MATHEMATICS SIMPLIFICATION: BASIC CONCEPTS & RULES
1. SIGN RULE:
Addition/Subtraction:
If we do addition/subtraction in an expression follow below resultant’s action and sign rule
Sign
Resultant’s Action
Resultant’s sign
+
+
Add
Biggest number sign
-
-
+
-
Subtract
-
+
Examples:
2
+
4
=
6
(-2)
+
(-4)
=
-6
2
+
(-4)
=
-2
(-2)
+
4
=
2
2
-
4
=
-2
(-2)
-
(-4)
=
-2+4 = 2
2
-
(-4)
=
2+4 = 6
(-2)
-
4
=
-6
Multiplication/Division:
If we do Multiplication/Division in an expression follow below resultant’s sign rule
Sign
Resultant’s sign
+
+
+
-
-
+
-
-
-
+
Examples:
8
X
4
=
32
(-8)
X
(-4)
=
32
8
X
(-4)
=
-32
(-8)
X
4
=
-32
8
÷
4
=
2
(-8)
÷
(-4)
=
2
8
÷
(-4)
=
-2
(-8)
÷
4
=
-2
2. TRANSPOSE / SWAP RULE:
If we move an operands to right to left/left to right of equation(=) follow the below rule
+
-
-
+
X
÷
÷
X
√x(root)
Xn (power)
Xn (power)
√x(root)
Examples:
a + 2 = 4
a = 4 - 2
a = 2
a - 2 = 4
a = 4 + 2
a = 6
2a = 4
a = 4 / 2
a = 2
a/2 = 4
a = 4 x 2
a = 8
√x = 4
X = 42
X = 16
X2 = 4
X = √4
X = 2
3. BODMAS RULE:
According to BODMAS rule, in a given mathematical expression that contains combination of signs: brackets ((), {}, [], −), multiplication, of, addition, subtraction, division, we must first solve or simplify the brackets followed by of (powers and roots etc.), of, then division, multiplication, addition and subtraction .
B – Bracket
( ), { }, [ ]
O – Order or power
√x(root), Xn (power)
D – Division
÷
M – Multiplication
X
A – Addition
+
S – Subtraction
-
Examples:
1) 5 × ( 7 – 3) = 5 × 4 = 20
2) 24 ÷ ( 8 – 5 ) = 24 ÷ 3 = 8
3) 7 + 22 = 7 + 4 = 11
4) 10 – 32 = 10 – 9 = 1
5) 9 + 12 ÷ 3 = 9 + 4 = 13
6) 10 – 6 ÷ 2 = 10 – 3 = 7
7) 10 + 2× 3 = 10 + 6 = 16
8) 9 – 4 × 2 = 9 – 8 = 1
9) 4 × 3 + 5 = 12 + 5 = 17
10) 2 × 7 + 8 = 14 + 8 = 22
11) 10 ÷ 2 – 2 = 5 – 2 = 3
12) 9 ÷ 3 – 1 = 3 – 1 = 2
4. SIMPLIFICATIONS TIPS:
1. Understand the concepts of the topic.
2. Memorize the formulas.
3. Read the question 2-3 times to understand given and what to find.
4. Keep the required value in left side of an equation and move others on the right side of an equation to solve the given questions.
5. Understand and practice BODMAS.
6. Memorize the multiplication table.
YouTube link – Shortcut to remember tables in hand: https://youtu.be/WakN4OAeEOM
7. In a fraction identify a common factor of the denominator and numerator. The denominator and numerator are both divided by the common factor. The division operation is repeated until there are no more factors.
8. You need to memorize squares and cubes of numbers.
9. Learn strategies and tricks to easily solve topics such as square roots, cubes, etc.
YouTube Video link: