Free MATHS for Class V by www.sainikrimc.com

Free MATHS for Class V by www.sainikrimc.com

Regular Maths classes and coaching for Sainik School- RMS and RIMC conducted by 

Step by step working to succeed at Mathematics  School level ( Elementary Mathematics for all)

Write all formula

a)      Test of Divisibility

b)      Average

c)       Meaning of Unitary Method

d)      Time, speed and distance

e)      Profit and Loss

f)       Simple Interest

g)      Geometry

h)      Area, Perimeter

i)        Volume

j)        BODMAS

k)      Triangles

l)        Types of Fractions

m)    Misc

Divisibility Rules

1.   Any integer (not a fraction) is divisible by 1

2.   The last digit is even (0,2,4,6,8) ( Eg:128  Yes, 129  No)

3.   he sum of the digits is divisible by 3

381 (3+8+1=12, and 12÷3 = 4) Yes

217 (2+1+7=10, and 10÷3 = 3 ¹/₃) No

This rule can be repeated when needed:

99996 (9+9+9+9+6 = 42, then 4+2=6) Yes

4.   The last 2 digits are divisible by 4

1312 is (12÷4=3) Yes

7019 is not (19÷4=4 ³/₄) No

A quick check (useful for small numbers) is to halve the number twice and the result is still a whole number.

12/2 = 6, 6/2 = 3, 3 is a whole number. Yes

30/2 = 15, 15/2 = 7.5 which is not a whole number. No

5.   The last digit is 0 or 5 (E.g:175  Yes, 809  No)

6.   Is even and is divisible by 3 (it passes both the 2 rule and 3 rule above)

114 (it is even, and 1+1+4=6 and 6÷3 = 2) Yes

308 (it is even, but 3+0+8=11 and 11÷3 = 3 ²/₃) No

7.   Double the last digit and subtract it from a number made by the other digits. The result must be divisible by 7. (We can apply this rule to that answer again)

672 (Double 2 is 4, 67-4=63, and 63÷7=9) Yes

105 (Double 5 is 10, 10-10=0, and 0 is divisible by 7) Yes

905 (Double 5 is 10, 90-10=80, and 80÷7=11 ³/₇) No

8.   The last three digits are divisible by 8

109816 (816÷8=102) Yes

216302 (302÷8=37 ³/₄) No

A quick check is to halve three times and the result is still a whole number:

816/2 = 408, 408/2 = 204, 204/2 = 102 Yes

302/2 = 151, 151/2 = 75.5 No

9.   The sum of the digits is divisible by 9

(Note: This rule can be repeated when needed)

1629 (1+6+2+9=18, and again, 1+8=9) Yes

2013 (2+0+1+3=6) No

10.        The number ends in 0(220  Yes,221  No)

11.        Add and subtract digits in an alternating pattern (add digit, subtract next digit, add next digit, etc). Then check if that answer is divisible by 11.

1364 (+1−3+6−4 = 0) Yes

913 (+9−1+3 = 11) Yes

3729 (+3−7+2−9 = −11) Yes

987 (+9−8+7 = 8) No

12.        The number is divisible by both 3 and 4 (it passes both the 3 rule and 4 rule above)

648
(By 3? 6+4+8=18 and 18÷3=6 Yes)
(By 4? 48÷4=12 Yes)
Both pass, so Yes

524
(By 3? 5+2+4=11, 11÷3= 3 ²/₃ No)
(Don't need to check by 4) No

Factors are the numbers you multiply to get another number:

This can be useful, because:

When a number is divisible by another number ...

... then it is also divisible by each of the factors of that number.

Test for Chapter 1.

1.     Use 'Divisibility Rules' to determine which of the following numbers 237 is divisible by:  A.2                B.3                  C 4                  D.7

2.     Use 'Divisibility Rules' to determine which of the following numbers 833 is divisible by:  A.2                B.3                  C.7                  D.9

3.     Use 'Divisibility Rules' to determine which of the following numbers 6,488 is divisible by: A. 3             B. 7                 C.8                  D.11

4.     Use 'Divisibility Rules' to determine which of the following numbers 6,721 is divisible by: A. 3             B.7                  C.8                  D.11

5.     Tom picked a natural number and multiplied it by 3. 
Use 'Divisibility Rules' to determine which number CANNOT be the result of this multiplication.A.987           B.444              C.105              D.103

6.     Use 'Divisibility Rules' to determine which of the following numbers 3,528 is NOT divisible by: A.7      B.8                  C.9                  D.11

7.     Use 'Divisibility Rules' to determine which of the following numbers 8,712 is NOT divisible by:A.7            B.8                  C.9                  D.11

8.     Use 'Divisibility Rules' to determine which one of the following numbers is divisible by 7:  A. 5,990      B. 5,992     C.5,994          D.5,996

9.     Use 'Divisibility Rules' to determine which one of the following numbers is divisible by 11: A.6,915          B.6,917          C.6,919          D.6,921

10. Use 'Divisibility Rules' to determine which of the following numbers 2,376 is NOT divisible by: A.3      B.7                  C.11                D.12   

Use 'Divisibility Rules' to determine which of the following numbers 237 is divisible by:   A. 2              B.3                        C.7                  D.9

The questions are for you! So you can get practice.

Don't cheat yourself. Work hard on each question. Don't hurry, there is no time limit.

In this case you need to check each choice ... is 237 divisible by 2? is it divisible by 3? etc.

Q.1.  Correct answer is B.3

Solution:

Test for divisibility by 2
237 cannot be divisible by 2 since the last digit is odd

Test for divisibility by 3
Sum of the digits = 2 + 3 + 7 = 12
12 is divisible by 3, so 237 is also divisible by 3

Test for divisibility by 7
Double the last digit 7 is 14, 23 - 14 = 9, and 9 is not divisible by 7
Therefore 237 is not divisible by 7

Test for divisibility by 9
Sum of the digits = 2 + 3 + 7 = 12
12 is not divisible by 9, so 237 is not divisible by 9

Q.2. Use 'Divisibility Rules' to determine which of the following numbers 833 is divisible by:

A.2                  B.3                  C.7                  D.8

Solution:

Answer is (C) 7.

Test for divisibility by 2
833 cannot be divisible by 2 since the last digit is odd

Test for divisibility by 3
Sum of the digits = 8 + 3 + 3 = 14
14 is not divisible by 3, so 833 is not divisible by 3

Test for divisibility by 7
Double the last digit 3 is 6, 83 - 6 = 77, and 7 is divisible by 7
So 833 is divisible by 7

Test for divisibility by 9
Sum of the digits = 8 + 3 + 3 = 14
14 is not divisible by 9, so 833 is not divisible by 9

Q.3. Solution: Answer is C

Test for divisibility by 3
Sum of the digits = 6 + 4 + 8 + 8 = 26
26 is not divisible by 3, so 6,488 is not divisible by 3

Test for divisibility by 7
Double the last digit 8 is 16, 648 - 16 = 632
Double 2 is 4, 63 - 4 = 59, and 59 is not divisible by 7
Therefore 6,488 is not divisible by 7

Test for divisibility by 8
The last three digits are 488
488 = 8 × 61, so is divisible by 8
So  6,488 is also divisible by 8

Test for divisibility by 11
Add and subtract digits in an alternating pattern (add first, subtract second, add third, etc):
6 − 4 + 8 − 8 = 2 + 0 = 2
2 is not divisible by 11, so 6,488 is not divisible by 11

Q.4. Solution: Correct answer is D

Test for divisibility by 3
Sum of the digits = 6 + 7 + 2 + 1 = 16
16 is not divisible by 3, so 6,721 is not divisible by 3

Test for divisibility by 7
Double the last digit 1 is 2, 672 - 2 = 670
Again: Double the last digit 0 is 0, 67 - 0 = 67, and 67 is not divisible by 7
Therefore 6,721 is not divisible by 7

Test for divisibility by 8
The last three digits are 721
721 is odd, so can't be divisible by 8
So 6,721 is not divisible by 8

Test for divisibility by 11
Add and subtract digits in an alternating pattern (add first, subtract second, add third, etc):
6 − 7 + 2 − 1 = -1 + 1 = 0
The answer is 0, so 6,721 is divisible by 11

Q.5. D is the correct answer

Solution:

Use the divisibility rule for 3: The sum of the digits is divisible by 3

Test each number in turn:
987 ⇒ 9 + 8 + 7 = 24 ⇒ 2 + 4 = 6
6 is divisible by 3, so 987 is divisible by 3

444 ⇒ 4 + 4 + 4 = 12 ⇒ 1 + 2 = 3
3 is divisible by 3, so 444 is divisible by 3

105 ⇒ 1 + 0 + 5 = 6
6 is divisible by 3, so 105 is divisible by 3

103 ⇒ 1 + 0 + 3 = 4 
4 is not divisible by 3, so 103 is not divisible by 3

Q.6.Answer D

Solution:

Test for divisibility by 7
Double the last digit 8 is 16, then 352 - 16 = 336
Again: Double the last digit 6 is 12, then 33 - 12 = 21, and 21 is divisible by 7
So 3,528 is divisible by 7

Test for divisibility by 8
The last three digits are 528
528 = 8 × 66, so is divisible by 8
So 3,528 is also divisible by 8

Test for divisibility by 9
Sum of the digits = 3 + 5 + 2 + 8 = 18 and 1 + 8 = 9
So 3,528 is divisible by 9

Test for divisibility by 11
Add and subtract digits in an alternating pattern (add first, subtract second, add third, etc):
3 − 5 + 2 − 8  = -2 + (-6) = -8
The answer is not 0 or divisible by 11, so 3,528 is not divisible by 11

Q.7. A is the correct answer

Solution:

Test for divisibility by 7
Double the last digit 2 is 4, then 871 - 4 = 867
Again: Double the last digit 7 is 14, then 86 - 14 = 72, and 72 is not divisible by 7
So 8,712 is not divisible by 7

Test for divisibility by 8
The last three digits are 712
712 = 8 × 89, so is divisible by 8
So 8,712 is also divisible by 8

Test for divisibility by 9
Sum of the digits = 8 + 7 + 1 + 2 = 18 and 1 + 8 = 9
So 8,712 is divisible by 9

Test for divisibility by 11
Add and subtract digits in an alternating pattern (add first, subtract second, add third, etc):
8 − 7 + 1 − 2 = 1 + (-1) = 0
The answer is 0, so 8,712 is divisible by 11

Q.8 B is the correct Answer

Solution:

Test 5,990 for divisibility by 7
Double the last digit 0 is 0, 599 - 0 = 599
Again: Double the last digit 9 is 18, 59 - 18 = 41, and 41 is not divisible by 7
Therefore 5,990 is not divisible by 7

Test 5,992 for divisibility by 7
Double the last digit 2 is 4, 599 - 4 = 595
Again: Double the last digit 5 is 10, 59 - 10 = 49, and 49 is divisible by 7
Therefore 5,992 is divisible by 7

Test 5,994 for divisibility by 7
Double the last digit 4 is 8, 599 - 8 = 591
Again: Double the last digit 1 is 2, 59 - 2 = 57, and 57 is not divisible by 7
Therefore 5,994 is not divisible by 7

Test 5,996 for divisibility by 7
Double the last digit 6 is 12, 599 - 12 = 587
Again: Double the last digit 7 is 14, 58 - 14 = 44, and 44 is not divisible by 7
Therefore 5,996 is not divisible by 7

Q.9. Correct answer is  C.

Test 6,915 for divisibility by 11
Add and subtract digits in an alternating pattern (add first, subtract second, add third, etc):
6 − 9 + 1 − 5 = -3 + (-4) = -7
The answer is not 0 or divisible by 11, so 6,915 is not divisible by 11

Test 6,917 for divisibility by 11
Add and subtract digits in an alternating pattern (add first, subtract second, add third, etc):
6 − 9 + 1 − 7 = -3 + (-6) = -9
The answer is not 0 or divisible by 11, so 6,917 is not divisible by 11

Test 6,919 for divisibility by 11
Add and subtract digits in an alternating pattern (add first, subtract second, add third, etc):
6 − 9 + 1 − 9 = -3 + (-8) = -11
The answer is divisible by 11, so 6,919 is divisible by 11

Test 6,921 for divisibility by 11
Add and subtract digits in an alternating pattern (add first, subtract second, add third, etc):
6 − 9 + 2 − 1 = -3 + 1 = -2
The answer is not 0 or divisible by 11, so 6,921 is not divisible by 11

Q.10 B is the correct answer

Solution:

Test for divisibility by 3
Sum of the digits = 2 + 3 + 7 + 6 = 18 and 1 + 8 = 9
9 is divisible by 3
So 2,376 is divisible by 3

Test for divisibility by 7
Double the last digit 6 is 12, then 237 - 12 = 225
Again: Double the last digit 5 is 10, then 22 - 10 = 12, and 12 is not divisible by 7
So 2,376 is not divisible by 7

Test for divisibility by 11
Add and subtract digits in an alternating pattern (add first, subtract second, add third, etc):
2 − 3 + 7 − 6 = -1 + 1 = 0
The answer is 0, so 2,376 is divisible by 11

Test for divisibility by 12
The last 2 digits, 76, are divisible by 4, so 2,376 is divisible by 4
We've already shown it's divisible by 3
Because 2,376 is divisible by both 3 and 4, it must also be divisible by 12

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