plz tell all the formulas and important things and definition of ch 7 class 7
Answers
Answer:
Step-by-step explanation:
Addition is commutative
a
+
b
=
b
+
a
Addition is associative
(
a
+
b
)
+
c
=
a
+
(
b
+
c
)
Product of even number of negative integers is positive
−
2
×
−
2
×
−
2
×
−
2
=
16
Product of odd number of negative integers is negative
−
2
×
−
2
×
−
2
=
−
8
Division of positive integer by a negative integer gives negative quotient
6
−
3
=
−
2
Division of a negative integer by another negative integer gives positive quotient
−
6
−
3
=
2
Not defined
a
÷
0
Defined
a
÷
1
=
a
2. Fractions and Decimals Formulas
Proper fraction
a
b
where
b
>
a
Example:
2
5
,
3
7
etc.
Improper fraction
a
b
where
a
>
b
Example:
5
2
,
7
3
etc.
Mixed fraction
1
1
2
Like fractions (same denominator)
1
2
,
3
2
,
5
2
,
7
2
etc.
Product of two fractions
3
5
×
7
3
=
3
×
7
5
×
3
=
21
15
Reciprocal fractions
3
2
and
2
3
Addition of fractions
p
q
+
x
y
=
p
y
+
q
x
q
y
Example:
2
3
+
3
5
=
2
×
5
+
3
×
3
3
×
5
=
10
+
9
15
=
19
15
Subtraction of fractions
p
q
−
x
y
=
p
y
−
q
x
q
y
Example:
2
3
−
3
5
=
2
×
5
−
3
×
3
3
×
5
=
10
−
9
15
=
1
15
Multiplication of fractions
a
b
×
c
d
=
a
×
c
b
×
d
=
a
c
b
d
Division of fractions
a
b
÷
c
d
=
a
×
d
b
×
c
=
a
d
b
c
3. The Triangle and its Properties Formulas
Six elements of triangle Three sides and three angles
Angle sum property of triangle Sum of three angles:
∠
A
+
∠
B
+
∠
C
=
180
∘
Right angled triangle Adjacent Side
Opposite Side
Hypotenuse
Pythagoras Theorem
(
H
)
2
=
(
A
S
)
2
+
(
O
S
)
2
H
=
Hypotenuse
A
S
=
Adjacent Side
O
S
=
Opposite Side
Equilateral triangles All sides are equal
Isosceles triangle Two sides are equal
4. Congruence of Triangles Formulas
Congruent Triangles Their corresponding parts are equal
SSS Congruence of two triangles Three corresponding sides are equal
SAS Congruence of two triangles Two corresponding sides and an angle are equal
ASA Congruence of two triangles Two corresponding angles and a side are equal
5. Comparing Quantities Formulas
Fraction can be written as Ratio
200
150
can be written as
200
:
150
6. Perimeter and Area
Perimeter of a Square
4
×
S
i
d
e
Perimeter of a Rectangle
2
×
(
Length
+
Breadth
)
Area of a Square
Side
×
Side
Area of a Rectangle
Length
×
Breadth
Area of a Parallelogram
Base
×
Height
Area of a Triangle
1
2
×
Base
×
Height
Area of a Circle
π
r
2
r
=
Radius of the circle
7. Algebraic Expressions Formulas
(
x
+
y
)
2
=
x
2
+
y
2
+
2
x
y
(
x
−
y
)
2
=
x
2
+
y
2
−
2
x
y
(
x
+
y
)
(
x
−
y
)
=
x
2
−
y
2
(
x
+
y
)
(
x
+
z
)
=
x
2
+
x
(
y
+
z
)
+
y
z
(
x
+
y
)
(
x
−
z
)
=
x
2
+
x
(
y
−
z
)
−
y
z
x
2
+
y
2
=
(
x
+
y
)
2
−
2
x
y
(
x
+
y
)
3
=
x
3
+
y
3
+
3
x
y
(
x
+
y
)
(
x
−
y
)
3
=
x
3
−
y
3
−
3
x
y
(
x
−
y
)
(
x
+
y
+
z
)
2
=
x
2
+
y
2
+
z
2
+
2
x
y
+
2
y
z
+
2
z
x
(
x
−
y
−
z
)
2
=
x
2
+
y
2
+
z
2
−
2
x
y
+
2
y
z
−
2
z
x
8. Exponents and Powers Formulas
a
m
×
a
n
=
a
m
+
n
a
m
÷
a
n
=
a
m
−
n
(
a
m
)
n
=
a
m
n
a
m
×
b
m
=
(
a
b
)
m
a
m
÷
b
m
=
(
a
b
)
m
a
0
=
1
(
−
1
)
Even Number
=
1
(
−
1
)
Odd Number
=
−
1