Chapter: Multiplication and Division

Multiplication and Division

Elementary Mathematics - Class Five

📖 1. Key Facts & Formulas

Multiplicand: The number to be multiplied is called the multiplicand. (e.g., In 5 × 4 = 20, 5 is the multiplicand).
Multiplier: The number by which we multiply is called the multiplier. (e.g., In 5 × 4 = 20, 4 is the multiplier).
Product: The result obtained after multiplication is called the product. (e.g., In 5 × 4 = 20, 20 is the product).
Use of Multiplication: If the price or quantity of a single item is known, we multiply to find the total price or quantity of multiple items.
Rule of Multiplication: If we break down the multiplicand or multiplier and multiply them side by side, the product remains unchanged.
Multiplication with Zeros: If there are zeros at the end of the numbers, multiply the non-zero parts first and then place the total number of zeros at the right of the product. (e.g., For 8900 × 5000, multiply 89 × 5 = 445 and then put 5 zeros at the end: 44500000).
Easy Method of Multiplication: If the multiplier is 99 or 999, it can be written as (100 - 1) or (1000 - 1) to multiply easily.
Dividend: The number to be divided is called the dividend.
Divisor: The number by which we divide is called the divisor.
Quotient & Remainder: The result of division is the quotient, and the number left over is the remainder.
Most Important Rule of Division: The remainder must always be smaller than the divisor.
Division Formula: Dividend = (Divisor × Quotient) + Remainder.
Rule for Exact Division (No Remainder): If we subtract the remainder from the dividend, the resulting number is exactly divisible by the divisor.
Easy Division (by 10, 100, or 1000): Count the zeros in the divisor. Remove the same number of digits from the right side of the dividend. The removed digits form the 'Remainder', and the rest of the number forms the 'Quotient'.

✍️ 2. Fill in the Blanks

1. Multiplicand = Product ÷ (divided by) Multiplier.
(Explanation: Dividing the product by the multiplier gives the multiplicand)
2. If any number is multiplied by 1, the product and the multiplicand will be the same.
3. If any number is multiplied by 0 (zero), the product is always zero.
4. The smallest 4-digit number × 8325 = 8325000.
5. In 6042 × 514; 514 is the Multiplier.
6. If we break down the multiplicand or multiplier and multiply, the Product remains unchanged.
7. In case of division without remainder: Dividend ÷ Quotient = Divisor.
8. Dividend - Remainder = Divisor × Quotient.
9. If the largest 5-digit number is divided by 10, the remainder will be 9.
10. 2041 × 191 = 389831.
11. In 5340 × 457; 457 is the Multiplier.
12. If the price of 1 toy is 280 Taka, the price of 370 such toys is 103600 Taka.
13. 5[ 8 ]29 × 100 = 582900; the blank space will be filled with 8.
14. 580 × 3070 = 580 × (3000 + 70).
15. Mr. Roni earns 1850 Taka daily. In 180 days, he will earn 333000 Taka.
16. If the digits in the ones place of the product and multiplicand are 6 and 7 respectively, the digit in the ones place of the multiplier could be 8.
17. 5000 × 800 = 4 million (4000000).
18. There are 79 students in a classroom. If 3 students sit on each bench, 1 student will have to stand.
19. If the price of 45 pencils is 360 Taka, the price of one pencil is 8 Taka.
20. If 1445 Taka profit is made by selling 85 kg of apples, the profit per kg of apples is 17 Taka.
21. If 8500 is divided by 708, the quotient is 12 and the remainder is 4.
22. 1312 ÷ 32 = 41.
23. If a minimum of 6 is subtracted from 102, the result will be exactly divisible by 8.
24. 110 kg of sugar can be bought for 14850 Taka at the rate of 135 Taka per kg.
25. 63970 ÷ 100 = 639, Remainder 70.
26. If the price of 1 packet of tea is 220 Taka, the price of 110 such packets is 24200 Taka.
27. 1 box contains 99 oranges. 231 such boxes will contain 22869 oranges.
28. The product of the smallest and largest 3-digit numbers is 99900.
29. 10609 × 9999 = 106079391.
30. 799 × 8001 = 6392799.
31. A flyover earns 26500 Taka daily from tolls. In 110 days, it will earn a total of 2915000 Taka.
32. Mr. Sharif imported 230 headphones at the rate of 1097 Taka each. The total price of the headphones is 252310 Taka.
33. Dividend = (Divisor × Quotient) + Remainder.
34. The remainder is always smaller than the Divisor.
35. If a number is divided by 100, the quotient is 5 and the remainder is 12. The number is 512.
36. If 3342 is divided by 100, the remainder will be 42.
37. If 5400 is divided by 100, the quotient will be 54.
38. In a division problem, if the dividend is 2189 and the divisor is 180, the remainder will be 29.
39. 3600 ÷ 60 = 60.
40. In a division problem, if the dividend and the divisor are equal, the quotient will be 1.

📝 3. Short Questions

Short Q

1. In a multiplication problem, what do we get if we divide the product by the multiplicand?

Answer: Multiplier. (Explanation: Multiplicand × Multiplier = Product. Therefore, dividing the product by one of the numbers gives the other.)

Short Q

2. 5300 × 6000 = What?

Answer: 31800000 (Explanation: 53 × 6 = 318, then put the total 5 zeros at the right end to get 31800000)

Short Q

3. If the price of 1 packet of milk powder is 220 Taka, what is the price of 110 such packets?

Answer: 24200 Taka. (Explanation: 220 × 110 = 24200)

Short Q

4. A basket contains 99 apples. How many apples will 231 such baskets contain in total?

Answer: 22869. (Explanation: 231 × (100 - 1) = 23100 - 231 = 22869)

Short Q

5. What will be the product of the smallest and the largest 3-digit numbers?

Answer: 99900 (Explanation: 100 × 999 = 99900)

Short Q

6. 10609 × 9999 = What?

Answer: 106079391 (Explanation: 10609 × 10000 - 10609 = 106079391)

Short Q

7. A fair earns 26500 Taka daily by selling tickets. If the fair continues for 110 days, what will be the total earnings?

Answer: 2915000 Taka. (Explanation: 26500 × 110 = 2915000)

Short Q

8. Mr. Rafiq bought 230 keyboards at the rate of 1097 Taka each. How much money did he spend in total?

Answer: 252310 Taka. (Explanation: 1097 × 230 = 252310)

Short Q

9. For a cricket match, 23467 tickets were sold. If the price of each ticket is 175 Taka, what is the total amount of money earned from ticket sales?

Answer: 4106725 Taka. (Explanation: 23467 × 175 = 4106725)

Short Q

10. An orphanage received donations from 1260 people. If each person donated 2050 Taka, what is the total amount received?

Answer: 2583000 Taka. (Explanation: 1260 × 2050 = 2583000)

Short Q

11. Mr. Kamal distributed 530 notes of 500 Taka and 220 notes of 100 Taka among the helpless. How much money did he distribute in total?

Answer: 287000 Taka. (Explanation: 530×500 + 220×100 = 265000 + 22000 = 287000)

Short Q

12. What is the correct formula to find the divisor in a division problem?

Answer: Divisor = (Dividend - Remainder) ÷ Quotient.

Short Q

13. If you eat 6 chocolates every day from a packet of 50 chocolates, on which day will the packet be completely empty?

Answer: On the 9th day. (Explanation: 50 ÷ 6 leaves a remainder of 2. After 8 days, 2 chocolates will be left, which must be eaten on the 9th day.)

Short Q

14. What is the quotient when 55670 is divided by 100?

Answer: 556 (Explanation: When dividing by 100, the last 2 digits on the right become the remainder, and the rest becomes the quotient)

Short Q

15. If 2890 Taka is divided equally among 17 workers, how much money will each worker get?

Answer: 170 Taka. (Explanation: 2890 ÷ 17 = 170)

Short Q

16. If the dividend is 250, quotient is 16, and remainder is 10, what is the divisor?

Answer: 15 (Explanation: (250 - 10) ÷ 16 = 240 ÷ 16 = 15)

Short Q

17. How many meritorious students can be given a scholarship of 500 Taka each from a total fund of 9500 Taka?

Answer: 19 students. (Explanation: 9500 ÷ 500 = 19)

Short Q

18. A carton can hold 75 soaps. How many such cartons will be required to pack 15375 soaps?

Answer: 205 cartons. (Explanation: 15375 ÷ 75 = 205)

Short Q

19. If the divisor is 199, quotient is 83, and remainder is 110, what is the dividend?

Answer: 16627 (Explanation: (199 × 83) + 110 = 16627)

Short Q

20. What is the minimum number that should be subtracted from 9650 so that it becomes exactly divisible by 120?

Answer: 50 (Explanation: Dividing 9650 by 120 leaves a remainder of 50. Subtracting this remainder makes it completely divisible.)

📚 4. Competency-based / Structured Questions

Structured - 1

In an international cricket match, 13310 tickets were sold. The price of each ticket is 625 Taka. A portion of the collected money will be donated to a charity organization.
a. How much money was collected in total by selling tickets?
b. If the price of each ticket were 99 Taka, calculate the total sales money using an easy method.
c. If the total money collected (obtained in 'a') is divided equally among 125 poor people, how much will each person get?

Solution:
a. Price of 1 ticket = 625 Taka
Therefore, price of 13310 tickets = 13310 × 625 = 8318750 Taka. (Answer)

b. If the price of 1 ticket is 99 Taka:
13310 × 99 = 13310 × (100 - 1)
= (13310 × 100) - (13310 × 1)
= 1331000 - 13310 = 1317690 Taka. (Answer)

c. Total collected money = 8318750 Taka.
If this money is divided among 125 people, each person will get:
8318750 ÷ 125 = 66550 Taka. (Answer)

Structured - 2

To repair the village school building, the villagers decided to collect an equal amount of subscription from each family. 170 families in the village gave 400 Taka each. But a total of 79900 Taka is needed to repair the school.
a. How much money did the 170 families collect in total?
b. How much more money is needed to repair the school?
c. If the remaining required money for repairing the school has to be given equally by those 170 families, how much more money will each family have to pay?

Solution:
a. 1 family gives = 400 Taka
170 families give = 170 × 400 = 68000 Taka. (Answer)

b. Money needed for repair = 79900 Taka
Money collected = 68000 Taka
More money needed = 79900 - 68000 = 11900 Taka. (Answer)

c. More money needed is 11900 Taka. If 170 families give it equally, 1 family will have to pay:
11900 ÷ 170 = 70 Taka. (Answer)

Structured - 3

Before Eid, the owner of a readymade garments factory distributed 296192 Taka equally as Eid bonus among 356 workers of his factory. Besides, he donated one 500 Taka note to each of the 320 poor people in the area.
a. How much bonus did each worker of the factory get?
b. How much money did the owner donate in total among the poor people?
c. What is the difference between the total bonus given to the workers and the total donation given to the poor?

Solution:
a. 356 workers get bonus = 296192 Taka
1 worker gets = 296192 ÷ 356 = 832 Taka. (Answer)

b. Donated to 1 poor person = 500 Taka
Donated to 320 persons = 320 × 500 = 160000 Taka. (Answer)

c. Total bonus of workers = 296192 Taka
Total donation to the poor = 160000 Taka
Difference = 296192 - 160000 = 136192 Taka. (Answer)

Structured - 4

A student named Rafsan saves 840 Taka per month in a clay bank with the intention of buying a laptop with his saved money.
a. How much money does he save daily in the month of February (not a leap year)? (Assume, February = 28 days)
b. How much money will he save in total in 20 months?
c. In which month will his saved money cross 60,000 Taka?

Solution:
a. Savings in 28 days = 840 Taka
Daily (in 1 day) savings = 840 ÷ 28 = 30 Taka. (Answer)

b. Savings in 1 month = 840 Taka
Savings in 20 months = 840 × 20 = 16800 Taka. (Answer)

c. To save 60000 Taka, time needed = 60000 ÷ 840 months.
Dividing it, we get quotient 71 and remainder 360.
That means after 71 months, 360 Taka is left which he will save in the next month.
Therefore, in the (71 + 1) or 72nd month, his saved money will cross 60000. (Answer)

Structured - 5

A charity organization will distribute relief goods among 6018 cyclone-affected families. The organization gave relief goods worth 2999 Taka and a cash grant of 500 Taka to each family.
a. What was the total value of help (relief goods + cash) received by each family?
b. How much money did the organization distribute in total as cash grants?
c. Using an easy method, calculate the total cost incurred by the organization only for distributing relief goods.

Solution:
a. Relief goods = 2999 Taka, Cash = 500 Taka
Total help = 2999 + 500 = 3499 Taka. (Answer)

b. 1 family gets cash = 500 Taka
6018 families get = 6018 × 500 = 3009000 Taka. (Answer)

c. Value of relief goods for 6018 families = 6018 × 2999 Taka
In easy method:
= 6018 × (3000 - 1)
= (6018 × 3000) - (6018 × 1)
= 18054000 - 6018 = 18047982 Taka. (Answer)

Structured - 6

A publication company prints 25920 storybooks. The books were packed equally in 72 large boxes to be sent to the stores.
a. How many books will be there in each box?
b. If the price of each book is 125 Taka, what will be the total price of the books in one box?
c. If the publication company sells 99 such boxes of books, calculate using an easy method how many books will be sold in total.

Solution:
a. Books in 72 boxes = 25920
Books in 1 box = 25920 ÷ 72 = 360. (Answer)

b. Price of 1 book = 125 Taka
Price of 360 books = 360 × 125 = 45000 Taka. (Answer)

c. Books in 1 box = 360
Books in 99 boxes = 360 × 99
In easy method: = 360 × (100 - 1) = 36000 - 360 = 35640 books. (Answer)

🎯 5. Multiple Choice Questions (MCQ)

1. The number by which we multiply another number is called what in mathematics?

(a) Multiplier ✅

(b) Multiplicand

(d) Result

💡 Explanation: According to the rule of multiplication, the number by which we multiply is the multiplier, and the number to be multiplied is the multiplicand.

2. In a math problem, the multiplicand is 721 and the product is 0. What was the multiplier in that problem?

(a) 721

(b) 1

(d) None of these

💡 Explanation: Multiplying any number by zero (0) always results in a product of zero.

3. What will be the correct product if 111 is multiplied by 111?

(a) 12321 ✅

(b) 111111

(d) 321123

💡 Explanation: Multiplying 111 by 111 using the standard method gives 12321.

4. A shop sells each fish for 1245 Taka. If the shopkeeper sells 138 fish, how much money will he get in total?

(a) 171610

(b) 171710

(d) 171910

💡 Explanation: Multiplying the price of 1 fish by 138 gives the total price (1245 × 138 = 171810 Taka).

5. In division, how does the remainder compare to the divisor?

(a) Larger

(b) Smaller ✅

(d) None of these

💡 Explanation: When a division is complete, the remainder is always smaller than the divisor.

6. What will be the remainder if the number 20150 is divided by 1000?

(a) 50

(b) 20

(d) 2015

💡 Explanation: When dividing by 1000, the 3 digits on the right side of the dividend (150) become the remainder, and the rest becomes the quotient.

7. A company makes a total profit of 1560000 Taka in one year. How much profit does the company make per month?

(a) 120000

(b) 130000 ✅

(d) 150000

💡 Explanation: 1 year equals 12 months. So dividing the total profit by 12 gives the monthly profit (1560000 ÷ 12 = 130000).

8. 999 × 13 = What? To do this multiplication using an easy method, what can be written instead of 999?

(a) (100 - 1)

(b) (1000 - 1) ✅

(d) (1000 + 1)

💡 Explanation: The number 999 is 1 less than 1000, so it can be written as (1000 - 1) to multiply easily.

9. Which of the following formulas is correct for exact division (without remainder)?

(a) Dividend = Divisor × Quotient ✅

(b) Dividend = Divisor + Quotient

(d) Quotient = Dividend × Divisor

💡 Explanation: If there is exact division, there is no remainder (Remainder = 0), so Dividend = Divisor × Quotient.

10. If the dividend is equal to the remainder, what can be said about the divisor in that problem?

(a) The divisor is smaller than the remainder

(b) The math problem is incorrect ✅

(d) The divisor is twice the dividend

💡 Explanation: According to the rules of division, the remainder can never be equal to the divisor or the dividend; it is always smaller than the divisor.

11. What is the product of 4500 and 0?

(a) 4500

(b) 0 ✅

(d) 1

💡 Explanation: Any number multiplied by 0 results in 0.

12. If the multiplicand is 150 and the multiplier is 20, what is the product?

(a) 170

(b) 300

(d) 1500

💡 Explanation: 150 × 20 = 3000. Multiply 15 by 2 to get 30, then add the two zeros.

13. What is the quotient of 4500 ÷ 100?

(a) 45 ✅

(b) 450

(d) 500

💡 Explanation: When dividing by 100, remove two zeros from the right of the dividend. The remaining number is 45.

14. According to the division formula: (Divisor × Quotient) + Remainder = ?

(a) Multiplier

(b) Product

(d) Total

💡 Explanation: This is the fundamental formula used to check division problems.

15. If a dozen eggs cost 120 Taka, what is the cost of 5 dozen eggs?

(a) 600 Taka ✅

(b) 500 Taka

(d) 480 Taka

💡 Explanation: 120 × 5 = 600 Taka.

16. If the remainder is 5, quotient is 10, and divisor is 12, what is the dividend?

(a) 120

(b) 125 ✅

(d) 115

💡 Explanation: Dividend = (Divisor × Quotient) + Remainder = (12 × 10) + 5 = 120 + 5 = 125.

17. 785 × 1000 = ?

(a) 78500

(b) 785000 ✅

(d) 700000

💡 Explanation: Simply place the three zeros from 1000 at the right side of 785.

18. If 50 apples are distributed equally among 8 children, how many apples will be left over?

(a) 1

(b) 2 ✅

(d) 4

💡 Explanation: 50 ÷ 8 = 6 with a remainder of 2. So, 2 apples are left over.

19. Using an easy method, calculate 99 × 99.

(a) 9999

(b) 9899

(d) 9000

💡 Explanation: 99 × (100 - 1) = 9900 - 99 = 9801.

20. What is the product of the smallest 3-digit number and the largest 2-digit number?

(a) 9000

(b) 990

(d) 9990

💡 Explanation: Smallest 3-digit number is 100, largest 2-digit number is 99. 100 × 99 = 9900.

21. In a division problem, if the dividend is 0 and the divisor is 5, what is the quotient?

(a) 5

(b) 0 ✅

(d) None

💡 Explanation: 0 divided by any non-zero number is always 0.

22. Which mathematical operation is known as repeated addition?

(a) Subtraction

(b) Multiplication ✅

(d) Addition

💡 Explanation: Multiplication is basically adding a number to itself a certain number of times.

23. Which mathematical operation is known as repeated subtraction?

(a) Multiplication

(b) Division ✅

(d) Subtraction

💡 Explanation: Division involves subtracting a number repeatedly to find how many times it fits into the dividend.

24. What is the result of 10500 ÷ 10?

(a) 10500

(b) 1050 ✅

(d) 1500

💡 Explanation: Dividing by 10 removes one zero from the right side of the number.

25. If 1 kg of rice costs 65 Taka, how much does 100 kg cost?

(a) 650 Taka

(b) 6000 Taka

(d) 5600 Taka

💡 Explanation: 65 × 100 = 6500 Taka.

26. A bus travels 45 km in 1 hour. How far will it travel in 12 hours?

(a) 500 km

(b) 540 km ✅

(d) 600 km

💡 Explanation: Distance = 45 × 12 = 540 km.

27. What is the value of (1234 × 0) + 5?

(a) 1239

(b) 5 ✅

(d) 0

💡 Explanation: 1234 × 0 = 0. Then 0 + 5 = 5.

28. In a division where Dividend = 48 and Divisor = 6, what is the remainder?

(a) 8

(b) 0 ✅

(d) 4

💡 Explanation: 48 is exactly divisible by 6 (6 × 8 = 48), so there is no remainder.

29. How many zeros will be at the end of the product of 400 × 500?

(a) 3

(b) 4

(d) 6

💡 Explanation: 4 × 5 = 20, then add the four zeros from 400 and 500 to get 200000, which has 5 zeros.

30. In the equation 850 ÷ 10 = 85, what is 85 called?

(a) Divisor

(b) Dividend

(d) Remainder

💡 Explanation: The result of a division is called the quotient.

31. What is the remainder when 703 is divided by 10?

(a) 7

(b) 0

(d) 70

💡 Explanation: When dividing by 10, the digit in the ones place is the remainder.

32. Calculate 25 × 4 × 10.

(a) 100

(b) 1000 ✅

(d) 250

💡 Explanation: 25 × 4 = 100. Then 100 × 10 = 1000.

33. If 1 packet contains 20 biscuits, how many biscuits are in 15 packets?

(a) 350

(b) 300 ✅

(d) 150

💡 Explanation: 15 × 20 = 300 biscuits.

34. Multiplier = Product ÷ ?

(a) Divisor

(b) Quotient

(d) Remainder

💡 Explanation: Dividing the product by the multiplicand gives the multiplier.

35. In an exact division, Dividend - Remainder = ?

(a) Divisor + Quotient

(b) Divisor × Quotient ✅

(d) Quotient - Divisor

💡 Explanation: Subtracting the remainder from the dividend leaves a number perfectly equal to Divisor × Quotient.

36. What is the value of 5000 ÷ 500?

(a) 10 ✅

(b) 100

(d) 5

💡 Explanation: Both numbers have zeros. 5000 ÷ 500 is the same as 50 ÷ 5, which equals 10.

37. The price of 5 books is 750 Taka. What is the price of 1 book?

(a) 100 Taka

(b) 150 Taka ✅

(d) 125 Taka

💡 Explanation: Divide the total price by the number of books: 750 ÷ 5 = 150.

38. Using the easy method, what is 999 × 25?

(a) 25000

(b) 24975 ✅

(d) 25975

💡 Explanation: 25 × (1000 - 1) = 25000 - 25 = 24975.

39. When you divide a non-zero number by itself, what is the quotient?

(a) 0

(b) 1 ✅

(d) 10

💡 Explanation: Any number fits exactly one time into itself (e.g., 5 ÷ 5 = 1).

40. The greatest 4-digit number divided by 1 gives what result?

(a) 9999 ✅

(b) 1000

(d) 9000

💡 Explanation: Any number divided by 1 remains the same number. The greatest 4-digit number is 9999.