NCERT Solutions for Class 7 Maths: Complete Chapter by Chapter Guide (2026)

Difficulty: Moderate. This chapter extends what you learned about integers in Class 6. You will work with addition, subtraction, multiplication, and division of integers, including negative numbers. The key properties to understand are closure, commutativity, associativity, and the role of additive identity (zero). For example, $(-3) \times (-4) = 12$ because the product of two negative numbers is always positive. Many students get confused with division of negative integers. Remember that $(-12) \div 3 = -4$ but $(-12) \div (-3) = 4$. Practice until the sign rules become second nature.

Difficulty: Moderate. This is one of the most practically useful chapters. You will learn multiplication and division of fractions and decimals. The big idea with fraction multiplication is straightforward: $\frac{2}{3} \times \frac{4}{5} = \frac{8}{15}$. For division, you flip the second fraction and multiply: $\frac{2}{3} \div \frac{4}{5} = \frac{2}{3} \times \frac{5}{4} = \frac{10}{12} = \frac{5}{6}$. With decimals, the key is placing the decimal point correctly. Students who master this chapter find percentages, ratios, and proportions much easier later.

Difficulty: Easy. This chapter introduces you to collecting, organising, and interpreting data. You will learn about the arithmetic mean, range, mode, and median. The mean of a data set is calculated as $\text{Mean} = \frac{\text{Sum of all observations}}{\text{Number of observations}}$. You will also learn to read and create bar graphs and double bar graphs. The chapter is straightforward but do not skip it. Data handling appears in board exams in Class 10 as the Statistics chapter, and students who ignored it early often struggle later.

Difficulty: Moderate. This chapter is your first real introduction to algebra, and it is incredibly important. You will learn to solve equations like $3x + 5 = 17$ by isolating the variable. The golden rule is: whatever you do to one side of the equation, you must do to the other side as well. So for $3x + 5 = 17$, subtract 5 from both sides to get $3x = 12$, then divide both sides by 3 to get $x = 4$. The word problems in this chapter are especially important. If you can translate a sentence into an equation, you have a skill that will carry you all the way through Class 10 and beyond.

Difficulty: Moderate. Geometry starts getting serious here. You will learn about complementary angles (adding up to $90°$), supplementary angles (adding up to $180°$), adjacent angles, vertically opposite angles, and angles formed by a transversal cutting two parallel lines. The key relationships to remember: vertically opposite angles are always equal. When a transversal crosses parallel lines, alternate interior angles are equal and co interior angles are supplementary (they add up to $180°$). Draw lots of diagrams. Geometry without diagrams is like cooking without tasting.

Difficulty: Moderate to Hard. This chapter lays the groundwork for all the geometry you will study in Class 9 and 10. The most important property is the angle sum property: the three angles of a triangle always add up to $180°$. You will also learn about the exterior angle property (an exterior angle equals the sum of the two opposite interior angles), medians, altitudes, and the Pythagorean theorem. For a right angled triangle with sides $a$, $b$ and hypotenuse $c$, the theorem states $a^2 + b^2 = c^2$. For example, in a triangle with legs 3 and 4, the hypotenuse is $\sqrt{3^2 + 4^2} = \sqrt{25} = 5$.

Difficulty: Moderate. Congruence means two figures are exactly the same shape and size. In this chapter, you learn the criteria for triangle congruence: SSS (all three sides equal), SAS (two sides and the included angle equal), ASA (two angles and the included side equal), and RHS (right angle, hypotenuse, one side equal). The trick is identifying which criterion applies in a given problem. Students often confuse SSA with SAS, so pay close attention to which angle is "included" between the two sides.

Difficulty: Easy to Moderate. This chapter covers ratios, percentages, profit and loss, and simple interest. These are concepts you will use throughout your life, not just in exams. The key formulas: Profit% $= \frac{\text{Profit}}{\text{Cost Price}} \times 100$ and Simple Interest $= \frac{P \times R \times T}{100}$ where $P$ is the principal, $R$ is the rate, and $T$ is the time in years. The word problems here are very practical and often based on shopping, banking, and everyday scenarios. Most students enjoy this chapter once they see how relevant it is.

Difficulty: Moderate. Rational numbers are numbers that can be written in the form $\frac{p}{q}$ where $q \neq 0$. This chapter extends your understanding of fractions to include negative fractions. You will learn about equivalent rational numbers, comparing rational numbers, and operations on them. A common point of confusion is finding rational numbers between two given numbers. Between any two rational numbers, there are infinitely many rational numbers. For instance, between $\frac{1}{3}$ and $\frac{1}{2}$, you can find $\frac{5}{12}$ by calculating $\frac{1}{2}\left(\frac{1}{3} + \frac{1}{2}\right)$.

Difficulty: Easy. This chapter is about constructions using a ruler, compass, and protractor. You will learn to construct parallel lines, triangles given different sets of measurements (SSS, SAS, ASA, RHS). The important thing is accuracy. Use a sharp pencil, do not change the compass width while drawing arcs, and always label your constructions clearly. This chapter is straightforward if you follow the steps carefully. It is also great practice for understanding the triangle congruence criteria from the previous chapter.

Difficulty: Moderate. You already know the area of rectangles and squares from earlier classes. This chapter introduces the area of parallelograms, triangles, and circles. The key formulas: area of a parallelogram $= \text{base} \times \text{height}$, area of a triangle $= \frac{1}{2} \times \text{base} \times \text{height}$, and area of a circle $= \pi r^2$ where $r$ is the radius. Circumference of a circle $= 2\pi r$. Common mistake: confusing the height of a parallelogram with the length of its side. The height is always perpendicular to the base, not the slanted side.

Difficulty: Moderate. Building on what you learned in Simple Equations, this chapter introduces terms, coefficients, and like and unlike terms. You will learn to add and subtract algebraic expressions. For example, adding $3x^2 + 2x + 1$ and $5x^2 + 4x + 3$ gives $8x^2 + 6x + 4$. The key is to combine only like terms (terms with the same variable raised to the same power). This chapter prepares you for factorisation and algebraic identities in Class 8, so make sure you understand it well.

Difficulty: Easy to Moderate. Exponents are a shorthand way of writing repeated multiplication. So $2^5 = 2 \times 2 \times 2 \times 2 \times 2 = 32$. The laws of exponents you must remember: $a^m \times a^n = a^{m+n}$, $a^m \div a^n = a^{m-n}$, $(a^m)^n = a^{mn}$, and $a^0 = 1$. You will also learn about expressing very large and very small numbers in standard form (scientific notation). For example, the distance from Earth to the Sun is about $1.496 \times 10^{11}$ metres. Once you memorise the laws, this chapter is quite scoring.

Difficulty: Easy. This chapter covers lines of symmetry and rotational symmetry. A figure has a line of symmetry if one half is the mirror image of the other half. Rotational symmetry means the figure looks the same after being rotated by a certain angle. For example, a square has 4 lines of symmetry and rotational symmetry of order 4 (it looks the same at $90°$, $180°$, $270°$, and $360°$). This is one of the easiest chapters in the textbook, but it builds your visual and spatial reasoning which helps in higher level geometry.

Difficulty: Easy. The final chapter introduces 3D shapes and how to visualise them from different perspectives. You will learn about faces, edges, and vertices of solids and Euler's formula: $F + V - E = 2$ where $F$ is the number of faces, $V$ is the number of vertices, and $E$ is the number of edges. For a cube, $F = 6$, $V = 8$, $E = 12$, and indeed $6 + 8 - 12 = 2$. The chapter also covers nets of 3D shapes (what a shape looks like when unfolded). It is short, visual, and quite enjoyable.

Start with Integers, then move to Fractions and Decimals. These two chapters are closely related and doing them together reinforces your number skills. Next, tackle Comparing Quantities for practical applications. Follow up with Rational Numbers, which extends your fraction knowledge. Finish this block with Exponents and Powers since it is relatively short and formula based. By the end of week 3, you should have five chapters done.

Data Handling is a lighter chapter, so start with it. Then move to Simple Equations, which needs focused practice especially for word problems. Round off this block with Algebraic Expressions. These three chapters build your abstract thinking and problem solving skills. Take your time with Simple Equations since it is the most important algebra chapter at this level.

The geometry block has more chapters but several are short and visual. Start with Lines and Angles, then do The Triangle and Its Properties. Follow with Congruence of Triangles while triangle concepts are fresh. Practical Geometry is a construction chapter that goes quickly. Perimeter and Area requires formula practice. Finish with Symmetry and Visualising Solid Shapes, both of which are the easiest chapters in the textbook.

Use the final week to revisit the chapters you found hardest. Solve the miscellaneous exercises and any problems you had marked as difficult. If your school gives sample papers or extra worksheets, this is the time to do them. Focus especially on the chapters that felt shaky during your first pass.