CBSE Class 5 Mathematics: Chapter 13 Ways To Multiply And Divide NCERT Solutions

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NCERT Solutions PDF Class 5 PDF

This chapter from CBSE Class 5 Mathematics, 'Ways To Multiply And Divide', delves into various techniques for multiplication. It guides students through different approaches to solve multiplication problems, using Bela's step-by-step method as an example. The solutions illustrate how to calculate monthly and yearly salaries for various jobs, highlighting the practical use of multiplication in everyday life. Learners will discover how to simplify complex multiplication tasks by breaking them down into smaller, more manageable steps. These NCERT Solutions offer clear explanations and thorough working for each exercise, helping students build confidence and proficiency in multiplication, which is essential for their academic progress.

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BoardCBSE
ClassClass 5
SubjectMathematics
Session2026
LanguageEnglish
TypeNCERT Solutions
Chapter13 Ways To Multiply And Divide

Chapter summary

Chapter 13, 'Ways To Multiply And Divide', for Class 5 Mathematics provides NCERT Solutions focused on mastering multiplication. It explains and demonstrates alternative multiplication strategies, such as Bela's method, which breaks down problems into smaller, manageable steps. The solutions cover practical applications like calculating daily and monthly salaries, reinforcing the importance of multiplication in everyday life. This chapter aims to build computational fluency and problem-solving skills in young learners.

Learning outcomes

  • Understand and apply Bela's method for multiplication.
  • Solve multiplication problems involving two-digit and three-digit numbers.
  • Calculate salaries and wages using multiplication.
  • Break down complex multiplication into simpler steps.
  • Apply multiplication skills to real-world scenarios.

Topics covered

Paper topics

  • Multiplication methods
  • Bela's multiplication method
  • Calculating daily salary
  • Calculating monthly salary
  • Calculating annual salary
  • Multi-digit multiplication
  • Word problems involving multiplication
  • Practical application of multiplication

Important topics

  • Bela's multiplication method
  • Multi-digit multiplication
  • Word problems involving multiplication
  • Calculating salaries

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Questions and Solutions

Maniratnam—The Cashier

Maniratnam is the cashier of king Jayan. His job is to find out the salary of all the people who work for the king. This chart shows how much salary each person gets in a day:

Person | Salary in a day

Minister | ₹ 195

Horse rider | ₹ 76

Cook | ₹ 65

Maniratnam wanted to calculate the salary of the cook for the month of January. He wrote:

60 \times 30 = 1800

5 \times 30 = 150

60 \times 1 = 60

5 \times 1 = 5

Rupees 1800 + 150 + 60 + 5 = 2015

Maniratnam's daughter Bela had learnt another method to multiply. She wrote like this and showed it to Bhanu, her brother.

65 \times 31

65 + 1950 = 2015

You can multiply 65 with 31 in two steps. You know that 31 is 30 + 1. So, in the first step multiply 65 with 1 and in the second step multiply 65 with 30. Now Bhanu tried to find the salary of a minister for the month of January. He wanted to multiply 195 x 31.

195 \times 31

195 + 5850 = 6045

First step: Multiply 195 by 1

Second step: Multiply 195 by 30

Solution:

To calculate the cook's salary for January (31 days), Maniratnam used a method that broke down the multiplication. He calculated the salary for 30 days and then added the salary for 1 day.

Salary for 30 days: 65 \times 30 = 1950

Salary for 1 day: 65 \times 1 = 65

Total salary for January: 1950 + 65 = 2015

Bela's method is a more structured way to do this. For 65 x 31:

Step 1: Multiply 65 by 1 (the ones digit). 65 \times 1 = 65

Step 2: Multiply 65 by 30 (the tens digit, which represents 30). 65 \times 30 = 1950

Step 3: Add the results from Step 1 and Step 2. 65 + 1950 = 2015

For Bhanu's calculation of the minister's salary for January (195 x 31):

Step 1: Multiply 195 by 1. 195 \times 1 = 195

Step 2: Multiply 195 by 30. 195 \times 30 = 5850

Step 3: Add the results. 195 + 5850 = 6045

So, the minister's salary for January is Rs 6045.

Practice Time

1. Use Bela's method to multiply these numbers.

  1. 32 \times 46
Solution:

We will use Bela's method to multiply 32 by 46.

Step 1: Multiply 32 by the ones digit, which is 6. 32 \times 6 = 192

Step 2: Multiply 32 by the tens digit, which is 4 (representing 40). 32 \times 40 = 1280

Step 3: Add the results from Step 1 and Step 2. 192 + 1280 = 1472

Therefore, 32 \times 46 = 1472.

2. Do these in your notebook using Bela's method.

  1. 47 x 19
  2. 188 x 91
  3. 63 x 57
  4. 225 x 22
  5. 360 x 12
  6. 163 x 42
Solution:

We will solve each multiplication problem using Bela's method.

  1. 47 x 19

    Step 1: Multiply 47 by 9. 47 \times 9 = 423

    Step 2: Multiply 47 by 10. 47 \times 10 = 470

    Step 3: Add the results. 423 + 470 = 893

    So, 47 \times 19 = 893.

  2. 188 x 91

    Step 1: Multiply 188 by 1. 188 \times 1 = 188

    Step 2: Multiply 188 by 90. 188 \times 90 = 16920

    Step 3: Add the results. 188 + 16920 = 17108

    So, 188 \times 91 = 17108.

  3. 63 x 57

    Step 1: Multiply 63 by 7. 63 \times 7 = 441

    Step 2: Multiply 63 by 50. 63 \times 50 = 3150

    Step 3: Add the results. 441 + 3150 = 3591

    So, 63 \times 57 = 3591.

  4. 225 x 22

    Step 1: Multiply 225 by 2. 225 \times 2 = 450

    Step 2: Multiply 225 by 20. 225 \times 20 = 4500

    Step 3: Add the results. 450 + 4500 = 4950

    So, 225 \times 22 = 4950.

  5. 360 x 12

    Step 1: Multiply 360 by 2. 360 \times 2 = 720

    Step 2: Multiply 360 by 10. 360 \times 10 = 3600

    Step 3: Add the results. 720 + 3600 = 4320

    So, 360 \times 12 = 4320.

  6. 163 x 42

    Step 1: Multiply 163 by 2. 163 \times 2 = 326

    Step 2: Multiply 163 by 40. 163 \times 40 = 6520

    Step 3: Add the results. 326 + 6520 = 6846

    So, 163 \times 42 = 6846.

Shantaram—A Special Cook

1. Shantaram is a special cook who comes only on party days. Last year he was called for only 28 days. For each day he has to be paid ₹ 165. Find out how much money he will get in all.

Solution:

To find the total money Shantaram will get, we need to multiply his daily wage by the number of days he worked.

Daily wage = ₹ 165

Number of days worked = 28

Total money = Daily wage × Number of days worked

We will use Bela's method for multiplication:

Step 1: Multiply 165 by 8 (the ones digit). 165 \times 8 = 1320

Step 2: Multiply 165 by 20 (the tens digit, representing 20). 165 \times 20 = 3300

Step 3: Add the results from Step 1 and Step 2. 1320 + 3300 = 4620

Therefore, Shantaram will get ₹ 4620 in all.

2. If he is called for all days of the year, how much salary will he get?

Solution:

To find Shantaram's salary for the entire year, we need to multiply his daily wage by the total number of days in a year.

Daily wage = ₹ 165

Number of days in a year = 365

Total salary for the year = Daily wage × Number of days in a year

We will use Bela's method for multiplication:

Step 1: Multiply 165 by 5 (the ones digit). 165 \times 5 = 825

Step 2: Multiply 165 by 60 (the tens digit, representing 60). 165 \times 60 = 9900

Step 3: Multiply 165 by 300 (the hundreds digit, representing 300). 165 \times 300 = 49500

Step 4: Add the results from all steps. 825 + 9900 + 49500 = 60225

Therefore, Shantaram will get ₹ 60225 if he is called for all days of the year.

Common mistakes

  • Errors in carrying over numbers during multiplication.
  • Incorrectly aligning numbers in multi-step multiplication.
  • Calculation mistakes in adding partial products.
  • Misinterpreting the problem to be solved (e.g., addition instead of multiplication).

Revision tips

  • Practice Bela's method for at least 5 problems to build speed and accuracy.
  • Focus on correctly adding the partial products obtained in each step.
  • Relate the multiplication problems to real-life situations like calculating costs or salaries.
  • Review the examples provided in the solutions to understand the logic behind each step.

Practice MCQs

Q1. What is the salary of a cook for 31 days if they earn Rs 65 per day?

Q2. Bela's method involves breaking down multiplication into which steps?

Q3. How much will Shantaram get if he works for 28 days and earns Rs 165 per day?

Q4. What is the result of 32 x 46?

Q5. To find the salary for a full year (365 days) at Rs 165 per day, what calculation is needed?

Frequently asked questions

What is the main concept taught in Chapter 13 of Class 5 Maths?

Chapter 13, 'Ways To Multiply And Divide', focuses on teaching different and efficient methods for multiplication, particularly Bela's method, and applying these to solve real-world problems.

How does Bela's method simplify multiplication?

Bela's method breaks down a multiplication problem into smaller, easier steps. For example, to multiply 65 by 31, it's done as (65 x 1) + (65 x 30), making the calculation less daunting.

Are these solutions helpful for exam preparation?

Yes, these NCERT Solutions provide clear, step-by-step explanations for each problem, helping students understand the methods and practice them, which is crucial for exam revision and success.

What kind of real-life problems are covered in this chapter?

The chapter includes problems related to calculating salaries for different numbers of days worked, demonstrating the practical use of multiplication in everyday financial scenarios.

How can I use these solutions effectively?

First, try to solve the problems yourself. Then, compare your method and answer with the provided solutions. Pay attention to the steps and reasoning to improve your understanding and accuracy.

Important links

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