NCERT Solutions for Class 6 Maths 2024-25

Chapter 1 Knowing Our Numbers

Number sense is very important in the process of learning. Numbers will be used in every aspect of life and in mathematics as well. Knowing numbers will help in developing the speed at which students can solve problems. When you open the Class 6 Maths NCERT Book PDF or hardcopy, the first chapter that you will see is Knowing Our Numbers. NCERT Maths Book Class 6 Chapter 1 Solutions deals with the number of values a particular number can reach. It tells about large quantities that can reach up to a crore, roman numerals, use of brackets, rounding off, and estimation of differences between two values.

1. Exercise 1.1: This exercise focuses on understanding place value of large numbers like lakhs, crores, and millions. You'll practice converting between these units and writing them correctly with commas.

2. Exercise 1.2: This exercise involves solving word problems. You'll practice adding whole numbers to find totals in situations like ticket sales or run scoring.

Here are the Topics Covered in Class 6 Maths Chapter 1 Knowing Our Numbers:

• Introduction to Numbers: This section revisits the concept of numbers, their types (natural numbers, whole numbers) and their uses in our daily lives.

• Comparing Numbers: This section covers methods for comparing numbers like greater than (<), less than (>), and equal to (=) signs. Students will learn how to arrange numbers in ascending and descending order.

• Place Value: This section revisits the concept of place value. It explains how the value of a digit changes based on its position in the number. For example, in the number 123, the digit 1 has a value of 100 (hundred's place), the digit 2 has a value of 20 (ten's place), and the digit 3 has a value of 3 (unit's place).

• Large Numbers: This section introduces students to larger numbers beyond four digits. It covers how to read, write, and compare numbers up to lakhs (100,000). It also introduces the concept of commas to separate large numbers for readability.

• Estimation: This section teaches students how to approximate numbers. Estimation helps in getting a close idea of the answer without performing the actual calculation. It is useful for checking calculations and rounding off numbers.

• Brackets: This section covers the order of operations using BODMAS rule (Bracket, Of, Division, Multiplication, Addition, Subtraction) when a mathematical expression includes brackets.

• Roman Numerals: This section introduces Roman numerals, a system of symbols used to represent numbers. Students will learn to read and write Roman numerals up to a certain value.

NCERT Solutions for Class 6 Maths Chapter 1 Exercises are given in the table below:

Students can access extra study materials for Knowing our Numbers on Vedantu. These resources are available for download, offering additional support for your studies.

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Chapter 2 Whole Numbers

Whole numbers are numbers that are not fragmented or added to a fractional or decimal part. Whole numbers are the most common and their use is generally in everyday lives, be it paying shopkeepers or counting heads. This chapter provides students with an introduction to whole numbers and their various properties. Students are for the first time familiarised with the concept of the number lines in this chapter. Using a number line, one can understand predecessor, successor, addition, and subtraction on the number line.

1. Exercise 2.1 in Chapter 2 of your Class 6 Maths textbook deals with basic concepts of whole numbers. It covers topics like understanding successors and predecessors of numbers, comparing whole numbers on the number line, and finding the number of whole numbers between two given numbers.

Here are the Main Topics Covered in Chapter 2 Whole Numbers:

• Introduction to Whole Numbers: This section introduces the concept of whole numbers. Whole numbers are the counting numbers starting from zero (0) and going on infinitely. They include 0, 1, 2, 3, and so on.

• The Number Line: The number line is a graphical representation of whole numbers. Numbers are placed at equal distances on the line, with zero in the middle. The number line helps visualize addition and subtraction of whole numbers.

• Predecessor and Successor: The successor of a number is the number that comes after it in counting order. For example, the successor of 5 is 6. The predecessor of a number is the number that comes before it in counting order. For example, the predecessor of 8 is 7.

• Properties of Operations on Whole Numbers: This section covers basic properties of arithmetic operations like addition, subtraction, multiplication, and division as applied to whole numbers. Here are some important properties:

• Closure Property: This property states that the result of an operation on two whole numbers is always another whole number. For addition and multiplication, this holds true. However, it is not always true for subtraction and division of whole numbers.

• Commutative Property: This property states that the order of operands in an addition or multiplication operation does not affect the result. In other words, a + b = b + a and a x b = b x a.

• Associative Property: This property states that the way we group the operands in an addition or multiplication operation does not affect the result. (a + b) + c = a + (b + c) and (a x b) x c = a x (b x c).

• Distributive Property: This property applies to multiplication and addition/subtraction. It states that a x (b + c) = (a x b) + (a x c).

• HCF and LCM: This section introduces the concepts of Highest Common Factor (HCF) and Least Common Multiple (LCM) of two or more whole numbers. HCF is the largest number that is a factor of both the numbers, while LCM is the smallest number that is a multiple of both the numbers.

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Chapter 3 Playing with Numbers

Playing with numbers is a great exercise and can greatly benefit students in developing their number sense. Students, in this chapter, learn about the concept of prime numbers, composite numbers, common multiples, coprime numbers, and common factors. This chapter broadens the concept of numbers for students with an introduction to HCF and LCM.

1. Exercise 3.1 focuses on writing numerals for number names. You'll practice representing numbers like "twenty-three" with the numeral "23".

2. Exercise 3.2 deals with place value. You'll learn how to expand numbers by breaking them down into their place values. For instance, you'll express 786 as 700 (hundred's place) + 80 (ten's place) + 6 (unit's place).

3. Exercise 3.3 covers comparing numbers. You'll use symbols like "<" (less than), ">" (greater than), and "=" (equal to) to compare different numbers.

4. Exercise 3.4 is about arranging numbers in order. You'll learn how to put numbers in ascending (increasing) order and descending (decreasing) order.

5. Exercise 3.5 introduces rounding numbers. You'll practice rounding numbers to the nearest ten or hundred, for example.

6. Exercise 3.6 teaches you how to estimate sums and differences of numbers. Estimation helps get a close answer without performing the exact calculation.

7. Exercise 3.7 introduces Roman numerals. You'll learn about symbols like I, V, X, L, C, D, and M, used in the Roman numeral system, and their corresponding decimal values.

Class 6 Maths Chapter 3 Playing with Numbers Covers the Following Topics:

• Factors of a number: A factor of a number is a number that divides exactly into that number. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.

• Finding factors of a number: There are different methods for finding factors of a number. The chapter discusses listing out all the possibilities and using divisibility rules.

• Prime and composite numbers: A prime number has exactly two factors: 1 and itself. Examples of prime numbers are 2, 3, 5, 7, 11, etc. A composite number has more than two factors (including 1 and itself). Examples of composite numbers are 4, 6, 8, 9, 10, etc.

• Playing with patterns: This section might involve activities or exercises to identify patterns related to factors and prime numbers.

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Chapter 4 Basic Geometrical Ideas

A student should possess the basic ideas of geometry in order to be able to identify shapes and structures and to learn and use the properties of different geometric shapes and concepts. The exciting chapter provides a student with the first-ever encounter with Geometry in 6th Standard Maths. The chapter includes 6 exercises relating to figures like polygons, quadrilaterals, circles, triangles, lines, angles, etc. The study material provided on this page covers detailed solutions to all questions in this chapter and helps a student in getting a clear understanding of geometry.

1. Exercise 4.1 Focuses on identifying basic geometrical shapes like points and lines in everyday surroundings. It helps students recognize these fundamental geometrical concepts in the real world.

2. Exercise 4.2 Introduces different types of lines: straight lines, curved lines, broken lines and closed lines. Students will learn to differentiate between these lines based on their shape and form.

3. Exercise 4.3 Deals with classifying lines based on their orientation and intersection. It covers horizontal lines, vertical lines, slanting lines, and intersecting lines.

 Here are the Main Topics Covered in Chapter 4 Basic Geometrical Ideas:

• Points, Lines and Line Segments: A point is a location considered to have no dimension (length, breadth or height). A line is a straight path that extends infinitely in both directions. A line segment is a part of a line with two distinct end points.

• Rays and Angles: A ray is a part of a line that starts at a point and extends infinitely in one direction only. An angle is formed by two rays with a common endpoint.

• Types of Angles: There are different types of angles based on their measure.

• Acute Angles: Angles with measure less than 90 degrees.

• Right Angles: Angles with measure exactly 90 degrees.

• Obtuse Angles: Angles with measure between 90 degrees and 180 degrees.

• Straight Angles: Angles with measure exactly 180 degrees.

• Polygons: A polygon is a closed figure formed by three or more straight line segments that meet only at their endpoints. Polygons are classified based on the number of sides they have. For example, a triangle has three sides, a quadrilateral has four sides, and so on.

• Triangles: Triangles are classified into different types based on their side lengths and angles.

• Equilateral Triangle: A triangle with all three sides equal and all three angles equal to 60 degrees.

• Isosceles Triangle: A triangle with two sides equal and the two angles opposite the equal sides also equal.

• Scalene Triangle: A triangle in which no two sides are equal and no two angles are equal.

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Chapter 5 Understanding Elementary Shapes

The importance of understanding elementary shapes lies in the utility of such shapes in real-life situations. This chapter of 9 exercises gets into a detailed study of geometric figures like quadrilateral, triangle, 3D shapes, and line segments. The chapter emphasizes on measurement and classification of angles. The given NCERT Solutions Class 6 Maths cover these topics in a very intricate manner and tries to clear all confusion a student faces in the best way possible.

1. Ex 5.1 & 5.2: Introduces the limitations of comparing line segments by just looking (observation) and highlights the benefits of using a divider for accurate measurement.

2. Ex 5.3 & 5.4: Deals with angles, introducing concepts like right angles, acute angles, obtuse angles, and reflex angles. You might also encounter relating angles to clock hands.

3. Ex 5.5 & 5.6: Explores classifying triangles based on their sides (scalene, isosceles, equilateral) and angles (acute, right angled, obtuse).

4. Ex 5.7: Focuses on basic understanding of quadrilaterals.

5. Ex 5.8: Introduces 3D shapes, laying the groundwork for future chapters.

Here's a Breakdown of What You'll Learn in Chapter 5 Understanding Elementary Shapes

• Lines and Line Segments: This section gets you started with understanding basic building blocks like lines and line segments. You'll learn how to measure these lengths using a ruler or a divider.

• Angles and their Types: Get ready to dive into the world of angles! You'll see how angles are formed by two rays and learn about different types of angles - right angles, straight angles, acute angles, obtuse angles, and reflex angles. You'll also be introduced to a handy tool called a protractor to measure angles in degrees.

• Lines and Angles Relationships: This section explores how lines can be related to each other. You'll learn what perpendicular lines are and how they create right angles.

• Triangles and their Classification: Buckle up for triangles! This part delves into these three-sided shapes, introducing different types based on their side lengths (scalene, isosceles, equilateral) and angles (acute, obtuse, right angled).

• Quadrilaterals and Polygons: The chapter moves on to four-sided shapes called quadrilaterals and introduces the broader concept of polygons, which are closed shapes with straight sides.

• 3D Shapes: Get ready for a jump into the third dimension! You'll explore common three-dimensional shapes like cubes, cuboids, spheres, cones, and cylinders.

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Chapter 6 Integers

Knowing about integers will help greatly in carrying out calculations involving positive and negative numbers. ‘Integers’ is the topic taught in most schools in the second half of the academic year. NCERT Class 6 Maths Chapter 6 discusses this topic along with how to perform addition, subtraction of integers on the number line. Solutions to the problems of this chapter have also been discussed elaborately in the Mathematics Success Book Class 6 Solutions.

1. Exercise 6.1 Focuses on recognizing integers. You might be asked to identify integers from a list of numbers or represent real-world situations with integers (positive or negative).

2. Exercise 6.2 Deals with representing integers on a number line. It helps you visualize addition and subtraction of integers.

3. Exercise 6.3 Introduces word problems involving addition and subtraction of integers. You'll need to apply your understanding of integers and number lines to solve these problems.

Here's a Breakdown of the Topics Covered in Chapter 6 Integers:

• Introduction to Integers: This section revisits whole numbers and introduces negative numbers. Integers are defined as the collection of whole numbers, including zero, and negative numbers.

• The Number System: This section briefly revisits different types of numbers like natural numbers, whole numbers and integers.

• Representing Integers on the Number Line:Integers can be visualized on a number line. The number line is a horizontal line with 0 in the middle. Positive integers are marked to the right of 0, with each point one unit away from the previous one. Negative integers are marked to the left of 0, also with each point one unit away from the previous one.

• Successor and Predecessor: The successor of a number is the number that comes after it. The predecessor of a number is the number that comes before it. This concept applies to integers as well.

• Ordering of Integers: On the number line, integers are arranged such that as you move to the right, the numbers increase, and as you move to the left, the numbers decrease. This helps in comparing integers.

• Addition of Integers: Adding integers can be visualized on the number line. If we are adding a positive integer, we move the given number of steps to the right. If we are adding a negative integer, we move the given number of steps to the left.

• Subtraction of Integers: Subtracting an integer is equivalent to adding its opposite. Subtracting integers can also be visualized on the number line.

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Chapter 7 Fractions

Fractions are used in identifying or defining portions of a whole object or quantity. Fractions are important when calculating or representing partial amounts in mathematics. The 7th segment of the Math 6th Class Solution shall deal with the topic of 'Fractions,' which can be considered an extension of the topic "division," which we learned in elementary school. This chapter covers the different types of fractions like proper, improper, mixed, equivalent, and like. The solutions provided in the pdf also include questions relating to the addition, subtraction of fractions, which constitutes a central part of the segment.

1. Exercise 7.1 Introduces fractions and uses examples to explain the concept. It explains how fractions represent parts of a whole.

2. Exercise 7.2 Deals with representing fractions on a number line. This helps visualize the value of fractions.

3. Exercise 7.3 Covers equivalent fractions. Fractions that have the same value even though they are written differently are called equivalent fractions. This exercise provides examples of finding equivalent fractions.

4. Exercise 7.4 Explains simplifying fractions. Simplifying a fraction means reducing it to its lowest terms by dividing both the numerator and denominator by their greatest common factor (GCD). This exercise includes examples of simplifying fractions.

5. Exercise 7.5 Focuses on adding and subtracting fractions with like denominators. Fractions have the same denominator if they refer to the same number of total parts. This exercise provides examples of adding and subtracting fractions with the same denominator.

6. Exercise 7.6 Covers adding and subtracting fractions with unlike denominators. Fractions have unlike denominators if they refer to a different number of total parts. This exercise includes examples of adding and subtracting fractions with different denominators.

 Here's a Breakdown of the Key Concepts You'll Learn in Chapter 7 Fractions:

1. Understanding Fractions: Fractions represent parts of a whole. A fraction is written as ba​ where a is called the numerator and b is called the denominator. The numerator represents the number of parts you consider, and the denominator represents the total number of parts the whole is divided into.

2. Representing Fractions on a Number Line: Fractions can be visualized on a number line. The number line is divided into equal parts, and each part represents a unit fraction. The location of the fraction on the number line depends on the numerator and denominator.

3. Types of Fractions: There are three main types of fractions you'll encounter in this chapter:

1. Proper Fractions: A proper fraction has a numerator that is smaller than the denominator. For example, 82​ and 53​are proper fractions.

2. Improper Fractions: An improper fraction has a numerator that is greater than or equal to the denominator. For example, 59​ and 44​are improper fractions.

3. Mixed Fractions: A mixed fraction is a combination of a whole number and a proper fraction. For example, 121​ and 332​are mixed fractions.

4. Equivalent Fractions: Fractions that represent the same quantity are called equivalent fractions. You can get equivalent fractions by multiplying or dividing the numerator and denominator by the same number. For example, 42​ and 21​ are equivalent fractions.

5. Simplest Form of Fractions: A fraction is in its simplest form when the numerator and denominator have no common factors other than 1. For example, 42​ can be simplified to 21​.

6. Addition and Subtraction of Fractions: Fractions can be added or subtracted only if they have the same denominator. To add or subtract fractions with the same denominator, you simply add or subtract the numerators and keep the denominator the same. When fractions have different denominators, you need to find a common denominator before you can add or subtract them.

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Chapter 8 Decimals

Decimals are used at a time when precision is of high priority in measuring quantities or amounts that are not whole, that is, partial or fragmented. The use of decimals gets quite severe in this part of the book but is easily covered on this page. With a thorough revision of decimals, the chapter extends the particular concept to more significant numbers and cases where decimals can be used to measure, compare, add, and subtract values.

1. Exercise 8.1 Focuses on writing decimals in different forms, including representing fractions as decimals and converting between decimals and expanded forms. You'll also practice representing decimals on a number line and comparing them.

2. Exercise 8.2 Deals with expanding decimals. You'll learn how to represent a decimal using its place values.

3. Exercise 8.3 Covers rounding decimals to a specific number of decimal places.

4. Exercise 8.4 Applies decimals to real-world contexts. You'll practice converting between different units of measurement, like meters and centimeters, rupees and paise, using decimals.

Here are the Topics covered in Chapter 8 Decimals:

• Understanding Decimals: This section introduces the concept of decimals. It explains how decimals are a way of representing parts of a whole where those parts are tenths, hundredths, and thousandths. For example, 0.5 represents 5 tenth parts of a whole, and 3.14 represents 3 ones, 1 tenth, and 4 hundredth parts of a whole.

• Representing Decimals on the Number Line: This section teaches students how to represent decimals on a number line. The number line is divided into equal parts, with each part representing a tenth, a hundredth, or a thousandth depending on the place value of the decimal.

• Fractions as Decimals: This section covers converting fractions into decimals. Not all fractions can be exactly represented as decimals, but this section teaches students how to convert fractions with denominators of 10, 100, and 1000 into decimals.

• Decimals as Fractions: This section deals with converting decimals into fractions. Students will learn how to write a decimal as a fraction with a denominator of 10, 100, or 1000.

• Comparing Decimals: This section teaches students how to compare decimals. They will learn techniques to compare decimals by looking at the digits in the tenths and hundredths places (and thousandths places if necessary).

• Using Decimals in the Real World: This section shows students how decimals are used in everyday life. Decimals are used in measurements of length, weight, and money. Students will learn how to add and subtract decimals in these contexts.

• Addition and Subtraction of Decimals: This section covers the basic concepts of adding and subtracting decimals. Students will learn how to line up the decimals by their decimal places and then add or subtract each place value column.

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Chapter 9 Data Handling

Data handling will help in conducting the research and playing with and using data and information retrieved from various sources. The only chapter on the whole page to contain graphs in solutions for the NCERT Maths Class 6 is this one. Data Handling is a relatively easy chapter of Class VI Maths. A scoring chapter, and rather fun to study! You will feel the same way once you download NCERT Solution for Class 6 Maths.

1. Exercise 9.1 in Class 6 Maths Chapter 9 on Data Handling deals with introducing students to interpreting data. It involves questions about arranging data, finding how many times a number appears (frequency), and comparing the number of times different numbers appear.

Here are the Topics Covered in Class 6 Maths Chapter 9 Data Handling:

• Introduction to Data: Data is a collection of information that can be used to understand a particular situation or topic. Data can be quantitative (numerical) or qualitative (descriptive).

• Collection of Data: There are many different ways to collect data, such as through surveys, experiments, and observations.

• Organization of Data: Once data has been collected, it needs to be organized in a way that makes it easy to understand and analyze. This can be done by creating tables, charts, and graphs.

• Pictographs: A pictograph is a type of chart that uses symbols or pictures to represent data. Pictographs are a good way to introduce students to the concept of data handling.

• Bar Graphs: A bar graph is a type of chart that uses bars to represent data. Bar graphs are a good way to compare different categories of data.

• Interpretation of Data: Once data has been organized and presented in a visual format, it can be interpreted. This means drawing conclusions from the data.

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Chapter 10 Mensuration

Mensuration is used to determine areas, perimeters, volumes, etc. of spaces or objects. Once you have the 6th Class Maths book Download, a simple look at this chapter will give you an idea about how tricky and tough Mensuration can be! But no trick or toughness has not been dealt with in detail and the easy-to-do manner in the given NCERT Solutions. The key to being good at this topic depends on the level of understanding and confidence in measuring perimeters, the area of various shapes in maths.

1. Exercise 10.1 This exercise introduces you to the concepts of perimeter and area. Perimeter is the total length of all the sides of a closed figure, like a square or a triangle. Area is the amount of space a flat shape fills. You'll practice finding the perimeter of various shapes.

2. Exercise 10.2 Here, you'll get some hands-on practice finding the perimeters of different shapes like rectangles, squares, triangles, and even regular hexagons. Remember, the perimeter is the total distance around the whole shape.

3. Exercise 10.3 This exercise focuses on finding the area of various shapes. Area tells you how much space is covered by a flat shape. You'll solve problems to find the areas of rectangles, squares, and even find areas of more complex shapes by splitting them into simpler shapes like rectangles.

Here are the Specific Topics  Covered in Class 6 Maths Chapter 10 Mensuration:

• Perimeter: The perimeter of a closed figure is the total length of its boundary. Imagine you have a piece of string that goes around the whole shape exactly once, the length of that string would be the perimeter.

• Area: The area is the amount of space occupied by a flat shape.

• Rectangle: A rectangle has four straight sides, with opposite sides equal in length. Perimeter of a rectangle is found by adding the lengths of all its sides. Area of a rectangle is found by multiplying the length and breadth.

• Square: A square is a special type of rectangle where all sides are equal. Perimeter and area formulas for a square are the same as those for a rectangle, but you only need the side length.

• Triangle: A triangle has three straight sides and three angles that add up to 180°. There are different types of triangles based on their side lengths (equilateral, isosceles, scalene). Perimeter of a triangle is found by adding the lengths of all its sides. Finding the area of a triangle is a little more tricky, and a formula will be explained in class.

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Chapter 11 Algebra

Learning algebra will help students in representing problems or situations in terms of mathematical expressions to be able to solve them in a systematic manner Chapter 11 provides students with an insight into a new topic called algebra. The Class 6 Maths Solutions contains solutions to exercises concerning algebraic concepts such as variables, equations, matchstick patterns, etc. Algebra is essential for students willing to take up Maths in higher classes, and hence, the basic concepts of this chapter are very well enumerated in NCERT Solution for Class 6.

1. Exercise 11.1 in Chapter 11 of your Class 6 Maths textbook focuses on introducing the concept of algebra through representing patterns using variables. It involves looking at various patterns like matchstick squares, triangles and finding a rule that expresses the number of elements (matchsticks) in the pattern based on the number of repeating units (number of squares, triangles). For instance, the number of matchsticks required to make squares can be expressed as a rule involving the number of squares.

Here are the Major Topics Covered in Chapter 11 Algebra:

• Introduction to Algebra: This section provides a basic overview of what algebra is and its importance in mathematics.

• Matchstick Problems: This section uses matchstick patterns to introduce the concept of variables. Students are shown how to represent unknown quantities with letters like x, y, and z. They are then required to find the rule that determines the number of matchsticks needed to make a particular pattern based on the number of elements (squares, triangles, etc.) in the pattern.

• The Idea of a Variable: This section builds on the concept of variables introduced through matchstick problems. It explains how variables can be used to represent unknown numbers and how they can be used in expressions and equations.

• Use of Variables in Common Rules: This section showcases how variables can be used to represent unknowns in real-world scenarios. Students are given everyday situations and asked to write expressions involving variables to represent the quantities involved.

• Expressions with Variables: This section formally defines expressions and explains how they can be formed using variables, numbers, and arithmetic operations (+, -, *, /). Students learn how to simplify expressions by following the order of operations (PEMDAS - Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right).

• Practical Applications of Expressions: This section provides further examples of how expressions with variables can be used to solve real-world problems.

• What is an Equation?: This section introduces the concept of equations. An equation is a mathematical statement that shows two expressions are equal. The equal sign (=) signifies that both sides of the equation have the same value.

• Solution to an Equation: This section explains how to solve equations for the variable. Solving an equation means finding the value of the variable that makes the equation true.

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Chapter 12 Ratio and Proportion

Ratio and proportion is an important chapter in mathematics that helps students in defining the relationship between quantities of objects, two or more in number. Solutions to exercises of Ratio and Proportion have been provided in NCERT Maths Class 6 Solutions Chapter 12. Along with introducing students to the concept of ratio and proportion, several examples are provided so that they can have a better understanding of the same. Students can also check solutions to critical problems if they are overcome with doubt at any point.

1. Exercise 12.1 This exercise is about understanding the concept of ratios. You'll be asked to find the ratio between two quantities. Ratios express how much of one thing you get compared to another thing. For instance, if there are 4 red marbles and 3 blue marbles, the ratio of red to blue marbles would be 4:3.

2. Exercise 12.2 Here, you'll practice dividing a whole quantity into parts based on a given ratio. Imagine you have 10 meters of ribbon, and you want to cut it into two pieces in a 2:3 ratio. This exercise will help you figure out how much ribbon goes in each piece.

3. Exercise 12.3 This exercise introduces unitary method, a technique for solving proportion problems. You'll be given the ratio of two parts and the value of one part, and then asked to find the whole quantity. For example, if the cost of 2 apples is ₹4, the unitary method helps you determine the cost of a single apple and then the cost of any other number of apples (like 5 apples).

Class 6 Maths Chapter 12 Covers the Following Topics Related to Ratio and Proportion:

• Introduction to Ratio: Ratio is a way of comparing two quantities of the same kind. It expresses the relationship between two numbers by dividing them. Ratios can be written in a colon format (a:b) or fraction format (a/b). For example, a ratio of 3:2 for apples and oranges means that there are 3 apples for every 2 oranges.

• Writing Ratios: Ratios can be written in three ways:

• Colon format (a:b) - This is the most common way to write ratios. For example, 4:3 represents a ratio of 4 to 3.

• Fraction format (a/b) - Ratios can also be expressed as fractions. For example, 4:3 can be written as 4/3.

• Word phrase - Ratios can be written in words. For example, 4:3 can be written as "4 to 3" or "4 out of 3".

• Types of Ratios: There are different ways to classify ratios. Here are two common classifications:

• Equivalent Ratios: Two ratios are said to be equivalent if they express the same relationship between the quantities. For example, 2:1 and 4:2 are equivalent ratios.

• Simplest Ratio: A ratio is in its simplest form when the greatest common factor (GCD) of the numerator and denominator is 1. You can find the simplest ratio by dividing both the numerator and denominator by their GCD.

• Introduction to Proportion: A proportion is an equality statement between two ratios. It indicates that two ratios are equivalent. Proportions are written in the form a:b :: c:d (or a/b = c/d), where a, b, c, and d are all numbers.

• Solving Proportions: Proportions can be used to solve for unknown quantities. There are different methods to solve proportions, including the cross-multiplication method. The cross-multiplication method states that the product of the means (numbers in the middle) is equal to the product of the extremes (numbers on the outside) in a proportion.

• Applications of Ratio and Proportion: Ratios and proportions have various applications in real-life situations. They are used in mixing paints in different colors, dividing recipes, scaling down or up drawings, and many other areas.

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Conclusion

The NCERT Solutions for Class 6 Maths are an essential resource that provides comprehensive, curriculum-aligned explanations for fundamental mathematical concepts. They help students develop a strong foundation, enhance problem-solving skills, and encourage independent learning. These solutions are valuable for both students and educators, ensuring a clear understanding and effective preparation for exams.