Kerala Syllabus Class 5 Mathematics - Unit 4 Division Methods - Questions and Answers | Teaching Manual 


Questions and Answers for Class 5 Mathematics - Unit 4 Division Methods - Study Notes | Text Books Solution STD 5 - Maths: Unit 4 Division Methods - Questions and Answers | ഹരണരീതികൾ - ചോദ്യോത്തരങ്ങൾ 

അഞ്ചാം ക്ലാസ്സ്‌  Mathematics - Unit 4 Division Methods  എന്ന പാഠം ആസ്പദമാക്കി തയ്യാറാക്കിയ ചോദ്യോത്തരങ്ങള്‍. ഈ അധ്യായത്തിന്റെ Teachers Handbook, Teaching Manual എന്നിവ ഡൗൺലോഡ് ചെയ്യാനുള്ള ലിങ്ക് ചോദ്യോത്തരങ്ങളുടെ അവസാനം നൽകിയിട്ടുണ്ട്.

STD 5 - Maths: Unit 4 Division Methods- Questions and Answers

♦ Textbook Activities - Page 48
1.Total price of  7 pens of equal rate is 98 rupees. What’s the price of a pen?
Answer:
Method 1
We have to find 98 ÷ 7
98 = 70 + 28
Dividing 70 rupees to 7 pens will give 10 rupees to each pen.
And dividing the remaining 28 rupees to 7 pens will give 4 rupees to each pen. So each pen will have 10 + 4 = 4 rupees

Method 2:

Also like this: 
98 means 70 + 28
In 70, 10 times 7
In 28, 4 times 7
So, a total of 14 times
2. If 168 rupees is shared equally among 8 persons, how much will each get?
Answer:
168 ÷ 8
Method 1
Let's like this
168 = 160 + 8
Since 2 x 8 = 16, we can easily find 20 x 8 = 160 
In 160, there are 20 times 8
In 8, there is 1 time 8.
So a total of 20 + 1 = 21 times
3. The school store needs 1825 notebooks. How many packs of  25 notebooks are to be bought?
Answer:
1825 ÷ 25
Method 1
1825 ÷ 25 = 40 + 20 + 10 + 3 = 73
So, the number of packs of notebooks = 73
Method 2
Let's think like this
40 times 25 equals 1000, right? (4 x 25 = 100, 40 x 25 = 1000)
80 times 25 will be 2000 (80 x 25 = 2000)
So, the number of notebooks will be 175 less than 2000.
That is 175 ÷ 25 = 7 packs
So, the total packs will be 80 - 7 = 73
Relation between quotient
16 ÷ 8 = 2
32 ÷ 16 = 2
8 ÷ 4 = 2
4 ÷ 2 = 2
2 ÷ 1 = 2
If the two numbers are doubled or halved, their quotient will never change.
100 ÷ 50 = 50 ÷ 25 = 2

Reminders
Oftentimes, a number cannot be split into equal parts, a remainder may be left over. In such cases, we need to write the number as a product, added with the remainder.

Quotient & Remainder
When dividing, the number that tells how many parts is called the quotient. The number showing the leftover is called the remainder.
E.g.: 54 ÷ 10
Quotient 5, remainder 4

Any number can be expressed as the times of a non-zero number along with a remainder. The remainder will always be less than that non-zero number.
♦ Textbook Activities - Page 50
1. What are the numbers which leave remainder 0 on division by 2? And those that leave remainder 1?
Answer:
The numbers that leave no remainders are the even numbers
(2, 4, 6, 8, 10, 12, .................)
The numbers that leave 1 as the remainder are the odd numbers.
(1, 3, 5, 5, 7, 9, 11, .................)

2. What are the possible remainders on dividing a number by 3 ? Write the pattern of numbers leaving the same remainder for each of these.
Answer:
Answer:
The possible remainders are 0, 1 and 2
Numbers leaving remainder 0: 0, 3, 6, 9, 12, ...........
Numbers leaving remainder 1: 1, 4, 7, 10, 13, ..............
Numbers leaving remainder 2: 2, 5, 8, 11, 14, ...............

3. See the way numbers are arranged below:
i.  Is there any relation between the quotients on dividing the numbers in any one row by 5? And the remainders?
Answer:
• When dividing numbers in the same row by 5, we get the same quotient
(e.g, 10, 11, 12, 13, 14, when divided by 5, gives the quotient 2)
• When dividing numbers in the same row by 5, the remainders are the corresponding numbers in the top row. 
(eg, 16 ÷ 5 = 3 remainder 1. Corresponding to 16, there is 1 on the top row. Similarly, 13 ÷ 5 = 2. remainder 3)

ii.  What if numbers in any one column are divided by 5?
Answer:
• As we move downward, the quotient will increase by 1. 
(eg, 0 ÷ 5 = 0, 5 ÷ 5 = 1, 10 ÷ 5 = 2, 15 ÷ 5 = 3)
• Dividing the numbers in the same column by 5, we get the same remainder.
Reminder in the first column: 0
Reminder in the second column: 1
......................................................
......................................................

iii. What are the first and last numbers of the 10th row?
Answer:
• First number in the first row = 0 x 5 = 0
First number in the second row = 1 x 5 = 5
First number in the third row = 2 x 5 = 10
................................................................
First number in the tenth row = 9 x 5 = 45

• Last number in the first row = 0 x 5 + 4 = 4
Last number in the second row = 1 x 5 + 4 = 9
Last number in the third row = 2 x 5 + 4 = 14
.......................................................................
Last number in the tenth row = 9 x 5 + 4 = 49

iv.  What is the 4th number in the 12th row?
Answer:
Fourth number in the 12th row = 11 x 5 + 3 = 58

v.  Which column and row does the number 123 belong to?
Answer:
If we write 123 as times and remainder of 5
123 = 24 x 5 + 3
The first number in the 25th row = 24 x 5 = 120
Since the remainder is 3, 123 is the fourth number in the 25th row.

4. Write each of  the numbers as certain times 9 and a remainder
(a) 11  (b) 111 (c) 1111
Answer:
a) 11 = 1 x 9 + 2 (11 ÷ 9 = 1, remainder 2)
b) 111 = 12 x 9 + 3 (111 ÷ 9 = 12, remainder 3)
c) 1111 =123 x 9 + 4 (1111 ÷ 9 = 123, remainder 4)

i.  Can you guess how 11111 is written like this? Check your guess by actual division.
Answer:
Following (a), (b), (c) given above,
We can make a guess 11111 = 123 x 9 + 5
11111 ÷ 9 = 1234 x 9 + 5 (This is correct)

ii.  Write out this number pattern.
Answer:
1 x 9 + 2,  12 x 9 + 3, 123 x 9 + 4,
   (11)           (111)          (1111)
1234 x 9 + 5,  12345 x 9 + 6
   (11111)            (111111) 

5. Write each of  the numbers as certain times 8 and a remainder
(a) 9  (b) 98  (c) 987
Answer:
(a) 9 = 1 x 8 + 1 (9 ÷ 8 = 1, remainder 1)
(b) 98 = 12 x 8 + 2 (98 ÷ 8 = 12, remainder 2)
(c) 987 = 123 x 8 + 3 (987 ÷ 8 = 123, remainder 3)

i.  Can you guess how 9876 is written like this? Check your guess by actual division.
Answer:
9876 = 1234 x 8 + 4
9876 ÷ 8 = 1234 remainder 4 (This is correct) 
 
ii.  Write out this number pattern.
Answer:
9, 98, 987, 9876, 98765, 987654, 9876543, ............................

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