Kerala Syllabus Class 5 Mathematics - Unit 3 Multiplication Methods - Questions and Answers | Teaching Manual 


Questions and Answers for Class 5 Mathematics - Unit 3 Multiplication Methods - Study Notes | Text Books Solution STD 5 - Maths: Unit 3 Multiplication Methods - Questions and Answers | ഗുണനരീതികൾ - ചോദ്യോത്തരങ്ങൾ 

അഞ്ചാം ക്ലാസ്സ്‌  Mathematics - Unit 3 Multiplication Methods  എന്ന പാഠം ആസ്പദമാക്കി തയ്യാറാക്കിയ ചോദ്യോത്തരങ്ങള്‍. ഈ അധ്യായത്തിന്റെ Teachers Handbook, Teaching Manual എന്നിവ ഡൗൺലോഡ് ചെയ്യാനുള്ള ലിങ്ക് ചോദ്യോത്തരങ്ങളുടെ അവസാനം നൽകിയിട്ടുണ്ട്.

STD 5 - Maths: Unit 3 Multiplication Methods- Questions and Answers

♦ Textbook Activities - Page 31
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    ;   18 × 2 
12 × 8 is larger. (8 - 2) x 10 = 6 x 10 = 60 more

(2) 17 × 6   ;   16 × 7 
16 × 7 is larger. (7 - 6) x 10 = 1 x 10 = 10 more

(3) 13 × 9    ;   19 × 3 
13 × 9 is larger. (9 - 3) x 10 = 6 x 10 = 60 more

(4) 25 × 6   ;    26 × 5
25 × 6 is larger. (6 - 5) x 20 = 1 x 20 = 20 more

♦ Textbook Activities - Page 34
Now try computing the products below like this:
♦ Textbook Activities - Page 35
Now try these problems on your own:
1. Compute the products below:
i. 12 × 34 
ii. 23 × 45 
iii. 75 × 75 
iv. 123 × 45 
v.  320 × 78
Answer:
i) 12 x 4
Method 1
Method 2 (10 x 34) + (2 x 34) = 340 + 68 = 408
Method 3 (10 x 30) + (2 x 30) + (10x 4) + (2 x 4) = 300 + 60 + 40 + 8 = 408
Method 4  
ii. 23 × 45
Method 1
Method 2 (20 x 45) + (3 x 45) = 900 + 135 = 1035
Method 3 (20 x 40) + (20 x 5) + (3 x 40) + (3 x 5) = 800 + 100 + 120 + 15 = 1035
Method 4
iii. 75 × 75 
Method 1
Method 2 (75 x 70) + (75 x 5) = 5250 + 375 = 5625
Method 3 (70 x 70) + (5 x 70) + (5 x 70) + (5 x 5) = 4900 + 350 + 350 + 25 = 5625
Method 4
iv. 123 × 45
Method 1
Method 2 (100 x 45) + (20 x 45) + (3 x 45) = 4500 + 900 + 135 = 5535
Method 3 (100 x 40) + (20 x 40) + (3 x 40) + (100 x 5) + (20 x 5) + (3 x 5) = 4000 + 800 + 120 + 500 + 100 + 15 = 5535
Method 4
v.  320 × 78
Method 1
Method 2 (300 x 78) + (20 x 78) = 23400 + 1560 = 24960
Method 3 (300 x 70) + (20 x 70) + (300 x 8) + (20 x 8) = 21000 + 1400 + 2400 + 160 = 24960
Method 4
2. Given that 36 × 15 = 540; Compute the following products in your head:
i. 36 × 16 
ii. 37 × 15 
iii. 36 × 14 iv. 35 × 15
Answer:
i. 36 × 16 = (36 x 15) + 36 = 540 + 36 = 576 (36 more than 36 x 15)
ii. 37 × 15 = (36 x 15) + 15 = 540 + 15 = 555 (15 more than 36 x 15)
iii. 36 × 14 = (36 x 15) - 36 = 540 - 36 = 504 (36 less than 36 x 15)
iv. 35 × 15 = (36 x 15) - 15 = 540 - 15 = 525 (15 less than 36 x 15)

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. What will be the product if the next number is multiplied by 16?
1360 + 16 = 1376 (16 more than 1360)
ii. What will be the product if the number just before this is multiplied by 16?
1360 - 16 = 1344 (16 less than 1360)
♦ Textbook Activities - Page 37
Now try these problems on your own:
1. 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 x 111 = 12321
ii. 1111 × 1111 = 1234321
iii. 11111 × 11111 = 123454321
    111111 × 111111 = 12345654321
    1111111 × 1111111 = 1234567654321

2. Look at the following calculations:
 1 + 3 = 4
 4 + 5 = 9
 9 + 7 = 16
Continue this to compute the squares up to 100
Answer:
1 + 3 = 4
4 + 5 = 9
9 + 7 =16
16 + 9 = 25
25 + 11 = 36
36 + 13 = 49
49 + 14 = 64
64 + 17 = 81
81 = 19 = 100

3. i.  How many odd numbers like 1, 3, 5, are to be added to get 400?
Answer: 400 = 20 x 20
             So 400 is the sum of the first 20 odd numbers.
              1 + 3 + 5 + 7 ...........+ 39 = 400

ii. Which is the last odd number added in this?
Answer: The last odd number to be added is the 20th odd number. This is 1 less than the 20th even number. 
That is (20 x 2) - 1 = 40 - 1 = 39
20 x 2 - = 40 - 1 = 39

4.  i. Which is the fiftieth odd number?
Answer: 50th odd number = 50 x 2 - 1 = 100 - 1 = 99

ii. What is the sum of the odd numbers from 1 to this number?
Answer: 50 x 50 = 2500, ie, 2500 is the 50th square number. So 2500 is the sum of the first fifty-odd numbers.l

5.  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
♦ Textbook Activities - Page 38
1.  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 x 3 x 4 x 4
             = (3 x 4) x (3 x 4)
             = 12 x 12

ii. 16 × 36  = 4 x 4 x 6 x 6
                 = (4 x 6) x (4 x 6)
                 = 24 x 24

iii. 36 × 49 = 6 x 6 x 7 x 7
                 = (6 x 7) x (6 x 7)
                 = 42 x 42

iv. 49 × 64  = 7 x 7 x 8 x 8
                  = (7 x 8) x (7 x 8)
                  = 56 x 56

2.  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  = 100

ii.  25 × 16  = 400 (4 times of 25 x 4 = 4 times of 100 = 400)

iii.  25 × 36  = 900 (25 x 36 = half of half of 36 x 100. half of half of 3600. half of 1800 = 900
OR
(5 x 5) x (6 x 6) = (5 x 6) x (5 x 6) = 30 x 30 = 900

iv.  25 × 64 = 1600 ( half of half of 64 x 100 = half of half of 6400 = half of 3200 = 1600)
OR
(5 x 5) x (8 x 8) = (5 x 8) x (5 x 8) = 40 x 40 = 1600

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