WELCOME : WELCOME
Basic Arithmetic : Basic Arithmetic Arithmetic expression involves one or combination of following mathematical operations - Addition, Subtraction, Multiplication and Division.
BODMAS Rule to solve a mathematical expression:
Slide 3 : The Hierarchy of operations followed is :
(i) B – Bracket ( to be solved)
(ii) O - Of
(iii) D – Division
(iv) M – Multiplication
(v) A – Addition
(vi) S – Subtraction
The sequence of solving is from left to right.
Slide 4 : When a expression involves more than one bracket the sequence of solving is from innermost to the outer most bracket.
A viniculum is shown as bar(dash) over the part of expression desired to be bracketed.
A mathematical expression may involve use of a percent (%) sign. It means “per one hundred”.
Percentage can be converted into a fraction and vice versa.
Dividing 100% into 10 equal parts : Dividing 100% into 10 equal parts 10% = 1 = 0.1
10
20% = 1 = 0.2
5
30% = 3 = 0.3
10
40% = 2 = 0.4
5
50% = 1 = 0.5
2 6. 60% = 3 = 0.6
5
7. 70% = 7 = 0.7
10
8. 80% = 4 = 0.8
5
9. 90% = 9 = 0.9
10
10. 100% = 1.0, 5 % = 1 = 0.05
20
Dividing 100% into 6 equal parts : Dividing 100% into 6 equal parts
Non – conventional percentages : Non – conventional percentages
Multiplications commonly used in competitive examinations : Multiplications commonly used in competitive examinations 16 x 12 = 192
15 x 25 = 375
16 x 25 = 400
3 x 37 = 111
Example:
888 ÷ 37 + 1 = ?
Master the techniques of Short Cuts : Master the techniques of Short Cuts Be acquainted with the following:
The tables from 2 to 30
The Squares of the numbers from 1 to 30
The cubes of the numbers from 1 to 15
SQUARES OF NUMBERS FROM 2 TO 30 : SQUARES OF NUMBERS FROM 2 TO 30 Number Square
1 1
2 4
3 9
4 16
5 25
6 36
7 49
8 64
9 81
10 100
11 110
12 144
13 169
14 196
15 225 Number Square
16 256
17 289
18 324
19 361
20 400
21 441
22 484
23 529
24 576
25 625
26 676
27 729
28 784
29 841
30 900
CUBES OF NUMBERS FROM 1 TO 15 : CUBES OF NUMBERS FROM 1 TO 15 Number Cube
1 1
2 8
3 27
4 64
5 125
6 216
7 343 Number Cube
8 512
9 729
10 1000
11 1331
12 1728
13 2197
14 2744
15 3375
RATIO & PROPORTION : RATIO & PROPORTION The ratio of two numbers “a” and “b” means
“a divided by b”. It is normally expressed as a:b .
2. The term proportion indicates equality of two ratios. Thus, if a:b = c:d, then a, b, c, d are in proportion. It is expressed as a:b::c:d (The symbol :: indicates = sign).
Slide 13 : 3. When the term proportion is applied to only 3 numbers a, b, c, it is known as “continued proportion” (i.e) a:b :: b:c.
4. If a:b :: c:d, we have a x d = b x c.
5. If a:b :: b:c, we have a x c = b x b = b2