Maths formulas for class 7

teachask Sunday, November 08, 2020

Maths formulas for class 7

Most of us gradually start disliking Math formulas and equations at some point as they seem difficult to grasp. But if you understand the logic behind them instead of mugging it, you will realize they help you solve complex problems easily and quickly!

Our team of Math experts have created a list of Class 7 Maths formulas for you with logical explanations as well as the method of how and where to use them. By using this list of important formulas in your exam preparations, you can easily understand their logic, solve complex problems faster and score higher marks in your school exams!

1. Integers Formulas

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	$- 2 \times - 2 \times - 2 \times - 2 = 16$
Product of odd number of negative integers is negative	$- 2 \times - 2 \times - 2 = - 8$
Division of positive integer by a negative integer gives negative quotient	$\begin{aligned} \frac{6}{- 3} = - 2 \end{aligned}$
Division of a negative integer by another negative integer gives positive quotient	$\begin{aligned} \frac{- 6}{- 3} = 2 \end{aligned}$
Not defined	$\begin{aligned} a \div 0 \end{aligned}$
Defined	$\begin{aligned} a \div 1 = a \end{aligned}$

2. Fractions and Decimals Formulas

Proper fraction	$\begin{aligned} \frac{a}{b} \end{aligned}$ where $\begin{aligned} b > a \end{aligned}$ Example: $\begin{aligned} \frac{2}{5}, \frac{3}{7} \end{aligned}$ etc.
Improper fraction	$\begin{aligned} \frac{a}{b} \end{aligned}$ where $\begin{aligned} a > b \end{aligned}$ Example: $\begin{aligned} \frac{5}{2}, \frac{7}{3} \end{aligned}$ etc.
Mixed fraction	$\begin{aligned} 1 \frac{1}{2} \end{aligned}$
Like fractions (same denominator)	$\begin{aligned} \frac{1}{2}, \frac{3}{2}, \frac{5}{2}, \frac{7}{2} etc. \end{aligned}$
Product of two fractions	$\begin{aligned} \frac{3}{5} \times \frac{7}{3} = \frac{3 \times 7}{5 \times 3} = \frac{21}{15} \end{aligned}$
Reciprocal fractions	$\begin{aligned} \frac{3}{2} \end{aligned}$ and $\begin{aligned} \frac{2}{3} \end{aligned}$
Addition of fractions	$\begin{aligned} \frac{p}{q} + \frac{x}{y} = \frac{p y + q x}{q y} \end{aligned}$ Example: $\begin{aligned} \frac{2}{3} & + \frac{3}{5} \\ = \frac{2 \times 5 + 3 \times 3}{3 \times 5} \\ = \frac{10 + 9}{15} \\ = \frac{19}{15} \end{aligned}$
Subtraction of fractions	$\begin{aligned} \frac{p}{q} - \frac{x}{y} = \frac{p y - q x}{q y} \end{aligned}$ Example: $\begin{aligned} \frac{2}{3} & - \frac{3}{5} \\ = \frac{2 \times 5 - 3 \times 3}{3 \times 5} \\ = \frac{10 - 9}{15} \\ = \frac{1}{15} \end{aligned}$
Multiplication of fractions	$\begin{aligned} \frac{a}{b} \times \frac{c}{d} & = \frac{a \times c}{b \times d} \\ = \frac{a c}{b d} \end{aligned}$
Division of fractions	$\begin{aligned} \frac{a}{b} \div \frac{c}{d} & = \frac{a \times d}{b \times c} \\ = \frac{a d}{b c} \end{aligned}$

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: $\begin{aligned} ∠ A + ∠ B + ∠ C = 180^{\circ} \end{aligned}$
Right angled triangle	Adjacent Side Opposite Side Hypotenuse
Pythagoras Theorem	$\begin{aligned} {(H)}^{2} = {(A S)}^{2} + {(O S)}^{2} \end{aligned}$ $H =$ 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

\begin{aligned} \frac{200}{150} \end{aligned}

can be written as

\begin{aligned} 200 : 150 \end{aligned}

6. Perimeter and Area

Perimeter of a Square	$\begin{aligned} 4 \times S i d e \end{aligned}$
Perimeter of a Rectangle	$\begin{aligned} 2 \times (Length + Breadth) \end{aligned}$
Area of a Square	$\begin{aligned} Side \times Side \end{aligned}$
Area of a Rectangle	$\begin{aligned} Length \times Breadth \end{aligned}$
Area of a Parallelogram	$\begin{aligned} Base \times Height \end{aligned}$
Area of a Triangle	$\begin{aligned} \frac{1}{2} \times Base \times Height \end{aligned}$
Area of a Circle	$\begin{aligned} π r^{2} \end{aligned}$
$r = Radius of the circle$

Important Maths Formulas | Area Formulas

Area of a Circle Formula = π r2
where
r – radius of a circle
Area of a Triangle Formula A= $\frac{1}{2} b h$
where
b – base of a triangle.
h – height of a triangle.
Area of Equilateral Triangle Formula = $\frac{\sqrt{3}}{4} s^{2}$
where
s is the length of any side of the triangle.
Area of Isosceles Triangle Formula = $\frac{1}{2} b h$

where:
a be the measure of the equal sides of an isosceles triangle.
b be the base of the isosceles triangle.
h be the altitude of the isosceles triangle.
Area of a Square Formula = a2
Area of a Rectangle Formula = L. B
where
L  is the length.
B is the Breadth.
Area of a Pentagon Formula = $\frac{5}{2} s . a$
Where,
s is the side of the pentagon.
a is the apothem length.
Area of a Hexagon Formula = $\frac{3 \sqrt{3}}{2} x^{2}$
where
where “x” denotes the sides of the hexagon.

Area of a Hexagon Formula = $\frac{3}{2} . d . t$
Where “t” is the length of each side of the hexagon and “d” is the height of the hexagon when it is made to lie on one of the bases of it.
Area of an Octagon Formula = $2 a^{2}(1+\sqrt{2})$
Consider a regular octagon with each side “a” units.
Area of Regular Polygon Formula:
By definition, all sides of a regular polygon are equal in length. If you know the length of one of the sides, the area is given by the formula:
where
s  is the length of any side
n  is the number of sides
tan  is the tangent function calculated in degrees
Area of a Parallelogram Formula = b . a
where
b is the length of any base
a is the corresponding altitude
Area of Parallelogram: The number of square units it takes to completely fill a parallelogram.
Formula: Base × Altitude
Area of a Rhombus Formula = b . a
where
b is the length of the base
a is the altitude (height).
Area of a Trapezoid Formula = The number of square units it takes to completely fill a trapezoid.
Formula: Average width × Altitude

The area of a trapezoid is given by the formula
where
b1, b2 are the lengths of each base
h is the altitude (height)
Area of a Sector Formula (or) Area of a Sector of a Circle Formula =   $\pi r^{2}\left(\frac{C}{360}\right)$
where:
C is the central angle in degrees
r is the radius of the circle of which the sector is part.
π is Pi, approximately 3.142
Sector Area – The number of square units it takes to exactly fill a sector of a circle.
Area of a Segment of a Circle Formula
Area of a Segment in Radians $A =1 / 2 \times r^{2}(\theta-\sin \theta)$
Area of a Segment in Degrees $A =\frac{1}{2} r^{2}\left(\frac{\pi}{180} \theta-\sin \theta\right)$
Area of a Segment of a Circle Formula
Area under the Curve Formula:
The area under a curve between two points is found out by doing a definite integral between the two points. To find the area under the curve y = f(x) between x = a & x = b, integrate y = f(x) between the limits of a and b. This area can be calculated using integration with given limits.

7. Algebraic Expressions Formulas

\begin{aligned} {(x + y)}^{2} = x^{2} + y^{2} + 2 x y \end{aligned}

\begin{aligned} {(x - y)}^{2} = x^{2} + y^{2} - 2 x y \end{aligned}

\begin{aligned} (x + y) (x - y) = x^{2} - y^{2} \end{aligned}

\begin{aligned} (x + y) (x + z) = x^{2} + x (y + z) + y z \end{aligned}

\begin{aligned} (x + y) (x - z) = x^{2} + x (y - z) - y z \end{aligned}

\begin{aligned} x^{2} + y^{2} = {(x + y)}^{2} - 2 x y \end{aligned}

\begin{aligned} {(x + y)}^{3} = x^{3} + y^{3} + 3 x y (x + y) \end{aligned}

\begin{aligned} {(x - y)}^{3} = x^{3} - y^{3} - 3 x y (x - y) \end{aligned}

\begin{aligned} {(x + y + z)}^{2} = x^{2} + y^{2} + z^{2} + 2 x y + 2 y z + 2 z x \end{aligned}

\begin{aligned} {(x - y - z)}^{2} = x^{2} + y^{2} + z^{2} - 2 x y + 2 y z - 2 z x \end{aligned}

8. Exponents and Powers Formulas

\begin{aligned} a^{m} \times a^{n} = a^{m + n} \end{aligned}

\begin{aligned} a^{m} \div a^{n} = a^{m - n} \end{aligned}

\begin{aligned} {(a^{m})}^{n} = a^{m n} \end{aligned}

\begin{aligned} a^{m} \times b^{m} = {(a b)}^{m} \end{aligned}

\begin{aligned} a^{m} \div b^{m} = {(\frac{a}{b})}^{m} \end{aligned}

\begin{aligned} a^{0} = 1 \end{aligned}

\begin{aligned} {(- 1)}^{Even Number} = 1 \end{aligned}

\begin{aligned} {(- 1)}^{Odd Number} = - 1 \end{aligned}

1 Comments

Unknown said…

Piyush Sagar

November 10, 2020 at 12:33 PM

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Maths formulas for class 7