,994 metres of cloth.
5If the Government gave ₹ 34,62,950 worth of computers and ₹ 3,26,578 worth of TV sets to the schools, what is the total amount it spent on this equipment?
34,62,950+ 3,26,578 37,89,528
The Government spent ₹ 37,89,528 on this equipment.
Problem Set 10
QSubtract:
(1) 64,293− 28,547 35,746
(2) 37,058− 23,469 13,589
(3) 71,540− 58,628 12,912
(4) 50,432− 48,647 1,785
- 64,293 − 28,547 = 35,746
- 37,058 − 23,469 = 13,589
- 71,540 − 58,628 = 12,912
- 50,432 − 48,647 = 1,785
Check (1): 35,746 + 28,547 = 64,293. The sum equals the upper number, so the answer is correct. The other answers can be checked the same way.
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Problem Set 11
QSubtract:
(1) 8,57,513− 4,82,256 3,75,257
(2) 13,17,519− 10,07,423 3,10,096
(3) 68,34,501− 23,57,823 44,76,678
(4) 45,43,827− 12,05,938 33,37,889
(5) 70,12,345− 28,64,547 41,47,798
(6) 38,01,213− 37,54,648 46,565
- 8,57,513 − 4,82,256 = 3,75,257
- 13,17,519 − 10,07,423 = 3,10,096
- 68,34,501 − 23,57,823 = 44,76,678
- 45,43,827 − 12,05,938 = 33,37,889
- 70,12,345 − 28,64,547 = 41,47,798
- 38,01,213 − 37,54,648 = 46,565
Problem Set 12
1Prathamesh wants to buy a laptop worth 27,450 rupees. He has 22,975 rupees. What is the amount he still needs to be able to buy the laptop?
Prathamesh still needs ₹ 4,475.
2A company produced 44,730 scooters in a certain year and 43,150 in the next. How many more scooters did they produce in the previous year?
The company produced 1,580 more scooters in the previous year.
3In a certain city, the number of men is 16,37,856 and the number of women is 16,52,978. By how many does the number of women exceed the number of men?
16,52,978− 16,37,856 15,122
The number of women exceeds the number of men by 15,122.
4An organization decided to collect 25,00,000 rupees for a certain project. They collected 26,57,340 through donations and other kinds of aid. By how much did they exceed their target?
26,57,340− 25,00,000 1,57,340
They exceeded their target by ₹ 1,57,340.
5Use the numbers 23,849 and 27,056 to make a subtraction problem. Solve the problem.
Problem: A school library had 23,849 books last year. This year it has 27,056 books. How many new books were added to the library this year?
3,207 new books were added this year.
Students may frame any problem of their own. In every subtraction problem with these numbers, the smaller number 23,849 is subtracted from the bigger number 27,056, and the answer is 3,207.
Problem Set 13
1The Forest Department planted 23,078 trees of khair, 19,476 of behada besides trees of several other kinds. If the Department planted 50,000 trees altogether, how many trees were neither of khair nor of behada?
Step 1: Add the known parts.
Step 2: Subtract that sum from the total.
Khair + behada trees 23,078+ 19,476 42,554
Total − khair and behada 50,000− 42,554 7,446
Check: parts add up to the total 23,078+ 19,476+ 7,446 50,000
7,446 trees were neither khair nor behada.
2A city has a population of 37,04,926. If this includes 11,24,069 men and 10,96,478 women, what is the number of children in the city?
Step 1: Add the known parts.
Step 2: Subtract that sum from the total.
Men + women 11,24,069+ 10,96,478 22,20,547
Population − men and women 37,04,926− 22,20,547 14,84,379
Check: parts add up to the total 11,24,069+ 10,96,478+ 14,84,379 37,04,926
The number of children in the city is 14,84,379.
3The management of a certain factory had 25,40,600 rupees in the labour welfare fund. From this fund, 12,37,865 rupees were used for medical expenses, 8,42,317 rupees were spent on the education of the workers’ children and the remaining was put aside for a canteen. How much money was put aside for the canteen?
Step 1: Add the known parts.
Step 2: Subtract that sum from the total.
Medical + education 12,37,865+ 8,42,317 20,80,182
Fund − money spent 25,40,600− 20,80,182 4,60,418
Check: parts add up to the total 12,37,865+ 8,42,317+ 4,60,418 25,40,600
₹ 4,60,418 was put aside for the canteen.
4For a three-day cricket match, 13,608 tickets were sold on the first day and 8,955 on the second day. If, altogether, 36,563 tickets were sold in three days, how many were sold on the third day?
Step 1: Add the known parts.
Step 2: Subtract that sum from the total.
Day 1 + Day 2 13,608+ 8,955 22,563
Total − first two days 36,563− 22,563 14,000
Check: parts add up to the total 13,608+ 8,955+ 14,000 36,563
14,000 tickets were sold on the third day.
In each problem of Problem Set 13, the third box adds all the parts together. The sum equals the given total, which confirms the answer, just as in the textbook’s Example (3).
