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Class 7 Mathematics NCERT Solutions (Non-Rationalised)
Chapter 1 Integers
Chapter 1 – Integers revisits the concept of positive and negative numbers and extends the operations of addition, subtraction, multiplication, and division to include them. Students learn to represent integers on a number line and apply the rules of signs, such as $(-3) \times (-4) = 12$. The NCERT Class 7 Non-Rationalised Solutions guide learners in understanding real-life applications like temperature change, altitude differences, and financial transactions.
Chapter 2 Fractions and Decimals
Fractions and Decimals teaches operations involving multiplication and division of fractional and decimal numbers. For instance, $\frac{3}{5} \times \frac{10}{3} = 2$. Students explore real-world contexts like money, measurement, and comparison of quantities. The Non-Rationalised NCERT Solutions simplify problem-solving with step-by-step examples, enhancing computational accuracy and mathematical fluency.
Chapter 3 Data Handling
Data Handling focuses on how to collect, organize, and interpret data using bar graphs, double bar graphs, and chance or probability. Students learn to calculate the mean, median, and mode of a data set. Through Non-Rationalised Class 7 Maths Solutions, learners gain insights into representing data visually — a critical skill in statistics and data science.
Chapter 4 Simple Equations
Simple Equations introduces the idea of equality and the process of finding unknown values in an equation such as $3x + 5 = 11$. Students learn to balance both sides of an equation using inverse operations. The Non-Rationalised NCERT Class 7 Solutions provide step-by-step methods to solve equations, helping learners apply these concepts to daily life problems like finding prices, ages, or distances.
Chapter 5 Lines and Angles
Lines and Angles helps students identify types of angles — acute, obtuse, right, complementary, and supplementary. The chapter also covers intersecting and parallel lines, and relationships like vertically opposite angles. With Non-Rationalised NCERT Solutions, students explore geometric reasoning and proofs through diagrams and real-world contexts like railway tracks or bridges.
Chapter 6 The Triangle and its Properties
The Triangle and Its Properties focuses on fundamental concepts such as medians, altitudes, and the Pythagoras theorem $a^2 + b^2 = c^2$. Students understand the angle sum property of triangles and the role of inequalities. The Non-Rationalised NCERT Solutions simplify geometry through clear constructions and real-life applications like engineering and architecture.
Chapter 7 Congruence of Triangles
Congruence of Triangles introduces conditions for congruence such as SSS, SAS, ASA, and RHS. Students learn how two figures are identical in shape and size. Through Non-Rationalised NCERT Class 7 Maths Solutions, learners apply these criteria to real-world examples like constructing buildings, bridges, and other symmetrical designs.
Chapter 8 Comparing Quantities
Comparing Quantities strengthens students’ understanding of ratios, percentages, and proportion. They solve problems related to profit, loss, discount, and simple interest using formulas such as $\text{SI} = \frac{P \times R \times T}{100}$. The Non-Rationalised NCERT Solutions include step-by-step examples that make financial mathematics simple and practical for students.
Chapter 9 Rational Numbers
Rational Numbers extends the number system to include fractions of integers, represented as $\frac{p}{q}$ where $q \neq 0$. Students learn properties such as closure, commutativity, and distributivity. Using the Non-Rationalised Class 7 Solutions, they perform operations on rational numbers and represent them on a number line, strengthening algebraic fluency.
Chapter 10 Practical Geometry
Practical Geometry builds construction skills using compass and ruler. Students learn to draw triangles when specific sides and angles are given, using conditions like SSS, SAS, and ASA. The Non-Rationalised NCERT Solutions enhance accuracy through step-by-step constructions, an essential foundation for higher-level geometry.
Chapter 11 Perimeter and Area
Perimeter and Area focuses on finding the boundaries and surface measurements of 2D shapes such as rectangles, triangles, and circles. Students use formulas like $A = l \times b$ and $C = 2\pi r$. The Non-Rationalised Class 7 NCERT Maths Solutions provide practical examples involving gardens, fields, and walls to make the concept real and engaging.
Chapter 12 Algebraic Expressions
Algebraic Expressions introduces terms, coefficients, and algebraic identities. Students simplify and add expressions like $2x + 3y - y = 2x + 2y$. The Non-Rationalised NCERT Solutions provide logical approaches to identify like terms and simplify equations — a vital step toward mastering algebraic reasoning in higher classes.
Chapter 13 Exponents and Powers
Exponents and Powers explains how to represent large and small numbers using powers, such as $10^6$ or $10^{-3}$. Students learn the laws of exponents — $a^m \times a^n = a^{m+n}$. The Non-Rationalised NCERT Solutions include examples in scientific notation and standard form, essential for physics, chemistry, and computation.
Chapter 14 Symmetry
Symmetry introduces the beauty of balanced designs found in art, nature, and architecture. Students identify lines of symmetry and understand rotational symmetry. The Non-Rationalised Class 7 Maths Solutions make the concept interactive by providing hands-on geometric examples and mirror-image activities.
Chapter 15 Visualising Solid Shapes
Visualising Solid Shapes helps learners identify 3D objects and visualize their nets, faces, edges, and vertices. Using Non-Rationalised NCERT Solutions, students explore cube, cuboid, sphere, cone, and cylinder through 2D representations. This builds spatial awareness, crucial in engineering, architecture, and design.