Students often refer to Kerala State Syllabus SCERT Class 5 Maths Solutions and Class 5 Maths Chapter 3 Multiplication Methods Questions and Answers Notes Pdf to clear their doubts.
SCERT Class 5 Maths Chapter 3 Solutions Multiplication Methods
Class 5 Maths Chapter 3 Multiplication Methods Questions and Answers Kerala State Syllabus
Multiplication Methods Class 5 Questions and Answers Kerala Syllabus
Question 1.
Compute the products below:
(i) 12 × 34
Answer:
(ii) 23 × 45
Answer:
(iii) 75 × 75
Answer:
(iv) 123 × 45
Answer:
(v) 320 × 78
Answer:
Question 2.
Given that 36 × 15 = 540; compute the following products in your head:
(i) 36 × 16
Answer:
36 × (15 + 1)
= (36 × 15) + 36
= 540 + 36
= 576
(ii) 37 × 15
Answer:
(36 + 1) × 15
= (36 × 15) + (1 × 15)
= 540 + 15
= 555
(iii) 36 × 14
Answer:
36 × (15 – 1)
= (36 × 15) – 36
= 540 -36
= 504
(iv) 35 × 15
Answer:
(36 – 1) × 15
= (36 × 15) – 15
= 540 – 15
= 525
Question 3.
A number multiplied by 16 gave 1360.
(i) What will be the product, if the next number is multiplied by 16?
(ii) What will be the product if the number just before this is multiplied by 16?
Answer:
(i) If we look at the number just after our original number, we can find the new product by simply adding 16 to 1360
1360 + 16 = 1376
So, when the ne×t number is multiplied by 16, we get 1376
(ii) Now, let’s look at the number just before our original number. To find this new product, we subtract 16 from 1360
1360 – 16 = 1344
So, when the previous number is multiplied by 16, we get 1344
Question 4.
Rewrite each of the products below as the product of a number by itself:
(i) 9 × 16
(ii) 16 × 36
(iii) 36 × 49
(iv) 49 × 64
(v) 81 × 25
Answer:
(i) 9 × 16 = (3 × 4) × (3 × 4)
(ii) 16 × 36 = (4 × 6) × (4 × 6 )
(iii) 36 × 49 = (6 × 7) × (6 × 7 )
(iv) 49 × 64 = (7 × 8) × (7 × 8)
(v) 81 × 25 = (9 × 5) × (9 × 5 )
Question 5.
Calculate each of the products below in your head:
(i) 25 × 4
(ii) 25 × 16
(iii) 25 × 36
(iv) 25 × 64
Answer:
(i) 25 × 4 = (5 × 2)(5 × 2) =100
(ii) 25 × 16 = (5 × 4) × (5 × 4) = 400
(iii) 25 × 36 = (5 × 6) × (5 × 6) = 900
(iv) 25 × 64 = (5 × 8) × (5 × 8) = 1600
Question 6.
(i) Calculate 11 × 11 and 111 × 111
(ii) Can you guess what 1111 × 1111 would be? Check whether your guess is correct.
(iii) Write the pattern of such products.
Answer:
(i) 11 × 11 = 121
111 × 111 = 12321
(ii) 1111 × 1111= 1234321
Here the digits are count up to the middle and then count down.
(iii) 11111 × 11111 = 123454321
111111 × 111111 = 12345654321
1111111 × 1111111 = 1234567654321
11111111 × 11111111 = 123456787654321
Question 7.
Look at the following calculations:
1 + 3 = 4
4 + 5 = 9
9 + 7 = 16
Continue this to compute the squares up to 100.
Answer:
16 + 9 = 25
25 + 11 = 36
36 + 13 = 49
49 + 15 = 64
64 + 17 = 81
81 + 19 = 100
Question 8.
(i) How many odd numbers, like 1, 3, and 5, are to be added to get 400?
(ii) Which is the last odd number added to this ?
Answer:
(i) The sum of 20 odd numbers = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 + 25 + 27 + 29 + 31 + 33 + 35 + 37 + 39 = 400
(ii) 39 is the last odd number added to this.
Question 9.
(i) Which is the fiftieth odd number?
(ii) What is the sum of the odd numbers from 1 to this number?
Answer:
(i) The fiftieth odd number can be found by multiplying 50 by 2 and then subtracting 1,
50th odd number = (50 × 2) – 1 = 100 – 1 = 99
(ii) The sum of odd numbers from 1 to 99 = 50 × 50 = 2500
Question 10.
Look at these pictures.
(i) How do we write 25 as a sum like this?
(ii) How about 36?
(iii) Can you write 100 as such a sum.
Answer:
(i) 25 = 1 + 2 + 3 + 4 + 5 + 4 + 3 + 2 + 1
(ii) 36 = 1 + 2 + 3 + 4 + 5 + 6 + 5 + 4 + 3 + 2 + 1
(iii) 100 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1
Intext Questions And Answers
Starting with a question
Question 1.
Which sum is larger (15 + 8) or (18 + 5)?
Answer:
15 + 8 = (10 + 5) + 8= 10 + (5 + 8)
18 + 5 = (10 +8)+ 5 = 10 +(8+ 5)
Here, (5 + 8) and (8 + 5) both equals to 13.
Therefore, their sum is equal to each other
Question 2.
What about their product?
Answer:
15 × 8 = (10 + 5) × 8 = (10 × 8) + (5 × 8)
18 × 5 = (10 + 8) × 5 = (10 × 5) + (8 × 5)
Here, (5 × 8) and (8 × 5) both equal to 40.
But, (10 × 8) is greater than (10 × 5)
Therefore, (15 × 8) is a larger product than (18×5), and their difference is (10 × 8) – (10 × 5) = 80 – 50 = 30.
Question 3.
Without multiplying, can we determine if 16 × 9 or 19 × 6 is larger?
Answer:
16 × 9 = (10 + 6) × 9 = (10 × 9) + (6 × 9)
19 × 6 = (10 + 9) × 6 = (10 × 6) + (9 × 6)
Here, (6 × 9) and (9 × 6) both equal to 54.
But, (10 × 9) is greater than (10 × 6)
Therefore, (16 × 9) is larger than (19 × 6), and their difference is
(10 × 9) – (10 × 6) = 90 – 60 = 30.
Question 4.
Now in each of the pairs of products given below, can you figure out in your head which is larger and how much more?
(1) 12 × 8; 18 × 2
(2) 17 × 6; 16 × 7
(3) 13 × 9; 19 × 3
(4) 25 × 6; 26 × 5
Answer:
(1) (12 × 8) = (10 + 2) × 8 = (10 × 8) + (2 × 8)
(18 × 2) = (10 + 8) × 2 = (10 × 2) + (8 × 2)
Clearly, we can say that (10 × 8) is greater than (10 × 2)
Therefore, (12 × 8) is greater than (18 × 2), and their difference is
(10 × 8) – (10 × 2) = 80 – 20 = 60.
(2) (17 × 6) = (10 + 7) × 6 = (10 × 6) + (7 × 6)
(16 × 7) = (10 + 6) × 7 = (10 × 7) + (6 × 7)
Clearly, we can say that (10 × 7) is greater than (10 × 6)
Therefore, (16 × 7) is greater than (17 × 6) and their difference is (10 × 7) – (10 × 6) = 70 – 60 = 10.
(3) (13 × 9) = (10 + 3) × 9 = (10 × 9) + (3 × 9)
(19 × 3) = (10 + 9) × 3 = (10 × 3) + (9 × 3)
Clearly, we can say that (10 × 9) is greater than (10 × 3)
Therefore, (13 × 9) is greater than (19 × 3) and their difference is (10 × 9) – (10 × 3) = 90 – 30 = 60.
(4) (25 × 6) = (20 + 5) × 6 = (20 × 6) + (5 × 6)
(26 × 5) = (20 + 6) × 5 = (20 × 5) + (6 × 5)
Clearly, we can say that (20 × 6) is greater than (20 × 5)
Therefore, (25 × 6) is greater than (26 × 5) and their difference is (20 × 6) – (20 × 5) = 120 – 100 = 20.
Question 5.
How can we multiply 15 × 13?
Answer:
We can write 15 and 13 as the sides of rectangle as shown in the figure below
⇒ 15 × 13 = (10 × 10) + (10 × 5) + (10 × 3) + (3 × 5)
= 100 + 50 + 30+ 15
= 195
Question 6.
Compute 16 × 17
Answer:
⇒ 100 + 60 + 70 + 42 = 272
Question 7.
How to compute the following questions
(i) 18 × 19
Answer:
(ii) 14 × 18
Answer:
(iii) 15 × 15
Answer:
(iv) 345 × 26
Answer:
Note: by computing 18 × 12 we get
But, these calculations can be done in the head and the whole multiplication can be written in this shortened form
Question 8.
How can 36 dots be represented in a rectangle?
Answer:
We saw that we can arrange 36 dots in many ways to make rectangles.
But when we make a 6 × 6 square, it’s special because both sides are the same length.
When we arrange a number of dots into a grid where the rows and columns are equal,
we create a square shape. We call such numbers ‘square numbers’
Question 9.
Can you verify if the product of 25 and 16 is a square number?
Answer:
25 = 5 × 5
16 = 4 × 4
25 × 16 = (5 × 5) (4×4)
= (5 × 4)(5 × 4)
= 20 × 20 = 400
Therefore, the product of 25 and 16 is a perfect square.
When you multiply two perfect square numbers, the product will always be another square number
Class 5 Maths Chapter 3 Kerala Syllabus Multiplication Methods Questions and Answers
Question 1.
Look at the following calculations:
4 = 1 + 2 + 1
9 = 1 + 2 + 3 + 2 + 1
16 = 1 + 2 + 3 + 4 + 2 + 1
(i) How do we write 49 as a sum like this?
(ii) How about 81?
(iii) Can you write 121 as such a sum?
Answer:
(i) 49 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 6 + 5 + 4 + 3 + 2 + 1
(ii) 81 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1
(iii) 121 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1
Question 2.
Look at the following calculations:
1 + 3 = 4
4 + 5 = 9
9 + 7 = 16
Continue this to compute the squares up to 144.
Answer:
1 + 3 = 4
4 + 5 = 9
9 + 7 = 16
16 + 9 = 25
25 + 11 = 36
36+ 13 = 49
49+ 15 = 64
64 + 17 = 81
81 + 19 = 100
100 + 21 = 121
121 + 23 = 144
Question 3.
Calculate each of the products below in your head:
(i) 9 × 25
(ii) 4 × 36
(iii) 4 × 25
Answer:
(i) ( 3 × 5) × (3 × 5) = 15 × 15 = 225
(ii) (2 × 6) × (2 × 6) = 12 × 12 = 144
(iii) (2 × 5) × (2 × 5) = 10 × 10 = 100
Question 4.
(i) How many odd numbers like 1, 3, 5, are to be added to get 123?
(ii) Which is the last odd number added in this?
Answer:
(i) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 = 123
12 odd numbers are needed to get 123 .
(ii) 23 is the last odd number added in this.
Question 5.
A number multiplied by 24 gave 1560.
(i) What will be the product, if the ne×t number is multiplied by 24 ?
(ii) What will be the product if the number just before this is multiplied by 24 ?
Answer:
(i) If we look at the number just after our original number, we can find the new product by simply adding 24 to 1560 .
1560 + 24 = 1584
So, when the ne×t number is multiplied by 24, we get 1584
(ii) Now, let’s look at the number just before our original number. To find this new product, we subtract 24 from 1560
1560- 24 = 1536
So. when the previous number is multiplied by 24. we get 1536
Class 5 Maths Chapter 3 Notes Kerala Syllabus Multiplication Methods
Welcome to the world of multiplication methods. In this chapter, we will learn some amazing techniques to make multiplication easier and more fun. Let’s take a quick look at what we will explore:
- Product Difference: Learn how to compare numbers without actually multiplying them, so you can quickly tell which product is bigger or smaller.
- Rectangular Multiplication: Discover a visual way to multiply using rectangles, making multiplication easier to understand.
- Square Numbers: Explore the special numbers that result from multiplying a number by itself, and see their cool patterns.
- Product of Square Numbers: Find out what happens when we multiply two square numbers together and uncover some interesting facts.
Multiplication with a two-digit number and a one-digit number doesn’t give the same result as when multiplication is done by interchanging the digits in the ones place
More Examples of square numbers are
1 × 1 =1
2 × 2 = 4
3 × 3 = 9
4 × 4 = 16
5 × 5 = 25
Now look at the pictures given below
Here, 4 can be written as sum of first 2 odd numbers.
Here, 9 can be written as sum of first 3 odd numbers.
Here, 16 can be written as sum of first 4 odd numbers.
Here, 25 can be written as sum of first 5 odd numbers.
Note :
1 = 1 × 1 = 1
1 + 3 = 2 × 2 = 4
1 + 3 + 5 = 3 × 3 = 9
1 + 3 + 5 + 7 = 4 × 4 = 16
1 + 3 + 5 + 7 + 9 = 5 × 5 = 25
When we add up odd numbers starting from 1, like 1, 3, 5, 7, and so on, the total is always a square number. Each time we add more odd numbers, we get a bigger square number as the result.
- Multiplication with a two-digit number and a one-digit number doesn’t give the same result as when a multiplication is done by interchange the digits in the ones place.
- When we arrange a number of dots into a grid where the rows and columns are equal, we create a square shape. We call such numbers ‘square numbers’
- When we add up odd numbers starting from 1, like 1, 3, 5, 7, and so on, the total is always a square number. Each time we add more odd numbers, we get a bigger square number as the result.
- When you multiply two perfect square numbers, the product will always be another square number.