## 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$a+b=b+a$ Addition is associative (a+b)+c=a+(b+c)$\left(a+b\right)+c=a+\left(b+c\right)$ Product of even number of negative integers is positive −2×−2×−2×−2=16$-2×-2×-2×-2=16$ Product of odd number of negative integers is negative −2×−2×−2=−8$-2×-2×-2=-8$ Division of positive integer by a negative integer gives negative quotient 6−3=−2$\begin{array}{r}\frac{6}{-3}=-2\end{array}$ Division of a negative integer by another negative integer gives positive quotient −6−3=2$\begin{array}{r}\frac{-6}{-3}=2\end{array}$ Not defined a÷0$\begin{array}{r}a÷0\end{array}$ Defined a÷1=a$\begin{array}{r}a÷1=a\end{array}$

### 2. Fractions and Decimals Formulas

 Proper fraction ab$\begin{array}{r}\frac{a}{b}\end{array}$   where b>a$\begin{array}{r}b>a\end{array}$Example: 25,37$\frac{2}{5},\phantom{\rule{thickmathspace}{0ex}}\frac{3}{7}$ etc. Improper fraction ab$\begin{array}{r}\frac{a}{b}\end{array}$   where a>b$\begin{array}{r}a>b\end{array}$Example: 52,73$\frac{5}{2},\phantom{\rule{thickmathspace}{0ex}}\frac{7}{3}$ etc. Mixed fraction 112$\begin{array}{r}1\frac{1}{2}\end{array}$ Like fractions (same denominator) 12,32,52,72etc.$\frac{1}{2},\phantom{\rule{thickmathspace}{0ex}}\frac{3}{2},\phantom{\rule{thickmathspace}{0ex}}\frac{5}{2},\phantom{\rule{thickmathspace}{0ex}}\frac{7}{2}\phantom{\rule{thickmathspace}{0ex}}\phantom{\rule{thickmathspace}{0ex}}\text{etc.}$ Product of two fractions 35×73=3×75×3=2115$\begin{array}{r}\frac{3}{5}×\frac{7}{3}=\frac{3×7}{5×3}=\frac{21}{15}\end{array}$ Reciprocal fractions 32$\begin{array}{r}\frac{3}{2}\end{array}$  and  23$\begin{array}{r}\frac{2}{3}\end{array}$ Addition of fractions pq+xy=py+qxqy$\begin{array}{r}\frac{p}{q}+\frac{x}{y}=\frac{py+qx}{qy}\end{array}$Example:23+35=2×5+3×33×5=10+915=1915$\begin{array}{rl}\frac{2}{3}& +\frac{3}{5}\\ & =\frac{2×5+3×3}{3×5}\\ & =\frac{10+9}{15}\\ & =\frac{19}{15}\end{array}$ Subtraction of fractions pq−xy=py−qxqy$\begin{array}{r}\frac{p}{q}-\frac{x}{y}=\frac{py-qx}{qy}\end{array}$Example:23−35=2×5−3×33×5=10−915=115$\begin{array}{rl}\frac{2}{3}& -\frac{3}{5}\\ & =\frac{2×5-3×3}{3×5}\\ & =\frac{10-9}{15}\\ & =\frac{1}{15}\end{array}$ Multiplication of fractions ab×cd=a×cb×d=acbd$\begin{array}{rl}\frac{a}{b}×\frac{c}{d}& =\frac{a×c}{b×d}\\ & =\frac{ac}{bd}\end{array}$ Division of fractions ab÷cd=a×db×c=adbc$\begin{array}{rl}\frac{a}{b}÷\frac{c}{d}& =\frac{a×d}{b×c}\\ & =\frac{ad}{bc}\end{array}$

### 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∘$\begin{array}{r}\mathrm{\angle }\mathrm{A}+\mathrm{\angle }\mathrm{B}+\mathrm{\angle }\mathrm{C}={180}^{\circ }\end{array}$ Right angled triangle Adjacent SideOpposite SideHypotenuse Pythagoras Theorem (H)2=(AS)2+(OS)2$\begin{array}{r}{\left(\mathrm{H}\right)}^{2}={\left(\mathrm{A}\mathrm{S}\right)}^{2}+{\left(\mathrm{O}\mathrm{S}\right)}^{2}\end{array}$H=$H=$ HypotenuseAS=$AS=$ Adjacent SideOS=$OS=$ 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 200150$\begin{array}{r}\frac{200}{150}\end{array}$ can be written as 200:150$\begin{array}{r}200:150\end{array}$

### 6. Perimeter and Area

 Perimeter of a Square 4×Side$\begin{array}{r}4×\mathrm{S}\mathrm{i}\mathrm{d}\mathrm{e}\end{array}$ Perimeter of a Rectangle 2×(Length+Breadth)$\begin{array}{r}2×\left(\text{Length}+\text{Breadth}\right)\end{array}$ Area of a Square Side×Side$\begin{array}{r}\text{Side}×\text{Side}\end{array}$ Area of a Rectangle Length×Breadth$\begin{array}{r}\text{Length}×\text{Breadth}\end{array}$ Area of a Parallelogram Base×Height$\begin{array}{r}\text{Base}×\text{Height}\end{array}$ Area of a Triangle 12×Base×Height$\begin{array}{r}\frac{1}{2}×\text{Base}×\text{Height}\end{array}$ Area of a Circle πr2$\begin{array}{r}\pi {r}^{2}\end{array}$ r=Radius of the circle$r=\text{Radius of the circle}$

### 7. Algebraic Expressions Formulas

 (x+y)2=x2+y2+2xy$\begin{array}{r}{\left(x+y\right)}^{2}={x}^{2}+{y}^{2}+2xy\end{array}$ (x−y)2=x2+y2−2xy$\begin{array}{r}{\left(x-y\right)}^{2}={x}^{2}+{y}^{2}-2xy\end{array}$ (x+y)(x−y)=x2−y2$\begin{array}{r}\left(x+y\right)\left(x-y\right)={x}^{2}-{y}^{2}\end{array}$ (x+y)(x+z)=x2+x(y+z)+yz$\left(x+y\right)\left(x+z\right)={x}^{2}+x\phantom{\rule{thinmathspace}{0ex}}\left(y+z\right)+yz$ (x+y)(x−z)=x2+x(y−z)−yz$\left(x+y\right)\left(x-z\right)={x}^{2}+x\phantom{\rule{thinmathspace}{0ex}}\left(y-z\right)-yz$ x2+y2=(x+y)2−2xy$\begin{array}{r}{x}^{2}+{y}^{2}={\left(x+y\right)}^{2}-2xy\end{array}$ (x+y)3=x3+y3+3xy(x+y)$\begin{array}{r}{\left(x+y\right)}^{3}={x}^{3}+{y}^{3}+3xy\left(x+y\right)\end{array}$ (x−y)3=x3−y3−3xy(x−y)$\begin{array}{r}{\left(x-y\right)}^{3}={x}^{3}-{y}^{3}-3xy\left(x-y\right)\end{array}$ (x+y+z)2=x2+y2+z2+2xy+2yz+2zx$\begin{array}{r}{\left(x+y+z\right)}^{2}={x}^{2}+{y}^{2}+{z}^{2}+2xy+2yz+2zx\end{array}$ (x−y−z)2=x2+y2+z2−2xy+2yz−2zx$\begin{array}{r}{\left(x-y-z\right)}^{2}={x}^{2}+{y}^{2}+{z}^{2}-2xy+2yz-2zx\end{array}$

### 8. Exponents and Powers Formulas

 am×an=am+n$\begin{array}{r}{a}^{m}×{a}^{n}={a}^{m+n}\end{array}$ am÷an=am−n$\begin{array}{r}{a}^{m}÷{a}^{n}={a}^{m-n}\end{array}$ (am)n=amn$\begin{array}{r}{\left({a}^{m}\right)}^{n}={a}^{mn}\end{array}$ am×bm=(ab)m$\begin{array}{r}{a}^{m}×{b}^{m}={\left(ab\right)}^{m}\end{array}$ am÷bm=(ab)m$\begin{array}{r}{a}^{m}÷{b}^{m}={\left(\frac{a}{b}\right)}^{m}\end{array}$ a0=1$\begin{array}{r}{a}^{0}=1\end{array}$ (−1)Even Number=1$\begin{array}{r}{\left(-1\right)}^{\text{Even Number}}=1\end{array}$ (−1)Odd Number=−1$\begin{array}{r}{\left(-1\right)}^{\text{Odd Number}}=-1\end{array}$

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Piyush Sagar