Class 7 Maths Formula Sheets

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!

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Important Maths Formulas for Class 7

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 \(\begin{align}\frac{6}{{ - 3}} =  - 2\end{align}\)
Division of a negative integer by another negative integer gives positive quotient \(\begin{align}\frac{-6}{{ - 3}} =   2\end{align}\)
Not defined \(\begin{align}a \div 0\end{align}\)
Defined \(\begin{align}  a \div 1 = a  \end{align}\)

2. Fractions and Decimals Formulas

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

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:
\(\begin{align}  \angle {\rm{A}} + \angle {\rm{B}} + \angle {\rm{C}} = 180^\circ  \end{align}\)
Right angled triangle Adjacent Side
Opposite Side
Pythagoras Theorem \(\begin{align}  \left( {\rm{H}} \right)^2  = \left( {{\rm{AS}}} \right)^2  + \left( {{\rm{OS}}} \right)^2    \end{align}\)
\(H = \) Hypotenuse
\(AS = \) Adjacent Side
\(OS = \) 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 \(\begin{align} \frac{200}{150}  \end{align}\) can be written as \(\begin{align} 200:150  \end{align}\)

6. Perimeter and Area

Perimeter of a Square  \(\begin{align}  4 \times {\rm{Side}}  \end{align}\)
Perimeter of a Rectangle  \(\begin{align}   2 \times ( \text{Length} + \text{Breadth})  \end{align}\)
Area of a Square  \(\begin{align}   \text{Side} \times \text{Side}  \end{align}\)
Area of a Rectangle  \(\begin{align}    \text{Length} \times \text{Breadth}  \end{align}\)
Area of a Parallelogram  \(\begin{align}    \text{Base} \times \text{Height}  \end{align}\)
Area of a Triangle  \(\begin{align}     \frac{1}{2} \times \text{Base} \times \text{Height}  \end{align}\)
Area of a Circle \(\begin{align}      \pi r^2    \end{align}\)
\(r = \text{Radius of the circle}\)

7. Algebraic Expressions Formulas

\(\begin{align}  \left( {x + y} \right)^2  = x^2  + y^2  + 2xy   \end{align}\)
\(\begin{align}  \left( {x - y} \right)^2  = x^2  + y^2  - 2xy   \end{align}\)
\(\begin{align}  \left( {x + y} \right)\left( {x - y} \right) = x^2  - y^2    \end{align}\)
\(\begin{align}  (x + y)(x + z) = x^2  + x\,(y + z) + yz    \end{align}\)
\(\begin{align}  (x + y)(x - z) = x^2  + x\,(y - z) - yz    \end{align}\)
\(\begin{align}  x^2  + y^2  = \left( {x + y} \right)^2  - 2xy    \end{align}\)
\(\begin{align}  \left( {x + y} \right)^3  = x^3  + y^3  + 3xy\left( {x + y} \right)    \end{align}\)
\(\begin{align}  \left( {x - y} \right)^3  = x^3  - y^3  - 3xy\left( {x - y} \right)    \end{align}\)
\(\begin{align}  \left( {x + y + z} \right)^2  = x^2  + y^2  + z^2  + 2xy + 2yz + 2zx    \end{align}\)
\(\begin{align}  \left( {x - y - z} \right)^2  = x^2  + y^2  + z^2  - 2xy + 2yz - 2zx    \end{align}\)

8. Exponents and Powers Formulas

\(\begin{align} a^m  \times a^n  = a^{m + n}    \end{align}\)
\(\begin{align} a^m  \div a^n  = a^{m - n}    \end{align}\)
\(\begin{align} \left( {a^m } \right)^n  = a^{mn}    \end{align}\)
\(\begin{align} a^m  \times b^m  = \left( {ab} \right)^m    \end{align}\)
\(\begin{align} a^m  \div b^m  = \left( {\frac{a}{b}} \right)^m    \end{align}\)
\(\begin{align} a^0  = 1  \end{align}\)
\(\begin{align} \left( - 1 \right)^\text{Even Number}  = 1  \end{align}\)
\(\begin{align} \left( - 1 \right)^\text{Odd Number}  = -1  \end{align}\)


Our FREE CBSE Class 7 chapter-wise formulas PDF covers the following chapters:

  • Chapter-1   Integers
  • Chapter-2   Fractions and Decimals
  • Chapter-3   Data Handling
  • Chapter-4   Simple Equations
  • Chapter-5   Lines and Angles
  • Chapter-6   Triangle and Its Properties
  • Chapter-7   Congruence of Triangles
  • Chapter-8   Comparing Quantities
  • Chapter-9   Rational Numbers
  • Chapter-10 Practical Geometry
  • Chapter-11 Perimeter and Area
  • Chapter-12 Algebraic Expressions
  • Chapter-13 Exponents and Powers
  • Chapter-14 Symmetry
  • Chapter-15 Visualizing Solid Shapes
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CBSE Class 7 Formulas Sheet
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