CLASS 5 MATHEMATICS CH-5

                       

For Practice of Periodic Test 1 (ch 2 and 4)  Click here

COMPULSORY TO ALL

Ex- 5A

Copy Work:- (Q. 4,5,6,8,9)

4. (a) 5 and 3

         Multiples of 5 = 5,10,15,20,25,30,35,40,45,50

         Multiples of 3 = 3,6,9,12,15,18,21,24,27,30

         Two Common multiples of 5 and 3 = 15, 30 

4 (b) do yourself

5 (b)  Multiples of 2 = 2,4,6,8,10,12,14,16,18,20

         Multiples of 3 = 3,6,9,12,15,18,21,24,27,30

         Multiples of 6 = 6,12,18,24,30,36,42,48,54,60

         Three Common multiples of 2,3 and 6 =6,12,18  

5 (a) do yourself

6.  

rest parts do yourself.

8.  (a) 36

2x18=36

3x12=36

4x9=36

6x6=36

So Three Factors of 36 = 2, 3, 4, 

d) 165 

     3x55=165

     5x33=165

    15x11=165

 So Three factors of 165 = 3, 5, 15

Do 8 (b) and (c) yourself.

9 (a) 32

      

        2x16=32

        4x8=32

So All the factors of 32  = 2, 4, 8, 16    

(b) Do yourself 

Even Number

Numbers tat are multiples of 2 are even numbers. They have no remainder when divided by by 2. 

                              Odd Number

Numbers tat are not multiples of 2 are odd numbers. They have remainder when divided by by 2. 

Ex- 5B

Copy Work:- (Q. 3,4,5,7)

3 (a) First Six prime numbers greater than 20 = 23,29,31,37,41,43

        First Ten composite numbers greater than 31 = 32,33,34,35,36,38,39,40,42,44 

4 (a) 25 and 36

Factors of 25 = 1,5,25

Factors of 36 = 1,2,3,4,6,9,12,18,36

Common Factors of 25 and 36 = 1

Yes, these are co-prime numbers.

(d) 83 and 120

Factors of 83 = 1,83

Factors of 120 = 1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120 

Common Factors of 83 and 120 = 1

Yes, these are co-prime numbers.

(b) and (c) do yourself.

5. 

Do yourself rest of the parts.

7. (a) 12 and 18

Factors of 12 = 1,2,3,4,6,12

Factors of 18 = 1,2,3,6,9,18

Common Factors of 12 and 18 = 1,2,3,6 

(c) 30 and 105

Factors of 30 = 1,2,3,5,6,10,15,30

Factors of 105 = 1,3,5,7,15,21,35,105 

Common Factors of 30 and 105 = 1,3,5,15 

(b) and (d) do yourself.

 

EX- 5C

Divisibility

"Divisible By" means "when you divide one number by another the result is a whole number" or without leaving a reminder means zero.

  

Suppose, check whether 295 is divisible by 2.

Here when I divide 295 by 2, I get reminder 1 not zero.

So 295 is not divisible by 2.

This method of checking is called as "Divide Method".

In this Post we will learn how to check divisibility by different numbers like 2, 3, 4, 5. 6, 7, 8, 9, 10, 11. without doing Actual Division.

अपनी कॉपी में नीचे दिए गए तरीके से सोल्व करना है |

Lets start-

Divisibility by 2- 

                      If a number is even, it is divisible by 2.

 OR 

if ones place digit is divisible by 2, then that number is divisible by 2.

Divisibility by 3- 

                       If the sum of digits is divisible by 3, then number is divisible by 3.

Divisibility by 4- 

                       If the number formed by its last two digits is divisible by 4, then no. will be divisible by 4. 

Divisibility by 5- 

If the last digit of a number is 0  or 5, then the number is divisible by 5.

Divisibility by 6- 

If the number is divisible by both 2 and 3, then that number is divisible by 6.

  

4 d) 47322

        digit at ones place = 2

        2 is div. by 2

        so 47322 is divisible by 2.

      Sum of digits = 4 +7 +3 +2 +2 = 18

      18 is div. by 3.

      so 47322 is div. by 3.

As 47322 is div. by both 2 and 3. So 47322 will be divisible by 6.

Divisibility by 7- 

If difference between the double the last digit and the rest of the number is divisible by 7, then number will be divisible by 7.

6 b) 2135 

        Difference = 213 - 2 x 5

                          = 213 - 10

                          = 203

        203 is divisible by 7.

      S0 2135 is divisible by 7.

6 c) 5439

        Difference = 543 - 2 x 9

                          = 543 - 18

                          = 525

        525 is div. by 7

S0 5439 is div. by 7

Divisibility by 9- Same as divisibility by 3.

If the sum of digits is divisible by 9, then number is divisible by 9.

 

 Divisibility by 10-

If the last digit of the number is 0, then that number is divisible by 10.

Divisibility by 11-

if the difference between (sum of even places) and (sum of odd places) is divisible by 11, then that number is divisible by 11.

Here O means Odd place and E means Even place.

Divisibility by 12-

If the number is divisible by both 3 and 4, then the number will be divisible by 12.

Divisibility by 15-

If the number is divisible by both 5 and 3, then that number will be divisible by 15.

Divisibility by 18-

If the number is divisible by 2 and 9, then that no. will be divisible by 18.

Do in your copy (Q 7,8,9) These will be explained (with method) again in next class.

7.(a) 644

Number formed by last two digits = 44

44 is divisible by 4.

So, 644 is divisible by 4.

Now, Number formed by last three digits = 644

644 is not divisible by 8

So, 644 is divisible by 4 but not by 8.

3216

Number formed by last two digits = 16

16 is divisible by 4.

So, 3216 is divisible by 4.

Now, Number formed by last three digits = 216

216 is not divisible by 8.

So, 3216 is divisible by 8.

So, 3216 is divisible by both 4 and 8.

55100

Number formed by last two digits = 00

00 is divisible by 4.

So, 55100 is divisible by 4.

Now, Number formed by last three digits = 100

100 is not divisible by 8

So, 55100 is not divisible by 8.

So, 644 is divisible by 4 but not by 8.

7 (b) 234

Digit at last place = 4

4 is divisible 2.

So, 234 is divisible by 2.

Now, Sum of the digits = 2+3+4 = 9

9 is divisible by 3.

So, 234 is divisible by 3.

So, 234 is also divisible by 6.

So, 234 is divisible by both 2 and 6.

7016

Digit at last place = 6

6 is divisible 2.

So, 7016 is divisible by 2.

Now, Sum of the digits = 7+0+1+6 = 14

14 is not divisible by 3.

So, 7016 is not divisible by 3.

So, 7016 is also not divisible by 6.

So, 7016 is divisible by 2 but not by 6.

25314

Digit at last place = 4

4 is divisible 2.

So, 25314 is divisible by 2.

Now, Sum of the digits = 2+5+3+1+4 = 15

15 is divisible by 3.

So, 25314 is divisible by 3.

So, 25314 is also divisible by 6.

So, 25314 is divisible by both 2 and 6.

Q 8.      53__

Required greatest number = Multiple of 3 - (sum of digits)

                                       = 15 - 8 

                                       = 7

           652 __

Required greatest number = Multiple of 3 - (sum of digits)

                                       = 21 - 13

                                       = 8

           53__32

Required greatest number = Multiple of 3 - (sum of digits)

                                       = 21 - 13

                                       = 8

           7__344

Required greatest number = Multiple of 3 - (sum of digits)

                                       = 27 - 18

                                       = 9

Q 9. 

63__

The number formed by the last two digits has to be divisible by 4.

After keeping smallest digit 2, number = 32

32 is divisible by 4.

Now, 632 will be divisible by 4.

So, required no. = 2

345__

The number formed by the last two digits has to be divisible by 4.

After keeping smallest digit 2, number = 52

52 is divisible by 4.

Now, 3452 will be divisible by 4.

So, required no. = 2

104__2

The number formed by the last two digits has to be divisible by 4.

After keeping smallest digit 1, number = 12

12 is divisible by 4.

Now, 10412 will be divisible by 4.

So, required no. = 1

56__32

The number formed by the last two digits has to be divisible by 4.

After keeping smallest digit 0, number = 32

32 is divisible by 4.

Now, 56032 will be divisible by 4.

So, required no. = 0

CHECK YOURSELF CLICK HERE (CH 5)