NCERT Class 5 Mathematics • Classic CBSE Track

Chapter 13: Ways to Multiply and Divide

गुणा और भाग के तरीके (बेला का गुणन, शांताराम का वेतन एवं दिन गणना) | CBSE Session 2026–27

Core Pedagogical Competencies & Concepts
  • Bela's method of columnar multiplication using expanded place-value distributive property.
  • Multiplying 2-digit and 3-digit numbers by multi-step partial products.
  • Division algorithms: Quotients and remainders in commercial contexts.
  • Daily wage calculation, monthly salaries, and yearly earnings.
  • Total notebooks: 576.
  • Total boxes: 18.
Bela's Distributive Multiplication Algorithm: 65 × 32 65 × 32 130 ← 65 × 2 1950 ← 65 × 30 2080 ← Total Product Step 1: Multiply by 2 (ones) = 130 | Step 2: Multiply by 30 (tens) = 1950 | Sum = 2,080

All Textbook Exercises & In-Text Tasks (24 Questions)

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Q1 Textbook Exercise • Maniratnam the Cashier (Daily Wage Multiplications)
Maniratnam is the cashier of King Jayan. His job is to calculate the salary of all the workers: The cook gets ₹65 per day, the minister gets ₹195 per day, and the king's horse-keeper gets ₹86 per day. Calculate:
(a) The cook's salary for the month of January (31 days).
(b) The horse-keeper's salary for 1 full year (365 days).
(c) The minister's salary for 1 full year (365 days).
[4 Marks]
✅ Step-by-Step Solution & Working
Multiplication Calculations:
• (a) Cook's salary for January: 31 × ₹65 = 31 × (60 + 5) = 1,860 + 155 = ₹2,015.
• (b) Horse-keeper's annual salary: 365 × ₹86 = 365 × (80 + 6) = 29,200 + 2,190 = ₹31,390.
• (c) Minister's annual salary: 365 × ₹195 = 365 × (200 - 5) = 73,000 - 1,825 = ₹71,175.
CBSE Step-by-Step Marking Scheme
Cook: ₹2,015 1 M
Horse-keeper: ₹31,390 1.5 M
Minister: ₹71,175 1.5 M
Q2 Textbook Exercise • Bela's Method of Multiplication
Multiply 47 × 19 using Bela's method (distributive method by splitting 19 into 9 and 10). Show each partial product.
[3 Marks]
✅ Step-by-Step Solution & Working
Bela's Distributive Method:
Split 19 = 10 + 9:
• Step 1: Multiply 47 by 9 = 47 × 9 = 423.
• Step 2: Multiply 47 by 10 = 47 × 10 = 470.
• Step 3: Add partial products = 423 + 470 = 893.
Therefore, 47 × 19 = 893.
CBSE Step-by-Step Marking Scheme
47 × 9 = 423 1 M
47 × 10 = 470 1 M
Sum: 893 1 M
Q3 Textbook Exercise • Shantaram the Cook's Holiday Deduction
Shantaram is a special cook who is called only on party days. Last year he was called for only 28 days. For each day he is paid ₹165. (a) How much money did he earn in all? (b) If he was paid for all 365 days of the year, how much would he have earned?
[3 Marks]
✅ Step-by-Step Solution & Working
Calculations:
• (a) Actual earnings: 28 × ₹165 = 28 × (100 + 60 + 5) = 2,800 + 1,680 + 140 = ₹4,620.
• (b) Full year earnings: 365 × ₹165 = 365 × (100 + 60 + 5) = 36,500 + 21,900 + 1,825 = ₹60,225.
CBSE Step-by-Step Marking Scheme
28 days earnings: ₹4,620 1.5 M
Full year earnings: ₹60,225 1.5 M
Q4 Textbook Exercise • Sohanlal the Farmer's Loan
Sohanlal drank 8 glasses of water every day. (a) How many glasses will he drink in one month of 30 days? (b) How many glasses will he drink in one year (365 days)? (c) If 125 people in a village drink 8 glasses of water daily, how many glasses will they drink in one day?
[3 Marks]
✅ Step-by-Step Solution & Working
Water Multiplications:
• (a) 30 days: 30 × 8 = 240 glasses.
• (b) 1 year: 365 × 8 = 2,920 glasses.
• (c) 125 people in 1 day: 125 × 8 = 1,000 glasses.
CBSE Step-by-Step Marking Scheme
30 days: 240 glasses 1 M
1 year: 2,920 glasses 1 M
125 people: 1,000 glasses 1 M
Q5 Textbook Exercise • Heartbeat Counting
A person's heart beats about 72 times in one minute. (a) How many times does it beat in 1 hour? (b) How many times does it beat in 1 full day (24 hours)?
[3 Marks]
✅ Step-by-Step Solution & Working
Calculations:
• (a) In 1 hour (60 minutes): 72 × 60 = 4,320 beats.
• (b) In 1 day (24 hours): 4,320 × 24 = 4,320 × (20 + 4) = 86,400 + 17,280 = 1,03,680 beats.
CBSE Step-by-Step Marking Scheme
1 hour: 4,320 beats 1.5 M
24 hours: 1,03,680 beats 1.5 M
Q6 Textbook Exercise • Baby Blue Whale Milk Consumption
A baby blue whale drinks around 200 litres of milk every single day! (a) How many litres of milk will it drink in 8 months (assume 30 days per month)? (b) If your family consumes 2 litres of milk daily, how many days will 200 litres of milk last your family?
[3 Marks]
✅ Step-by-Step Solution & Working
Calculations:
• (a) Whale milk in 8 months:
- Total days = 8 × 30 = 240 days.
- Milk consumed = 240 × 200 litres = 48,000 litres.
• (b) Family consumption: 200 litres ÷ 2 litres/day = 100 days.
CBSE Step-by-Step Marking Scheme
Whale 8 months: 48,000 litres 1.5 M
Family duration: 100 days 1.5 M
Q7 Textbook Exercise • Sukhi's Farm Labor Wage
Sukhi works on a farm. He is paid ₹98 for one day. If he works for 52 days, how much money does he earn?
[2 Marks]
✅ Step-by-Step Solution & Working
Multiplication:
• Earnings = 52 × ₹98 = 52 × (100 - 2) = 5,200 - 104 = ₹5,096.
CBSE Step-by-Step Marking Scheme
Multiplication 52 × 98 1 M
Answer: ₹5,096 1 M
Q8 Textbook Exercise • Hariya's Fertilizer Loan & Installments
Hariya took a loan of ₹20,000 to buy fertilizer. He has to pay back ₹2,400 every month for 10 months. (a) What is the total money he paid back? (b) How much extra money did the bank charge as interest?
[2 Marks]
✅ Step-by-Step Solution & Working
Loan Repayment:
• (a) Total repayment: 10 × ₹2,400 = ₹24,000.
• (b) Interest charged: ₹24,000 - ₹20,000 = ₹4,000.
CBSE Step-by-Step Marking Scheme
Total paid: ₹24,000 1 M
Interest: ₹4,000 1 M
Q9 Textbook Exercise • Long Division Method (Hostel Rice)
A school hostel has 576 students. If each student gets 15 kg of rice per month, how much rice is needed for the hostel in one month?
[2 Marks]
✅ Step-by-Step Solution & Working
Multiplication:
• Rice required = 576 × 15 kg = 576 × (10 + 5) = 5,760 + 2,880 = 8,640 kg.
CBSE Step-by-Step Marking Scheme
Multiplication statement 1 M
Answer: 8,640 kg 1 M
Q10 Textbook Exercise • Division with Remainder (Laddoo Packing)
A sweet maker has 250 laddoos. He packs them into boxes of 12 laddoos each. (a) How many full boxes can he make? (b) How many laddoos will be left over? (c) How many more laddoos are needed to make another full box?
[3 Marks]
✅ Step-by-Step Solution & Working
Division: 250 ÷ 12:
• 250 ÷ 12 = 20 with remainder 10 (since 12 × 20 = 240, and 250 - 240 = 10).
• (a) Full boxes: 20 boxes.
• (b) Left over: 10 laddoos.
• (c) More needed for next box: 12 - 10 = 2 more laddoos.
CBSE Step-by-Step Marking Scheme
20 full boxes 1 M
10 left over 1 M
2 more needed 1 M
Q11 Textbook Exercise • Tanker Water Distribution
A water tanker carries 4,500 litres of water to a colony. If each family is given 150 litres of water, how many families can get water from the tanker?
[2 Marks]
✅ Step-by-Step Solution & Working
Division:
• Number of families = 4,500 ÷ 150 = 450 ÷ 15 = 30 families.
CBSE Step-by-Step Marking Scheme
Division setup 1 M
Answer: 30 families 1 M
Q12 Textbook Exercise • Verifying Division (Dividend Formula)
Dividend = (Divisor × Quotient) + Remainder. Divide 678 by 14 and verify your result using this formula.
[3 Marks]
✅ Step-by-Step Solution & Working
Division and Verification:
1. Division: 678 ÷ 14 = 48 with remainder 6 (since 14 × 40 = 560; 118 ÷ 14 = 8 with remainder 6: 14 × 8 = 112, 118 - 112 = 6).
2. Verification:
- Divisor × Quotient = 14 × 48 = 672.
- Adding remainder: 672 + 6 = 678 (Dividend). (Verified!).
CBSE Step-by-Step Marking Scheme
Quotient 48, Remainder 6 1.5 M
Formula verification shown 1.5 M
Q13 Textbook Exercise • Buying Land in Installments
Kamini buys a plot of land for ₹95,000. She pays ₹35,000 in cash and agrees to pay the rest in 12 equal monthly installments. How much must she pay each month?
[3 Marks]
✅ Step-by-Step Solution & Working
Installment Calculation:
1. Remaining balance = ₹95,000 - ₹35,000 = ₹60,000.
2. Monthly installment = ₹60,000 ÷ 12 = ₹5,000 per month.
CBSE Step-by-Step Marking Scheme
Remaining balance: ₹60,000 1.5 M
Monthly installment: ₹5,000 1.5 M
Q14 Textbook Exercise • Books in Boxes (Carton Packing)
A publishing house printed 3,456 math textbooks. They can pack 24 books in one cardboard carton. How many cartons are needed to pack all the books?
[2 Marks]
✅ Step-by-Step Solution & Working
Division: 3,456 ÷ 24:
• 3,456 ÷ 24 = 144 cartons (24 × 100 = 2400; remainder 1056; 24 × 40 = 960; remainder 96; 24 × 4 = 96. Total = 100 + 40 + 4 = 144).
CBSE Step-by-Step Marking Scheme
Division steps shown 1 M
Answer: 144 cartons 1 M
Q15 Textbook Exercise • Factory Production per Hour
A biscuit factory produces 14,400 packets of biscuits in a day. The factory runs for 16 hours every day. How many packets are produced in one hour?
[2 Marks]
✅ Step-by-Step Solution & Working
Division:
• Packets per hour = 14,400 ÷ 16 = 900 packets per hour.
CBSE Step-by-Step Marking Scheme
Division setup 1 M
Answer: 900 packets 1 M
Q16 Textbook Exercise • Bus Tickets for School Excursion
248 students and 12 teachers are going on an excursion. Each bus can seat 45 passengers. (a) How many total people are travelling? (b) How many buses must be hired so that everyone gets a seat?
[3 Marks]
✅ Step-by-Step Solution & Working
Bus Requirement:
• (a) Total passengers: 248 + 12 = 260 passengers.
• (b) Buses needed: 260 ÷ 45 = 5 with remainder 35 (since 45 × 5 = 225).
Since 35 passengers remain without seats, 1 extra bus must be hired.
Total buses needed = 5 + 1 = 6 buses.
CBSE Step-by-Step Marking Scheme
Total passengers: 260 1 M
Division: 5 remainder 35 1 M
Rounding up to 6 buses 1 M
Q17 Textbook Exercise • Multiplying 3-Digit Numbers
Calculate: 245 × 132 showing step-by-step partial products.
[3 Marks]
✅ Step-by-Step Solution & Working
3-Digit Multiplication:
• 245 × 2 = 490
• 245 × 30 = 7,350
• 245 × 100 = 24,500
• Sum: 490 + 7,350 + 24,500 = 32,340.
CBSE Step-by-Step Marking Scheme
Partial products shown 2 M
Final answer: 32,340 1 M
Q18 Textbook Exercise • Repeated Subtraction Division
Explain how 96 ÷ 16 can be solved using repeated subtraction. How many times can 16 be subtracted from 96?
[2 Marks]
✅ Step-by-Step Solution & Working
Repeated Subtraction:
• 96 - 16 = 80 (1st)
• 80 - 16 = 64 (2nd)
• 64 - 16 = 48 (3rd)
• 48 - 16 = 32 (4th)
• 32 - 16 = 16 (5th)
• 16 - 16 = 0 (6th)
16 was subtracted exactly 6 times. Therefore, 96 ÷ 16 = 6.
CBSE Step-by-Step Marking Scheme
Subtraction steps shown 1 M
Quotient = 6 1 M
Q19 Textbook Exercise • Monthly Budget from Daily Expense
A family spends ₹425 daily on groceries and food. How much do they spend in a leap year (366 days)?
[3 Marks]
✅ Step-by-Step Solution & Working
Multiplication:
• Expense = 366 × ₹425 = 366 × (400 + 25) = 146,400 + 9,150 = ₹1,55,550.
CBSE Step-by-Step Marking Scheme
Leap year = 366 days noted 1 M
Calculation: ₹1,55,550 2 M
Q20 Textbook Exercise • Unit Price Comparison
Shop A sells 5 kg rice for ₹225. Shop B sells 8 kg rice for ₹344. Which shop is cheaper per kg, and by how much?
[3 Marks]
✅ Step-by-Step Solution & Working
Unit Price (Cost per kg):
• Shop A: ₹225 ÷ 5 = ₹45 per kg.
• Shop B: ₹344 ÷ 8 = ₹43 per kg.
• Shop B is cheaper by ₹45 - ₹43 = ₹2 per kg.
CBSE Step-by-Step Marking Scheme
Shop A: ₹45/kg 1 M
Shop B: ₹43/kg 1 M
Shop B cheaper by ₹2 1 M
Q21 Textbook Exercise • Sharing an Inherited Sum
An amount of ₹72,960 is divided equally among 6 brothers. How much money does each brother receive?
[2 Marks]
✅ Step-by-Step Solution & Working
Division:
• Share per brother = ₹72,960 ÷ 6 = ₹12,160.
CBSE Step-by-Step Marking Scheme
Division setup 1 M
Answer: ₹12,160 1 M
Q22 Textbook Exercise • Estimation in Multiplication
Estimate the product of 48 × 73 by rounding off each number to the nearest ten. Then find the actual product and compare.
[3 Marks]
✅ Step-by-Step Solution & Working
Estimation & Comparison:
• 48 rounds to 50; 73 rounds to 70.
• Estimated product: 50 × 70 = 3,500.
• Actual product: 48 × 73 = 3,504.
The estimated product (3,500) is remarkably close to the actual product (3,504), differing by only 4!
CBSE Step-by-Step Marking Scheme
Estimated product: 3,500 1.5 M
Actual product: 3,504 & comparison 1.5 M
Q23 Textbook Exercise • Cinema Ticket Sales
A movie theatre has 35 rows with 28 seats in each row. For the evening show, all seats were booked at ₹120 per ticket. How much money was collected?
[3 Marks]
✅ Step-by-Step Solution & Working
Multi-step Multiplication:
1. Total seats = 35 × 28 = 35 × (20 + 8) = 700 + 280 = 980 seats.
2. Total collection = 980 × ₹120 = 980 × (100 + 20) = 98,000 + 19,600 = ₹1,17,600.
CBSE Step-by-Step Marking Scheme
Total seats: 980 1.5 M
Total collection: ₹1,17,600 1.5 M
Q24 Textbook Exercise • Division of Multiples of 100
Solve mental math divisions:
(a) 48,000 ÷ 600
(b) 35,000 ÷ 70
(c) 8,100 ÷ 90
[3 Marks]
✅ Step-by-Step Solution & Working
Mental Math:
• (a) 48,000 ÷ 600 = 480 ÷ 6 = 80.
• (b) 35,000 ÷ 70 = 3,500 ÷ 7 = 500.
• (c) 8,100 ÷ 90 = 810 ÷ 9 = 90.
CBSE Step-by-Step Marking Scheme
All 3 correct (1 M each) 3 M
🌟 NEP 2020 Competency-Based Case Study

NEP 2020 Competency Case: Ways to Multiply and Divide

A practical scenario involving Ways to Multiply and Divide in everyday life and community contexts.

Analytical Task: Analyze the quantitative relationships and state the conclusion.
Evaluation & Model Answer:
Apply the step-by-step formulas and concepts mastered in this chapter.
Rubric: 1M formula + 1M working + 1M answer