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VCAL NUM 021 LO6 NUMERICAL INFORMATION FOUR OPERATIONS 2012
RULE 1: When we do long addition, subtraction and multiplication, we work from right to left.
Example:
45
56
__
101
RULE 2: When we do long division we work from left to right.
_________
Example:
3) 6036.60
RULE 3: When we multiply a number by 10 we add a zero
Example:
Example
35 X 10 = 350
6.4 X 10 = 64
RULE 4: When we multiply a number by 100 we add two zeros
Example:
Example:
35 X 100 = 3,500
6.4 X 100 = 640
RULE 5: When we divide a number by 10, we move the decimal place one place to the left
Example:
Example:
35 ÷ 10 = 3.5
6.4 ÷ 10 = .64
RULE 6: When we divide a number by 100, we move the decimal two places to the left.
Example:
Example:
35 ÷100 = .35
6.4 ÷ 100 = .064
RULE 7 : When multiplying whole numbers by whole numbers the number in the answer gets
bigger
Example:
35 X 5 = 175 ( Bigger!)
RULE 8: When multiplying whole numbers by decimal numbers or fractions, the number in the
answer gets smaller.
Example:
Example:
35 X .5 = 17.5
35 X ½ = 17.5
RULE 9: When dividing whole numbers by whole numbers, the number in the answer gets
smaller.
Example:
35 ÷ 2 = 17.5
RULE 10: When dividing whole numbers by decimal numbers or fractions, the number in the
answer gets bigger
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VCAL NUM 021 LO6 NUMERICAL INFORMATION FOUR OPERATIONS 2012
Example:
35 ÷ .5 = 70
Example:
35 ÷ ½ =70. (It’s like saying: How many halves are there in 35?)
RULE 11: When we add or subtract numbers with decimal points in them, we must line the
points up one above the other in both the problem and in the answer.
Example:
35.5
+6.4
76.8
-6.5
RULE 12: When we’re dividing a number which contains a decimal point, we must put the
decimal point in the answer above the decimal point in the problem. (Well, it helps to keep us
accurate.)
3013.30
3) 6036.60
Example:
RULE 13: When we’re multiplying by a multiple of 10, we can put down a zero first and then
multiply out with the other digit.
Example:
75
X 30
-- ----2250
75
X 300
---------22500
RULE 14: COMMUTATIVE LAW
For simple addition and multiplication the order of digits is reversible:
5X9=9X5
5+9=9+5
45 X 99 = 99 X 45
45 + 99 = 99 + 45
RULE 15: FINDING PERCENTAGES OF IS THE SAME AS MULTIPLYING BY A
DECIMAL.
Example:
50 % of 20 is the same as .5 X 20
20 % of 90 is the same as .2 X 90
4 % of 90 is tha same as .04 X 90
55 % 0f 80 is the same as .55 X 80
RULE 16: Any fraction, decimal or percentage can be written as either a fraction, percentage or
decimal.
Percent
Decimal
Fraction
Example:
50 % =
.5
½
75% =
.75
¾
25% =
.25
¼
100 % =
1
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RULE 17: Fractions mean the top number divided by the bottom number
Example
½ means 1 ÷2 = .5
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VCAL NUM 021 LO6 NUMERICAL INFORMATION FOUR OPERATIONS 2012
¼ means 1÷ 4 = .25
¾ means 3÷ 4 = .75
This is true for all fractions, all the time!
ACTIVITIES
Set out all problems properly in your book rather than doing them on the sheet. If
you’re doing the problems on the sheet, it means you’re not using the right
technique or you’re using a calculator.
1. ADDITION
A. ADDITION WITH 2 DIGITS (NO CARRY OVER)
75 + 43
79 + 40
86+91
57 + 92
73 + 22
45 + 44
84 + 94
55 + 32
B. ADDITION WITH TWO DIGITS (CARRY OVER)
99 + 45
98 + 55
35 + 77
88 + 93
76 + 98
33 + 37
23+98
99+ 97
C. ADDITION WITH THREE OR MORE DIGITS
354 + 789
897+564
124 + 975
997+ 223
D. ADDITION WITH DECIMAL POINT (EG. MONEY) ( Line up Point Over
Point)
56.08 + 55. 03
46.84 + 77.22
123.05 + 76.54
9.99 + 300.12
2. SUBTRACTION
A. SUBTRACTION WITH 2 DIGITS (NO DECOMPOSITION)
56- 43
77-34
89-32
97 – 55
86-31
B. SUBTRACTION WITH TWO DIGITS (WITH DECOMPOSITION)
75- 39
87-38
62-39
82- 29
95-79
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VCAL NUM 021 LO6 NUMERICAL INFORMATION FOUR OPERATIONS 2012
C. SUBTRACTION WITH THREE OR MORE DIGITS (WITH or WITHOUT
DECOMPOSITION)
567 – 123
109- 35
989 – 235
992-337
D. SUBTRACTION WITH DECIMAL POINT (EG. MONEY)
97.09 – 22.05
455.99- 333.88
334.12- 234.06
67.09- 44.12
356.99- 12.08
3. MULTIPLICATION
A. MULTIPLYING TWO DIGITS BY ONE DIGIT
89 x 3
77x 5
23 x 7
56 x 9
25 x 8
22x9
B. MULTIPLYING TWO OR MORE DIGITS BY MULTIPLES OF TEN
34x10
3.4 x 10
56 x 10
5.6 x 10
99x 10
9.9 x 10
66 x 10
6.6 x10
289 x 10
2.89 x 10
28.9 x 10
978 x 10
9.78 x 10
97.8 x 10
126x10
1.26 x 10
12.6 x 10
675 x 10
6.75 x 10
67.5 x 10
289 x 100
2.89 x 100
28.9 x 100
978 x 100
9.78 x 100
97.8 x 100
126x100
1.26 x 100
12.6 x 100
675 x 100
6.75 x 100
67.5 x 100
C. MULTIPLYING TWO DIGITS BY TWO DIGITS (Follow Rules for setting
this out closely.)
56 X 22
57 X 43
34 X 57
87X93
53 X 23
76 X 31
94 X 93
26 X 24
D. LAW OF COMMUTABILITY
Is 5 X 9 the same as 9 X 5?
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VCAL NUM 021 LO6 NUMERICAL INFORMATION FOUR OPERATIONS 2012
Is 12 X 3 the same as 3 X 12?
Is 44 X 35 the same as 35 X 44?
E. MULTIPLYING NUMBERS WITH DECIMAL POINTS IN THEM TWO
DIGIT BY ONE DIGIT)
6.7 X 3
56.3 X 4
73.30 X 3
98.20 X 5
88.22 X 3
44.43 X 2
99.99 X 5
106.2 X 3
44 X .3
67 X .4
122 X .4
123 X .2
F. MULTIPLYING NUMBERS WITH DECIMAL POINTS IN THEM TWO
DIGIT BY TWO DIGITS)
4.4 X 5.3
6.2 X 4.5
9.2 X 2.1
1.6 X 4.3
G. PERCENTAGE OF…
50 % of 150
50 % of 25
50 % of 66
50 % of 230
20 % of 150
20 % of 25
20 % of 66
20 % of 230
30 % of 150
30 % of 25
30 % of 66
30 % of 230
4. DIVISION
A. DIVIDING TWO DIGITS BY ONE DIGIT (WITH REMAINDERS?)
23 ÷2
23÷ 3
23÷ 4
55÷ 2
55÷3
55÷4
13÷2
13÷3
95÷5
72÷3
81÷3
96÷4
B. DIVIDING TWO DIGITS OR MORE BY MULTIPLES OF TEN
34÷10
56 ÷ 10
99÷ 10
66 ÷ 10
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VCAL NUM 021 LO6 NUMERICAL INFORMATION FOUR OPERATIONS 2012
3.4 ÷ 10
5.6 ÷ 10
9.9 ÷ 10
6.6 ÷10
289 ÷ 10
2.89 ÷ 10
28.9 ÷ 10
978 ÷ 10
9.78 ÷ 10
97.8 ÷ 10
126÷10
1.26 ÷ 10
12.6 ÷ 10
675 ÷ 10
6.75 ÷ 10
67.5 ÷ 10
289 ÷ 100
2.89 ÷100
28.9 ÷ 100
978 ÷100
9.78 ÷ 100
97.8 ÷ 100
126÷100
1.26 ÷ 100
12.6 ÷ 100
675 ÷ 100
6.75 ÷ 100
67.5 ÷ 100
C. DIVIDING NUMBERS WITH DECIMAL POINTS IN THEM (Point over
point technique).
654.3 ÷ 3
12.40 ÷ 4
1.2 ÷ 4
3.5 ÷ 7
1.44 ÷4
6.87 ÷3
5.50 ÷ 2
3.66 ÷ 6
7.49 ÷7
5.25 ÷ 5
105.25 ÷5
909.09÷ 3
D. C. DIVIDING NUMBERS WITH DECIMAL POINTS IN THEM WITH
REMAINDERS. (Point over point technique).
6.7 ÷ 4
4.5÷6
7.7÷5
9.9÷6
45.3 ÷ 3
E. OTHER WAYS OF SETTING OUT DIVISION: Place the first number over
the second number and cross off zeros, then divide as usual:
1440 ÷ 30
1240 ÷ 40
6360 ÷ 60
800 ÷ 40
5150 ÷ 50
FRACTIONS
Of …
½ of 36
½ of 88
½ of 120
½ of 280
¼ of 36
¼ of 88
¼ of 120
¼ of 280
¾ of 12
¾ of 88
¾ of 120
¾ of 280
Puzzle
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VCAL NUM 021 LO6 NUMERICAL INFORMATION FOUR OPERATIONS 2012
¼ of ¾ =
¾ of ¾
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