Important Class 7 Maths Formulas

- June 03, 2020

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 $\begin{aligned} a > b \end{aligned}$ 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	$\begin{aligned} \frac{a}{b} \div \frac{c}{d} = \frac{a d}{b c} \end{aligned}$

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	$\begin{aligned} π r^{2} \end{aligned}$
$r = Radius of the circle$

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}

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Student E Knowledge

Important Class 7 Maths Formulas

1. Integers Formulas

2. Fractions and Decimals Formulas

3. The Triangle and its Properties Formulas

4. Congruence of Triangles Formulas

5. Comparing Quantities Formulas

6. Perimeter and Area

7. Algebraic Expressions Formulas

8. Exponents and Powers Formulas

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