Kerala Syllabus Class 5 Mathematics - Unit 9 Number Relations - Questions and Answers | Teaching Manual 

Questions and Answers for Class 5 Mathematics - Unit 9 Number Relations - Study Notes | Text Books Solution STD 5 - Maths: Unit 9 Number Relations - Questions and Answers | സംഖ്യാബന്ധങ്ങൾ - ചോദ്യോത്തരങ്ങൾ 

അഞ്ചാം ക്ലാസ്സ്‌  Mathematics - Unit 9 Number Relations എന്ന പാഠം ആസ്പദമാക്കി തയ്യാറാക്കിയ ചോദ്യോത്തരങ്ങള്‍. ഈ അധ്യായത്തിന്റെ Teachers Handbook, Teaching Manual എന്നിവ ഡൗൺലോഡ് ചെയ്യാനുള്ള ലിങ്ക് ചോദ്യോത്തരങ്ങളുടെ അവസാനം നൽകിയിട്ടുണ്ട്.

STD 5 - Maths: Unit 9 Number Relations - Questions and Answers

♦ Addition, Subtraction and Multiplication
To multiply the sum of two numbers by a number, we need to multiply each number in the sum and add them together.
This can be shortened:
The product of a sum is the sum of the products.
The product of a difference is the difference of the products
♦ Textbook Page 103
Now, see whether you can do these problems in your head.
(i) 15 × 6 
(ii) 18 × 7 
(iii) 24 × 9 
(iv) 29 × 8 
(v) 99 × 6
Answer:
(i) 15 × 6 
    15 x 6 = (10 + 5) x 6
              = (10 x 6) + (5 x 6)
              = 60 + 30 = 90

(ii) 18 × 7 
     18 × 7 = (20 - 2) x 7
               = (20 x 7) - (2 x 7)
               = 140 - 14 = 126

(iii) 24 × 9 
     24 × 9 = (20 + 4) x9
                = (20 x 9) + (4 x 9)
                = 180 + 36 = 216

(iv) 29 × 8 
      29 × 8 = (30 - 1) x 8
                 = (30 x 8) - (1 x 8)
                 = 240 - 8 = 232 

(v) 99 × 6
     99 × 6 = (100 - 1) x 6
                = (100 x 6) - (1 x 6)
                = 600 - 6 = 594

♦ Addition, Subtraction and Division
If two numbers can be divided without remainder by a number, then their sum can also be divided without remainder, and the quotient is the sum of the quotients.
In division without remainder, the quotient of a sum is the sum of the quotients.
♦ Textbook Page 106
Now can’t you do these problems mentally?
(i) 39 ÷ 3 
(ii) 52÷4  
(iii) 125 ÷ 5  
(iv) 396÷4  
(v) 135÷15
Answer:
(i) 39 ÷ 3 
    39 ÷ 3 = (30 + 9) ÷ 3
    30 ÷ 3 = 10;      9 ÷ 3 = 3
    39 ÷ 3 = 10 + 3 = 13 

(ii) 52 ÷ 4
     (40 + 12) ÷ 4;       40 ÷ 4 = 10
     12 ÷ 4 = 3;           52 ÷ 4 = 10 + 3 = 13

(iii) 125 ÷ 5  
     (100 + 25) ÷ 5;     100 ÷ 5 = 20
     25 ÷ 5 = 5            125 ÷ 5 = 20 + 5 = 25

(iv) 396÷4
      396 = 400 - 4;     400 ÷ 4 = 100
      4 ÷ 4 = 1;            396 ÷ 4 = 100 -1 = 99

(v) 135÷15
      135 = 150 - 15;    150 ÷ 15 = 10
       15 ÷ 15 = 1;        135 ÷ 15 = 10 - 1 = 9
♦ Remainders
The remainder on dividing any number by 10 is the last digit of the number
If the last digit of a number is less than 5, the remainder on dividing the number by 5 is the last digit itself. If the last digit is greater than or equal to 5, the remainder is 5 subtracted from the last digit.
If the last digit of a number is divisible by 2, then the number itself is divisible by 2; if the last digit is not divisible by 2, the remainder is 1 on division by 2.
For any number with three or more digits, the remainder on dividing it by 100 is the number formed by the last two digits.
For any number with two or more digits, the remainder on dividing it by 4 is the remainder on dividing the last two digits of the number by 4.
♦ Textbook Page 110
Now solve these problems:
(1) Find which of the numbers below are divisible by 2, 4, 5 or 10. For the others, find the remainder on division by each of  these:
(i) 3624 (ii) 3625  (iii) 3626  (iv) 3630
Answer:
(i) 3624 
• The last digit of 3624 is 4, which can be divided by 2 without any remainder. Therefore, 3624 is divisible by 2.
• The last two digits of 3624 form the number 24, which can be divided by 4 without any remainder. Therefore, 3624 can be divided by 4 without any remainder.
• Since the last digit of 3624, which is 4, is less than 5, the remainder when dividing 3624 by 5 is 4.
• The remainder when dividing 3624 by 10 is the last digit of 3624, which is 4.

ii) 3625
• The last digit is 5; therefore, the remainder obtained when divided by 2 is 1.
• The last two digits form the number 25, so the remainder when divided by 4 is 1.
• The last digit is 5, therefore the remainder when divided by 5 is 0.
• The last digit is 5, therefore the remainder when divided by 10 will be 5 itself.

iii) 3626
• The last digit is 6, therefore the remainder obtained when divided by 2 is 0.
• The last two digits form the number 26, so the remainder when divided by 4 is 2.
• The last digit is 6, therefore the remainder when divided by 5 is 1.
• The last digit is 6; therefore, the remainder when divided by 10 will be 6 itself.

iv) 3630
• The last digit is 0, therefore the remainder obtained when divided by 2 is 0.
• The last two digits form the number 30, so the remainder when divided by 4 is 2.
• The last digit is 0, therefore the remainder when divided by 5 is 0.
• The last digit is 0, therefore the remainder when divided by 10 will be 0.
• Numbers that are divisible by 2 are the numbers 3624, 3626 and 3630.
• A number that is divisible by 4 is the number 3624.
• Numbers that are divisible by 5 are the numbers 3625 and 3630.
• The number that is divisible by 10 is the number 3630.

(2) In any five consecutive natural numbers, one of them will be divisible by 5. Explain why this is so.
If we take 5 consecutive natural numbers, the last digit of one of them will be either 5 or 0. Therefore, that number can be divided by 5 without leaving any remainder.
Example (1): 6, 7, 8, 9 and 10. 
Here, the last digit of 10 is 0. 
Therefore, it is divisible by 5. 
Example (2): 11, 12, 13, 14 and 15, 
Here, the last digit of 15 is 5. 
Therefore, it is divisible by 5.
(3) For any number with three or more digits, the remainder on division by 8 is the remainder on dividing the number by the last 3 digits of the number by 8. Explain why this is so.
3786 = (1000 x 3) + (8 x 98) + 2
        = (8 x 125 x 3) + (8 x 98) + 2
        = (8 x 375) + (8 x 98) + 2
        = (8 x 473) + 2
Reminder obtained when 3786 is divided by 8 is 2
Here, 1000 = 8 x 125. So any multiple of 1000 will also be a multiple of 8.
3786 = (1000 x 3) + 786
         = (8 x 125 x 3) + 786 = (8 x 375) + 786
To find the remainder when dividing by 8, look at the remaining 786 and write it as a multiple and remainder of 8.
786 = (8 x 98) + 2
Therefore, we can write, 3786 = (8 x 375) + (8 x 98) + 2
                                               = 8 x 474 + 2
So the remainder when dividing by 8 is 2
When you divide any number with four or more digits by 8, the remainder will be the same as when you divide the number formed by the last three digits by 8.

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