1. WELCOME TO MATHEMATICS WORKSHOP

2. LET’S TEACH MATHS WITH PASSION!!!
A GENERAL ILLUSION-----MATHS IS VERY TOUGH….
LET’S TEACH MATHS WITH PASSION!!!

3. Let’s Make Teaching Maths Easier………
By Mr. T.Satya Prasad
H.O.D.MATHEMATICS

4. FEW TIPS TO MAKE TEACHING MATHS EASIER:

5. 1.LET’S SHOW THE INVOLVEMENT IN TEACHING
2.ENSURE THAT WHAT YOU HAVE COMMUNICATED TO THE STUDENTS IS EXACTLY WHAT YOU REALLY WANTED TO COMMUNICATE TO THEM.
3.MAKE YOUR CONCEPT CLEAR BEFORE YOU TEACH .
4.DIFFICULTY OF THE PARTICULAR CHAPTER ALSO DEPENDS ON YOUR TEACHING. INVENT NEW WAYS OF MAKING THINGS CLEAR RATHER THAN USING CONVENTIONAL EXAMPLES ONLY.
LETS PUT A PAUSE TO FUNDAS……………..

6. LETS BEGIN WITH…
DIVISION

7. Divisibility
DIVISIBILITY RULES
Rules

8. Divisibility Rules Helps you learn shortcuts to tell when a number can be divided by another number with NO remainder.

9. What is Divisibility? Divisibility
means that after dividing, there will be no remainder.

10. Divisibility by 2 A number is divisible by 2 if the number is even.
18 ÷ 2 = 9
22 ÷ 2 = 11
(Notice that both of these numbers are even.)
21 ÷ 2 = 10 R1
(Not an even number.)

11. Are these numbers divisible by 2?
127
(Not an even number)
937
4678

12. Divisibility by 3
A number is divisible by 3 if the sum of the digits is divisible by 3.
Is the number 135 divisible by 3?
Add the digits: = 9
Yes, 135 is divisible by 3 because the sum of the digits is divisible by 3.

13. Divisibility by 5
A number is divisible by 5 if it ends in 0 or 5.
25 ÷ 5 = 5
23 ÷ 5 = 4 R3

14. Divisibility by 6 A number is divisible by 6 if it is divisible
by both
2 and 3.
Is 42 divisible by 6?
Is 51 divisible by 6?

15. Divisibility by A number is divisible by 10 if it ends in 0.
30 ÷ 10 = 3
340 ÷ 10 = 34
67 ÷ 10 = 6 R7
784 ÷ 10 =78 R4

16. Divisibility By: 2 5 10
1825
346
510
1108

17. Divisibility by 9
A number is divisible by 9 if the sum of its digits is divisible by 9.
369 is divisible by 9
because
=18
1 + 8 = 9
AND
9 is divisible by 9.

18. 356,821 The divisibility rules can help YOU !!!
Can you tell by just looking at this number if it is divisible by 2?
by 5?
by 10?
by 3 ?
by 9?
By 6?
The divisibility rules
can help
YOU !!!

19. After All…DIVISIBILITY Rules!!

20. Lets move on to…
LONG Division

21. Long Division
Before we start this let’s introduce this family somewhat close to division family……
DAD—1.DIVIDE
MOM---2.MULTIPLY
SIS---SUBTRACT
REMO----REPEAT
OR REMAINDER
BROTHER
--BRING DOWN

22. DAD—1.DIVIDE
Step 1 in Long Division 4
1. Divide
2 ) 9 4 7
Divide 2 into first number in the dividend.
Think how many 2’s will fit into 9.
How many 2’s will go into 9?
Write that number directly above the number you divided into.

23. 2 ) 9 4 7 4 8 Step 2 in Long Division 2. Multiply 2 x 4 = 8
MOM---2.MULTIPLY 4
2. Multiply
2 ) 9 4 7 8
Multiply the divisor times the first number in the quotient.
2 x 4 = 8
Write your answer directly under the 9 or the number you just divided into.

24. 2 ) 9 4 7 4 8 1 Step 3 in Long Division 3. Subtract
SIS---SUBTRACT 4
3. Subtract
2 ) 9 4 7 8
Draw a line under the 8.
Write a subtraction sign next to the 8. 1
Subtract 8 from 9.
Write your answer directly below the 8.

25. 2 ) 9 4 7 4 8 1 4 Step 4 in Long Division 4. Bring down Brother
Go to the next number in the dividend to the right of the 9. 1 4
Write an arrow under the 4.
Bring the 4 down next to the 1.

26. Step 5 in Long Division
REMO----REPEAT
OR REMAINDER 4
2 ) 9 4 7 8
This is where you decide whether you repeat the 5 steps of division. 1 4
If your divisor can divide into your new number, 14, or if you have numbers in the dividend that have not been brought down, you repeat the 5 steps of division.

27. 2 ) 9 4 7 4 7 8 1 4 Step 1 in Long Division 1. Divide
DAD—1.DIVIDE
Step 1 in Long Division 4 7
1. Divide
2 ) 9 4 7 8
Divide 2 into your new number, 14. 1 4
Place your answer directly above the 4 in your quotient.

28. 2 ) 9 4 7 4 7 8 1 4 1 4 Step 2 in Long Division 2. Multiply Mom
MOM---2.MULTIPLY
Step 2 in Long Division 4 7
2. Multiply
2 ) 9 4 7
Mom 8
Multiply your divisor, 2, with your new number in the quotient, 7. 1 4 1 4
Place your answer directly under the 14.

29. 2 ) 9 4 7 4 7 8 1 4 1 4 Step 3 in Long Division 3. Subtract
SIS---SUBTRACT
Step 3 in Long Division 4 7
3. Subtract
2 ) 9 4 7 8
Draw a line under the bottom 14. 1 4
Draw a subtraction sign. 1 4
Subtract & place answer under the line.

30. 2 ) 9 4 7 4 7 8 1 4 1 4 7 Step 4 in Long Division 4. Bring down
Brother 8
Put an arrow under
the next number, 7,
in the dividend. 1 4 1 4
Bring the 7 down next to the 0. 7

31. Step 5 in Long Division
REMO----REPEAT
OR REMAINDER 4 7
2 ) 9 4 7 8
If the 2 will divide into your new number, 7, then repeat the steps of division. 1 4 1 4 7

32. 2 ) 9 4 7 4 7 3 8 1 4 1 4 7 Step 1 in Long Division 1. Divide
DAD—1.DIVIDE
Step 1 in Long Division 4 7 3
1. Divide
2 ) 9 4 7 8
Divide your divisor, 2, into your new number, 7. 1 4
Place your answer in the quotient next to the 7. 1 4 7

33. 2 ) 9 4 7 4 7 3 8 1 4 1 4 7 6 Step 2 in Long Division 2. Multiply Mom
MOM---2.MULTIPLY 4 7 3
2. Multiply
2 ) 9 4 7 8
Mom 1 4
Multiply your divisor, 2, by your new number in the quotient, 3. 1 4 7
Place your answer under the number you brought down, 7. 6

34. 2 ) 9 4 7 4 7 3 8 1 4 1 4 7 6 1 Step 3 in Long Division 3. Subtract
SIS---SUBTRACT
Step 3 in Long Division 4 7 3
3. Subtract
2 ) 9 4 7 8
Sister 1 4
Draw a line under the number 6. 1 4 7
Place your subtraction sign. 6
Subtract & put your answer directly under the 6. 1

35. 2 ) 9 4 7 4 7 3 8 1 4 1 4 7 6 1 Step 4 in Long Division 4. Bring down
Brother 1 4
Look at your dividend to see if there are any more numbers to bring down. 1 4 7 6
If not, move to step 5. 1

36. 2 ) 9 4 7 4 7 3 8 1 4 1 4 7 6 1 Step 5 in Long Division R1
REMO----REPEAT
OR REMAINDER 4 7 3 R1
2 ) 9 4 7 8 1 4
Since there are no more numbers to bring down & 2 will not divide into 1, you do not repeat the steps of division. 1 4 7 6 1
The number left over, 1, becomes the remainder.

37. FINALLY THIS IS HOW IT IS!!!!!4 7 3 R1
2 ) 9 4 7 8 1 4 1 4 7 6 1

38. LETS MOVE ON TO…..
2 DIGIT DIVISION

39. Step 1 in 2 Digit Long Division
DAD 4
1. Divide
2 1) 9 4 8
Divide 21 into first number in the dividend.
How many 20’s will go into 90?
21 will not go into 9 so
you look at 94.
Round off 21 and 94 in
your head.
Now divide 20 into 90 &
put your answer above the 4.

40. Step 2 in 2 Digit Long Division4
2. Multiply
2 1) 9 4 8
Mom 8 4
Multiply the divisor times the first number in your quotient. 21 x4 84
Write your answer directly under the 94 or the number you just divided into.

41. Step 3 in 2 Digit Long Division
SIS---SUBTRACT
Step 3 in 2 Digit Long Division 4
3. Subtract
2 1) 9 4 8 8 4
Draw a line under the 84.
Write a subtraction sign next to the 84. 1
Subtract 84 from 94.
Write your answer directly below the 84.

42. Step 4 in 2 Digit Long Division
4. Bring down
2 1) 9 4 8
Brother 8 4
Go to the next number in the dividend to the right of the 4. 1 8
Write an arrow under that
number.
Bring the 8 down next to the 10.

43. Step 5 in 2 Digit Long Division
REMO----REPEAT
OR REMAINDER 4
2 1) 9 4 8 8 4
This is where you decide whether you repeat the 5 steps of division. 1 8
If your divisor can divide into your new number, 108, or if you have numbers in the dividend that have not been brought down, you repeat the 5 steps of division.

44. Step 1 in 2 Digit Long Division
DAD—1.DIVIDE 4 5
2 1) 9 4 8 8 4
Divide 21 into your
new number, 108. 1 8
Round 21 and 108 off
in your head.
Divide 20 into 110
Place your answer directly
above the 8 in your quotient.

45. Step 2 in 2 Digit Long Division
MOM---2.MULTIPLY 4 5
2 1) 9 4 8 8 4
Multiply your divisor, 21, with your new number in the quotient, 5. 1 8 1 5
Place your answer directly under the

46. Step 3 in 2 Digit Long Division
SIS---SUBTRACT 4 5
2 1) 9 4 8 8 4
Draw a line under the bottom number, 105. 1 8
Draw a subtraction sign. 1 5
Subtract & place answer under the line. 3

47. Step 4 in 2 Digit Long Division5
4. Bring down
2 1) 9 4 8 8 4
Since there is nothing to
bring down, go to step
five. 1 8 1 5 3

48. Step 5 in 2 Digit Long Division4 5 R3
5. Repeat or Remainder
2 1) 9 4 8 8 4
If the 21 will not divide into your new number, 3, & there is nothing to bring down, you are done. 1 8 1 5 3
Write your left over 3 as the
remainder next to the 5.

49. THIS IS HOW IT LOOKS… 4 5 R3
2 1) 9 4 8 8 4 1 8 1 5 3

50. A DIVISION TEASER……

51. 2 ) 8 0 7 4 Step 1 in Long Division 1. Divide
DAD—1.DIVIDE
Step 1 in Long Division 4
1. Divide
2 ) 8 0 7
Divide 2 into first number in the dividend.
How many 2’s will go into 8?
Think how many 2’s will fit into 8.
Write that number directly above the number you divided into.

52. 2 ) 8 0 7 4 8 Step 2 in Long Division 2. Multiply 2 x 4 = 8
MOM---2.MULTIPLY
Step 2 in Long Division 4
2. Multiply
2 ) 8 0 7 8
Multiply the divisor times the first number in the quotient.
2 x 4 = 8
Write your answer directly under the 8 or the number you just divided into.

53. 2 ) 8 0 7 4 8 Step 3 in Long Division 3. Subtract
SIS---SUBTRACT
Step 3 in Long Division 4
3. Subtract
2 ) 8 0 7 8
Draw a line under the 8.
Write a subtraction sign next to the 8.
Subtract 8 from 8.
Write your answer directly below the 8.

54. 2 ) 8 0 7 4 8 Step 4 in Long Division 4. Bring down
Go to the next number in the dividend to the right of the 8.
Write an arrow under the 0.
Bring the 0 down next to the 0.

55. Step 5 in Long Division
REMO----REPEAT
OR REMAINDER 4
2 ) 8 0 7 8
This is where you decide whether you repeat the 5 steps of division.
If your divisor can divide into your new number, 00, or if you have numbers in the dividend that have not been brought down, you repeat the 5 steps of division.

56. 2 ) 8 0 7 4 8 Step 1 in Long Division 1. Divide
DAD—1.DIVIDE 4
1. Divide
2 ) 8 0 7 8
Divide 2 into your new number, 00.
Place your answer directly above the 0 in your quotient.

57. 2 ) 8 0 7 4 8 Step 2 in Long Division 2. Multiply
MOM---2.MULTIPLY
Step 2 in Long Division 4
2. Multiply
2 ) 8 0 7 8
Multiply your divisor, 2, with your new number in the quotient, 0.
Place your answer directly under the 00.

58. 2 ) 8 0 7 4 8 Step 3 in Long Division 3. Subtract
SIS---SUBTRACT
Step 3 in Long Division 4
3. Subtract
2 ) 8 0 7 8
Draw a line under the bottom 14.
Draw a subtraction sign.
Subtract & place answer under the line.

59. 2 ) 8 0 7 4 8 7 Step 4 in Long Division Put an arrow under
BROTHER
--BRING DOWN
Step 4 in Long Division 4
2 ) 8 0 7 8
Put an arrow under
the next number, 7,
in the dividend.
Bring the 7 down next to the 0. 7

60. Step 5 in Long Division
REMO----REPEAT
OR REMAINDER 4
2 ) 8 0 7 8
If the 2 will divide into your new number, 7, then repeat the steps of division. 7

61. 2 ) 8 0 7 4 3 8 7 Step 1 in Long Division 1. Divide
DAD—1.DIVIDE
Step 1 in Long Division 4 3
1. Divide
2 ) 8 0 7 8
Divide your divisor, 2, into your new number, 7.
Place your answer in the quotient next to the 7. 7

62. 2 ) 8 0 7 4 3 8 7 6 Step 2 in Long Division 2. Multiply
MOM---2.MULTIPLY 4 3
2. Multiply
2 ) 8 0 7 8
Multiply your divisor, 2, by your new number in the quotient, 3. 7
Place your answer under the number you brought down, 7. 6

63. 2 ) 8 0 7 4 3 8 7 6 1 Step 3 in Long Division 3. Subtract3
3. Subtract
2 ) 8 0 7 8
SIS---SUBTRACT
Draw a line under the number 6. 7
Place your subtraction sign. 6
Subtract & put your answer directly under the 6. 1

64. 2 ) 8 0 7 4 3 8 7 6 1 Step 4 in Long Division 4. Bring down
BROTHER
--BRING DOWN
Step 4 in Long Division 4 3
4. Bring down
2 ) 8 0 7 8
Look at your dividend to see if there are any more numbers to bring down. 7 6
If not, move to step 5. 1

65. 2 ) 8 0 7 4 3 8 7 6 1 R1 Step 5 in Long Division3 R1
REMO----REPEAT
OR REMAINDER
2 ) 8 0 7 8
Since there are no more numbers to bring down & 2 will not divide into 1, you do not repeat the steps of division. 7 6 1
The number left over, 1, becomes the remainder.

66. THIS IS HOW IT LOOKS… 4 3 R1
2 ) 8 0 7 8 7 6 1

67. LET’S SEE WHAT ARE PRIME NUMBERS

68. Prime Numbers Eratosthenes’ Sieve

69. Eratosthenes’ Sieve
A sieve has holes in it and is used to filter out the juice.
Eratosthenes’s sieve filters out numbers to find the prime numbers.

70. Definition
Factor – a number that is multiplied by another to give a product.
7 x 8 = 56
Factors

71. 7 Definition 7 is prime because the only numbers
Prime Number – a number that has only two factors, itself and 1. 7
7 is prime because the only numbers
that will divide into it evenly are 1 and 7.

72. Definition
Factor – a number that divides evenly into another.
56 ÷ 8 = 7
Factor

73. Hundreds Chart
On graph paper, make a chart of the numbers from 1 to 100, with 10 numbers in each row.

74. Hundreds Chart 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99
100

75. 1 – Cross out 1; it is not prime2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99
100

76. 2 – Leave 2; cross out multiples of 21 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99
100

77. 2 6 7 Total of digits = 15 3 divides evenly into 15
Hint For Next Step
To find multiples of 3, add the digits of a number; see if you can divide this number evenly by 3; then the number is a multiple of 3.
2 6 7
Total of digits = 15
3 divides evenly into 15
267 is a multiple of 3

78. 2 – Leave 2; cross out multiples of 21 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99
100

79. 3– Leave 3; cross out multiples of 31 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99
100

80. Hint For the Next Step
To find the multiples of 5 look for numbers that end with the digit 0 and 5.
385 is a multiple of 5
& 890 is a multiple of 5
because the last digit
ends with 0 or 5.

81. 4– Leave 5; cross out multiples of 51 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99
100

82. 5– Leave 7; cross out multiples of 71 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99
100

83. 6–Leave 11; cross out multiples of 112 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99
100

84. All the numbers left are prime1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99
100

85. The Prime Numbers from 1 to 100 are as follows:
2,3,5,7,11,13,17,19,
23,31,37,41,43,47,
53,59,61,67,71,73,
79,83,89,97

86. HECTIC Division

87. Dividing Difficult Large Numbers
31) 1719
31 will not go into 1
31 will not go into 17
31 will go into 171

88. Dividing Difficult Large Numbers
31) 1719
To figure what your
first number will be
cover the 1 in 31 &
the 1 in 171.

89. Dividing Difficult Large Numbers
31) 1719
Now ask how many
3’s will go into 17.

90. Dividing Difficult Large Numbers5
31) 1719
Be sure to put that
number directly above
the 1 not the 7.

91. Dividing Difficult Large Numbers5
31) 1719
Now multiply the 5
x 31 and place it
under the 171.

92. Dividing Difficult Large Numbers5
31) 1719
155 31 x5 16 9
155

93. Dividing Difficult Large Numbers5
31) 1719
155 16 9
Now cover
up the 1 in 31
& the 9 in 169

94. Dividing Difficult Large Numbers5 6
31) 1719
155 16 9
Now multiply
31 x 6.

95. Dividing Difficult Large Numbers5 6
31) 1719
155 31 x6 16 9
186
186

96. Dividing Difficult Large Numbers5 5
31) 1719
155 16 9
Subtract &
your answer
is 55R14
155 14

97. Can you identify the fractions?
Fraction Finder
Can you identify the fractions?

98. What fraction of this shape is yellow?

99. What fraction of this shape is yellow?1 4

100. What fraction of this shape is yellow?

101. What fraction of this shape is yellow?4 9

102. What fraction of this shape is yellow?

103. What fraction of this shape is yellow?1 2

104. What fraction of this shape is yellow?

105. What fraction of this shape is yellow?3 6 or 1 2

106. What fraction of this shape is green?

107. What fraction of this shape is green?2 4 or 1 2

108. What fraction of this shape is blue?

109. What fraction of this shape is blue?1 6

110. What fraction of this shape is pink?

111. What fraction of this shape is pink?6 12 or 1 2

112. What fraction of this shape is purple?

113. What fraction of this shape is purple?1 6

114. What fraction of this shape is green?

115. What fraction of this shape is green?4 or
1 whole

116. What fraction of this shape is RED?

117. What fraction of this shape is RED?1 2

118. What fraction of this shape is red?

119. What fraction of this shape is red?2 12

120. LET’S CHECK Fractions
HOW THEY LOOK LIKE!!!

121. 3 4 Parts of a Fraction = the number of parts
= the total number of parts that equal a whole

122. Parts of a Fraction 3
= numerator 4
= denominator

123. Which number is circled?3 4
= denominator

124. Which number is circled?3
= numerator 4

125. ¾ looks like
1/4
1/4 3 4
1/4

126. ¾ looks like
1/4 3
1/4 4
1/4

127. ¾ looks like
1/4
1/4 3 4
1/4

128. What fraction of the balls are red?1 4

129. What fraction of the balls are blue?3 4

130. What fraction of the balls are green?1 6

131. What fraction of the balls are purple?4 6

132. What fraction of the rectangle is purple?4 6

133. What fraction of the rectangle is purple?2 6

134. What fraction of the pie is purple?4 4

135. What fraction of the pie is purple?3 4

136. What fraction of the musical instruments have strings?2 5

137. What fraction of the fish have stripes?3 5

138. What fraction of the pins are knocked down?3 10

139. Let’s go the other way round

140. How many halves are in a whole?2
1/2 1/2

141. How many quarters are in a whole?
1/4 1/4 4

142. How many eighths are in a whole?
1/8 1/8
1/ /8 8
1/ /8
1/8 1/8

143. How many eighths are in a quarter?
1/8 2
1/4

144. How many eighths are in a half?
1/8 1/8
1/ /8 4
1/2

145. How many quarters are in a half?
1/4 2
1/2
1/4

146. How many thirds are in a whole?
1/3
1/3 3
1/3

147. How many sixths are in a whole?
1/6
1/6 6
1/6
1/6
1/6
1/6

148. How many sixths are in a third?
1/6 2
1/6
1/3

149. How many sixths are in a half?
1/6 3
1/6
1/2
1/6

150. How many fifths are in a whole?
1/5
1/5 5
1/5
1/5
1/5

151. How many tenths are in a whole?
1/10
1/10
1/10
1/10 10
1/10
1/10
1/10
1/10
1/10
1/10

152. How many tenths are in a fifth?
1/10
1/10 2
1/5

153. How many tenths are in a half?
1/10
1/10 5
1/10
1/2
1/10
1/10

154. You Be the Designer

155. 1 2 = 2 4 Equivalent Fractions
Name the same amount but have different numerators and denominators. 1 2 1 1 = 4 2 4 2 1 4

156. 1 2 = 2 4 Equivalent Fractions
Are sometimes called equal fractions: two or more fractions that name the same number. 1 2 1 1 = 4 2 4 2 1 4

157. Equivalent Fraction Models1 2 3 = = 2 4 6

158. Equivalent Fraction Models1 4 = 5 = 2 8 10

159. Equivalent Fraction Models1 4 = 2 8

160. Equivalent Fraction Models3 6 = 4 8

161. Equivalent Fraction Models2 4 = 3 6

162. What are the missing numbers?1 2 3 = = 2 4 6

163. What are the missing numbers?1 4 = 5 = 2 8 10

164. What are the missing numbers?1 4 = 2 8

165. What are the missing numbers?3 6 = 4 8

166. What are the missing numbers?2 4 = 3 6

167. To Find Equivalent Fractions
Multiply the numerator and the denominator by the same number. 1 3 3 x = 3 3 9

168. To Find Equivalent Fractions
Divide the numerator and the denominator by the same number. 4 4 1 ÷ = 12 4 3

169. Fractions -----LET’S Simplifying Fractions

170. Factor A number that divides evenly into another.
Factors of 24 are 1,2, 3, 4, 6, 8, 12 and 24.

171. What are the factors of 9?
Factors of 9 are 1, 3 and 9.

172. What are the factors of 10?
Factors of 10 are 1, 5 and 10.

173. What are the factors of 7?
Factors of 7 are 1 and 7.

174. What are the factors of 56?
Factors of 56 are 1, 2, 4, 7, 8, 14, 28, and 56.

175. Common Factor
When two numbers have the same factor it is called a common factor.
A common factor of 12 and 6 is 3.

176. Name a Common Factor of 9 and 27?
1, 3, 9

177. Name a Common Factor of 4 and 8?
1, 2, 4

178. Name a Common Factor of 4 and 8?
1, 2, 4

179. Name a Common Factor of 15 and 30?
1, 3, 5, 15

180. Name a Common Factor of 12 and 48?
1, 2, 3, 4, 6, 12

181. Name a Common Factor of 9 and 21?
1, 3, 9,

182. Name a Common Factor of 10 and 25?
1, 5, 10

183. Name a Common Factor of 3 and 4?1

184. Simplest Form
When the only common factor of the numerator and denominator is 1, the fraction is in simplest form. 3 1 3 ÷ = 4 1 4

185. Greatest Common Factor
The greatest common factor is the largest factor between two numbers.
12 = 1, 2, 3, 4, 6, 12
18 = 1, 2, 3, 6, 9, 18

186. What is the Greatest Common Factor?
8 = 1, 2, 4, 8
12 = 1, 2, 3, 4, 6, 12

187. What is the Greatest Common Factor?
8 = 1, 2, 4, 8
14 = 1, 2, 7,14

188. What is the Greatest Common Factor?
6 = 1, 2, 3, 6
18 = 1, 2, 3, 6, 9, 15

189. What is the Greatest Common Factor?
6 = 1, 2, 3, 6
12 = 1, 2, 3, 4, 6, 12

190. What is the Greatest Common Factor?
8 = 1, 2, 4, 8
16 = 1, 2, 4, 8, 16

191. What is the Greatest Common Factor?
8 = 1, 2, 4, 8
10 = 1, 2, 5, 10

192. What is the Greatest Common Factor?
3 = 1, 3
6 = 1, 2, 3, 6

193. What is the Greatest Common Factor?
4 = 1, 2, 4
6 = 1, 2, 3, 6

194. What is the Greatest Common Factor?
7 = 1, 7,
21 = 1, 3, 7, 21

195. What is the Greatest Common Factor?
15 = 1, 3, 5, 15
24 = 1, 2, 3, 8, 12, 24

196. How to Find the Simplest Form of a Fraction
Find the greatest common factor of the numerator and the denominator and divide both the numerator and the denominator by that number. 12 6 2 ÷ = 18 6 3

197. Simplify or Reduce This Fraction12 6 2 ÷ = 18 6 3

198. Simplify or Reduce This Fraction9 3 3 ÷ = 21 3 7

199. Simplify or Reduce This Fraction12 4 3 ÷ = 20 4 5

200. Simplify or Reduce This Fraction10 5 2 ÷ = 15 5 3

201. Simplify or Reduce This Fraction10 2 5 ÷ = 16 2 8

202. Simplify or Reduce This Fraction12 4 3 ÷ = 16 4 4

203. Simplify or Reduce This Fraction3 3 1 ÷ = 12 3 4

204. Simplify or Reduce This Fraction2 2 1 ÷ = 8 2 4

205. Simplify or Reduce This Fraction2 2 1 ÷ = 4 2 2

206. Simplify or Reduce This Fraction6 3 2 ÷ = 9 3 3

207. Simplify or Reduce This Fraction6 2 3 ÷ = 8 2 4

208. Fractions VII Adding Like Denominators

209. 3 4 Parts of a Fraction = the number of parts
= the total number of parts that equal a whole

210. Parts of a Fraction 3
= numerator 4
= denominator

211. Adding Like Denominators
Only add the numerators
1/4
1/4 3 1 4 + = 4 4 4
1/4
1/4

212. Simplify Your Answer 4 1 = 4

213. Add these fractions
1/5
1/5 3 1 4 + =
1/5 5 5 5
1/5

214. Add these fractions
1/4
1/4 2 1 3 + = 4 4 4
1/4

215. Add these fractions 1 1 1 6 6 6 3 2 5 + = 6 6 6 1 1 6 6

216. Add these fractions 1 1 1 6 6 6 2 2 4 + = 6 6 6 1 6

217. Simplify Your Answer 4 2 2 ÷ = 6 2 3

218. Add these fractions 5 3 8 + = 12 12 12

219. Simplify Your Answer 8 4 2 ÷ = 12 4 3

220. Add these fractions 1 3 4 + = 10 10 10

221. Simplify Your Answer 4 2 2 ÷ = 10 2 5

222. Add these fractions 4 3 7 + = 4 4 9 9 9

223. Add these fractions 3 1 4 + = 5 5 8 8 8

224. Simplify Your Answer 4 4 1 5 ÷ 5 = 8 4 2

225. Add these fractions 2 1 3 + 4 3 = 7 9 9 9

226. Simplify Your Answer 3 3 1 7 ÷ 7 = 9 3 3

227. Fractions----- Adding Unlike Denominators

228. Some multiples of 3 & 6 6, 12, 18, 24, 30, 36, 42 Common Multiple
A number that is a multiple of two or more numbers.
Some multiples of 3 & 6
6, 12, 18, 24, 30, 36, 42

229. Least Common Multiple
The smallest common multiple of a set of two or more numbers.
5 = 5, 10, 15, 20, 25, 30
6 = 6, 12, 18, 24, 30, 36

230. Shortcut for Finding the Least Common Denominator or Least Common Multiple
Check to see if the smaller denominator
divides evenly into the larger denominator.
If it does, use the larger denominator for
your LCD or LCM. 1
3 will divide evenly into 9,
so 9 is your LCD or LCM. 3 1 + 9

231. To Add or Subtract Fractions With Unlike Denominators
Find the multiples of each denominator. 1 5
= 5, 10, 15, 20, 25, 30 1 + 10
= 10, 20, 30, 40, 50

232. To Add or Subtract Fractions With Unlike Denominators
Compare the lists of multiples. Circle the common multiples between the two lists. 1
5 = 5, 10, 15, 20, 25, 30 1 +
10 = 10, 20, 30, 40, 50

233. To Add or Subtract Fractions With Unlike Denominators
Use the lowest common multiple as the denominator. 1
5 = 5, 10, 15 ,20 ,25 ,30 1 +
10 = 10, 20, 30, 40, 50

234. To Add or Subtract Fractions With Unlike Denominators
This number is also called the least common denominator. 1
5 = 5, 10, 15 ,20 ,25 ,30 1 +
10 = 10, 20, 30, 40, 50

235. To Add or Subtract Fractions With Unlike Denominators
Rewrite the fractions using the least common denominator or least common multiple. 1 5 10 1 + 10 10

236. To Add or Subtract Fractions With Unlike Denominators
Find the equivalent fractions for 1/5 & 1/10 with 10 as the denominator.
You know that 1/10
is equal to 1/10 so
Put a 1 over the
Bottom 10. 1 5 10 1 1 + 10 10

237. To Add or Subtract Fractions With Unlike Denominators
Find the equivalent fractions for 1/5 & 1/10 with 10 as the denominator.
To find the top
number, ask yourself
what do you multiply
the 5 by to get 10. 1 5 10 1 1 + 10 10

238. To Add or Subtract Fractions With Unlike Denominators
Find the equivalent fractions for 1/5 & 1/10 with 10 as the denominator.
That’s right 2. Since
you are looking for
the equivalent fraction
you know the top
number must also be
multiplied by 2. 1
x 2 = 5 10
x 2 = 1 1 + 10 10

239. To Add or Subtract Fractions With Unlike Denominators
Find the equivalent fractions for 1/5 & 1/10 with 10 as the denominator. 1 2
x 2 =
To find the top number
just multiply 2 x 1 to
get your equivalent
fraction. 5 10
x 2 = 1 1 + 10 10

240. To Add or Subtract Fractions With Unlike Denominators
Now just add the numerators. 1 2
x 2 = 5 10
x 2 =
Remember when
adding fractions you never add the denominators. 1 1 + 10 10 3 10

241. 1 2 8 1 + 8 8 Add these Fractions Use the short cut to find the
Least Common
Denominator
(LCD). 1 2 8 1 + 8 8

242. 1 2 8 1 + 8 8 Add these Fractions x 4 = x 1 = Now find the equivalent
fractions for
1/2 & 1/8. 1 2 8
x 4 = 1 + 8
x 1 = 8
Ask what do you multiply 2 by to get 8
and what do you multiply 8 by to get 8.

243. 1 2 8 1 + 8 8 Add these Fractions x 4 = x 4 = x 1 = x 1 =
Since you are
writing equivalent
fractions, now
multiply the top
numbers by the
same number you
did in the
bottom. 1
x 4 = 2 8
x 4 = 1
x 1 = + 8
x 1 = 8

244. 1 4 2 8 1 1 + 8 8 Add these Fractions x 4 = x 4 = x 1 = x 1 =
Now multiply
across.
x 4 = 2 8
x 4 = 1 1
x 1 = + 8
x 1 = 8

245. 1 4 2 8 1 1 + 8 8 5 8 Add these Fractions x 4 = x 4 = x 1 = x 1 =
Add your
new
numerators.
x 4 = 2 8
x 4 = 1 1
x 1 = + 8
x 1 = 8 5 8

246. 2 5 15 1 + 3 15 Add these Fractions Find the common Multiples for
5 and 3. Write
This number
As your new
denominator. 2 5 15 1 + 3 15

247. 2 5 15 1 + 3 15 Add these Fractions x 3 = x 5 = Ask yourself what you
multiply the
bottom number
by to get 15. 2 5 15
x 3 = 1 + 3
x 5 = 15

248. 2 5 15 1 + 3 15 Add these Fractions x 3 = x 3 = x 5 = x 5 =
Multiply the
top number
by the same
number you
did in the
bottom. 2
x 3 = 5 15
x 3 = 1
x 5 = + 3
x 5 = 15

249. 2 6 5 15 1 5 + 3 15 Add these Fractions x 3 = x 3 = x 5 = x 5 =
Multiply
across. 2 6
x 3 = 5 15
x 3 = 1 5
x 5 = + 3
x 5 = 15

250. 2 6 5 15 1 5 + 3 15 11 15 Add these Fractions x 3 = x 3 = x 5 = x 5 =
Now add
your new
numerators. 2 6
x 3 = 5 15
x 3 = 1 5
x 5 = + 3
x 5 = 15 11 15

251. Add these Fractions 1 2
x 2 = 6 12
x 2 = 1 3
x 3 = + 4
x 3 = 12 5 12

252. Add these Fractions 5 20
x 4 = 6 24
x 4 = 1 3
x 3 = + 8
x 3 = 24 23 24

253. Add these Fractions 2 6
x 3 = 3 9
x 3 = 1 1
x 1 = + 9
x 1 = 9 7 9

254. 4 12 5 15 2 10 + 3 15 22 15 Add these Fractions x 3 = x 3 = x 5 =

255. Simplify Your Answer 7 1 15 22
15) 22 15 15 7

256. Roman Numerals

257. Let’s learn the Roman Numerals: I = 1
V = 5
X = 10
L = 50
C = 100
D = 500
M = 1000

258. Click on the number that matches the Roman Numeral.

259. LXIII
A. 53
B. 63
C. 113

260. OOPS! Try again!

261. You are correct!
LXIII = = 63
Remember:
L=50; X=10; III=3

262. 2.DCXXIV
A. 624
B. 1624
C. 5524

263. OOPS! Try again!

264. You are correct!
DCXXIV= =
624

265. 3. CCL
A. 150
B. 250
C. 550

266. OOPS! Try again!

267. You are correct!
CCL = =250

268. THANK YOU