a, b, c, d, e, f, g are consecutive even numbers. j, k, l, m, n are consecutive odd numbers. The average of all the numbers is :
A. $3\left(\large\frac{a+n}{2}\right)$
B. $\left(\Large\frac{1+d}{2}\right)$
C. $\left(\Large\frac{a+b+m+n}{4}\right)$
D. $3\left(\Large\frac{j+c+n+g}{4}\right)$
Show Answer
AnswerB
Solution
Solution(By Apex Team)
$\begin{array}{l}\text{According to the question,}\\
\text{Consecutive even numbers}\\
\text{= a, b, c, d, e, f, g}\\
\text{Consecutive odd numbers}\\
\text{= j, k, l, m, n}\\
\text{Consecutive even numbers}\\
\text{2, 4, 6, 8, 10, 12, 14}\end{array}$
$\begin{array}{l}\Large\frac{2+4+6+8+10+12+14}{7}\\
=\Large\frac{56}{7}\\
=8\text{ middle term}\\
\text{Consecutive odd numbers}\\
1,3,5,7,9\\
\Large\frac{1+3+5+7+9}{2}\\
=\Large\frac{25}{5}\\
=5\text{ middle term }\end{array}$
∴ Same as in above situation.
Average of even numbers = d
Average of odd numbers = 1
∴ Average of all numbers
$=\left(\Large\frac{1+d}{2}\right)$
 Motion and measurements of distances
Motion and measurements of distances for class 6th
Motion and measurements of distances chapter of class 6 is very important for students. This chapter has questions and answers on topics like different modes of transport used to go from one place to another, measurement, SI units of measurement, the concept of meter, motion in a straight line, rectilinear motion, circular motion, and periodic motion.Objective Test:
Motion and Measurements for distances Subjective Test 1:
Q.01 Arrange the following lengths in their increasing order.[1 Mark] 1 meter, 1 centimeter, 1 Kilometer, 1 millimeter Q.02 What is the need of standard unit for measurements? [2 Marks] Q.03 Why is foot not used as the standard unit of length? [ 2 Marks] Q.04 Discuss the significance of measurement. Give examples where you use measurement. [ 3 Marks] Q.05 What do you mean by multiple motions? Explain it with an example.[ 3 Marks] Q.06 Classify the following into different types of motion. 1) The motion of man on a straight road. 2) The motion of wheels of a car. 3) The motion of a vertically falling stone. Q.07 Write the similarities and differences between the motion of a bicycle wheel and a ceiling fan that has been switched on.[ 5 marks] Q.08 How can you measure the length of a curved line? [ 5 Marks] Q.09 What are the different modes of transport? Give two examples for each. [ 5 Marks]Motion and Measurements for distances Subjective Test 2:
NCERT Examplar Multiple Choice Questions:
NCERT Examplar Very Short Questions:
These solutions will assist you in understanding the important topics which will be helpful in your future studies. In order to score good marks, students are advised to study the answers thoroughly. A proper understanding of this chapter will also help the students with a few other chapters in higher classes. Every question is explained concisely in simple language to better understand the students.  The Earth In The Solar SystemNCERT Solutions for Class 6 Social science Chapter 1 The Earth In The Solar System are provided here with simple stepbystep explanations. These solutions for The Earth In The Solar System are extremely popular among Class 6 students for Social science The Earth In The Solar System Solutions come handy for quickly completing your homework and preparing for exams.
Question 1: Answer the following questions briefly.
(a) How does a planet differ from a star? (b) What is meant by the ‘Solar System’? (c) Name all the planets according to their distance from the Sun. (d) Why is the Earth called a unique planet? (e) Why do we see only one side of the Moon always? (f) What is the Universe?Touch the Plus + icon and get your answer:
 whole numbers definition Class 6th mathNCERT Solutions for Class 6 Maths Chapter 2 Whole Numbers are a comprehensive study material for students preparing for the Class 6 Mathematics exam The chapter starts with the introduction of the predecessor and successor followed by the concept of whole numbers.
 If you add 1 to a natural number, we get its successor. If you subtract 1 from a natural number, you get its predecessor.
 Every natural number has a successor.
 Every natural number except 1 has a predecessor.
 Every whole number has a successor.
 Every whole number except zero has a predecessor.
 All natural numbers are whole numbers, but all whole numbers are not natural numbers.
 Closure property
 Division of a whole number by 0 is not defined.
 Commutativity of addition and multiplication
 Associativity of addition and multiplication
 Distributivity of multiplication over addition
 Zero is called an identity for addition of whole numbers or additive identity for whole numbers.
 Whole number 1 is the identity for multiplication of whole numbers.
 Knowing our numbers class 6th
NCERT Solutions for Class 6 Maths Chapter 1: Knowing Our Numbers
Objective Tests of Knowing our Numbers part01
Objective Tests of Knowing our Numbers part02
Objective Tests of Knowing our Numbers part03

Introduction to Numbers
 Understanding the Number System: This blog post will serve as an introduction to the number system, explaining the different types of numbers and their roles in mathematics. It will provide an overview of natural numbers, whole numbers, integers, fractions, decimals, and more.
 Exploring Place Value: Here, we will delve into the concept of place value and its significance in understanding and representing numbers accurately. We will discuss how each digit’s position affects the value of a number and provide examples to illustrate the concept.
 Number Forms and Notations: This section will explore the various forms and notations used to represent numbers, such as standard form, expanded form, and word form. We will explain how each notation is used and provide examples to help students grasp the different representations of numbers.

Whole Numbers and Their Properties
 Introduction to Whole Numbers: In this blog post, we will introduce whole numbers and explain their characteristics. We will define what constitutes a whole number and highlight their importance in counting and basic arithmetic operations.
 Properties of Whole Numbers: Here, we will explore the properties of whole numbers, such as the commutative property (changing the order of addition or multiplication does not affect the result), associative property (grouping of numbers in addition or multiplication does not affect the result), and distributive property (multiplication distributes over addition). We will provide examples and explanations to help students understand these properties.
 RealLife Applications: This section will focus on the practical applications of whole numbers in daily life. We will provide relatable examples, such as counting objects, measuring distances, and budgeting, to help students understand the relevance of whole numbers in realworld scenarios.

Integers and Their Operations
 Understanding Integers: This blog post will define integers and their relationship with whole numbers. We will explain that integers include both positive and negative numbers, as well as zero, and discuss their significance in representing quantities and positions on number lines.
 Addition and Subtraction of Integers: Here, we will explain the rules and techniques for adding and subtracting integers. We will cover concepts such as adding or subtracting integers with the same sign, different signs, and zero pairs, providing stepbystep explanations and examples to help students master these operations.

Fractions and Decimals
 Introduction to Fractions: This blog post will introduce fractions and their components, including numerators and denominators. We will explain the concept of a fraction representing a part of a whole and discuss different types of fractions, such as proper fractions, improper fractions, and mixed numbers.
 Converting Fractions to Decimals: Here, we will explain the process of converting fractions to decimals and vice versa. We will provide stepbystep instructions and examples to demonstrate how to convert between these two forms of representation

 Mastering Math Made Fun: Engaging Ratio and Proportion Worksheets for KidsNCERT Solutions for Class 6 Maths Chapter 12 Ratio and Proportion comprises exercisewise solved questions of Ratio and Proportion concept

Introduction to Ratio and Proportion
 Introduction: In this blog post, we will introduce the concept of ratio and proportion, explaining how they are fundamental mathematical concepts. We will discuss their importance in various reallife scenarios and emphasize their relevance to children’s mathematical understanding.
 Why Ratio and Proportion Matter: This section will delve into the practical applications of ratio and proportion, such as cooking, measurement, and financial planning. By showcasing these examples, we aim to demonstrate why understanding ratio and proportion is crucial for children’s daily lives.
 Making Learning Fun: Here, we will explore the significance of engaging worksheets in making math enjoyable for kids. We will discuss how incorporating interactive elements and visual aids in ratio and proportion worksheets can capture children’s attention, foster their interest in math, and enhance their learning experience.

Benefits of Using Engaging Worksheets
 Engaging Visuals: This section will focus on the benefits of incorporating visually appealing elements in ratio and proportion worksheets. We will explain how colorful illustrations, graphs, and charts can help children visualize and grasp mathematical concepts more effectively.
 HandsOn Activities: Here, we will discuss the advantages of including handson activities in the worksheets. We will provide examples of interactive exercises that involve manipulatives, such as blocks or measuring tools, to make abstract concepts more tangible and engaging for kids.
 Gamification Techniques: In this part, we will explore how turning worksheets into games can motivate children to actively participate in math learning. We will suggest gamification strategies, such as creating challenges, incorporating rewards, or using online math games, to make the process of practicing ratios and proportions exciting and enjoyable.

Creating Engaging Ratio and Proportion Worksheets
 Understanding Children’s Learning Styles: This section will emphasize the importance of considering different learning styles when designing ratio and proportion worksheets. We will explain how catering to visual, auditory, and kinesthetic learners can enhance their comprehension and retention of mathematical concepts.
 Incorporating RealLife Scenarios: Here, we will provide examples of reallife situations where ratios and proportions play a significant role. By including relatable scenarios, such as recipe measurements or scaling drawings, we can make the worksheets more relevant and relatable for kids.
 Encouraging Critical Thinking: In this part, we will discuss strategies for designing worksheets that promote critical thinking and problemsolving skills. We will suggest openended questions, puzzles, or challenges that require children to analyze and apply ratio and proportion concepts creatively.

Tips for Using the Worksheets Effectively
 Setting Clear Objectives: This section will emphasize the importance of setting clear learning goals and objectives when using ratio and proportion worksheets. We will explain how clearly defined objectives help guide children’s learning and provide a sense of purpose and direction.
 Individualized Instruction: Here, we will discuss the significance of adapting the worksheets to meet the needs of individual students. We will explore strategies for differentiating instruction, such as providing additional support or challenge options, to cater to various skill levels and learning styles.
 Tracking Progress: This part will focus on the importance of monitoring and assessing students’ progress using the worksheets as a tool. We will suggest methods for tracking their achievements, identifying areas that require further attention, and celebrating their growth and improvement.

Fun Activities to Supplement Ratio and Proportion Worksheets
 Math Games and Puzzles: In this section, we will suggest a variety of interactive math games and puzzles that reinforce ratio and proportion concepts. We will provide examples of board games
Frequently Asked Questions on NCERT Solutions for Class 6 Maths Chapter 12
Q1 Explain the golden ratio covered in Chapter 12 of NCERT Solutions for Class 6 Maths.Two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities.Q2 What are equivalent ratios covered in Chapter 12 of NCERT Solutions for Class 6 Maths?When the given ratios are equal, then these ratios are called equivalent ratios. Equivalent ratios can be obtained by multiplying and dividing the numerator and denominator with the same number. For example, ratios 10:30 (=1:3) and 11:33 (=1:3) are equivalent ratios.Q3 Where can I get the NCERT Solutions for Class 6 Maths Chapter 12?NCERT Solutions, available here, is the best reference guide for students to score well in the annual exam. These solutions contain detailed explanations for each and every concept covered in the chapter. Students who find it difficult to solve exercisewise problems can access the solutions which are available online to get their doubts cleared instantly. 