An Introduction to Playing with Numbers Class 6
Mathematics is a subject that helps to increase one’s reasoning ability and challenges their problem-solving skills to a certain extent. It is a medium that helps to route our critical thoughts accurately.
However, many of us find specific chapters tricky and confusing, such as permutation and combination, geometry and playing with numbers, etc. It happens because we lack in-depth knowledge about these concepts.
However, if you are dealing with problematic mathematical topics seek playing with numbers Class 6 NCERT solutions! We hope the solved answers will be beneficial for the exam guidance.
Let’s start gathering knowledge!
Solved Problem on Playing with Numbers Class 6 - Exercise 3.7
If you are studying class 8 playing with numbers, we would advise you to go through the following solutions. Ace your studies with these exercises!
1. Mohanty purchases two bags of mangoes, weighing 45 kg and 25 kg. Point out the maximum amount of weight for measuring the number of mangoes (number of times).
Ans: Since the weight of mangoes in two bags are present = 45 kg and 25 kg.
The maximum amount of weight will be = H.C.F. of the two bags (45, 25)
45 = 3 * 3 * 5
25 = 5 * 5
H.C.F. = 5
Therefore, 5 kg is the maximum amount of weight for two bags of mangoes (the exact number of times).
2. Two boys start stepping off from an identical place. The steps amount to 63 cm, 70 cm and 77 respectively. What will be the minimum distance that each of them should cover so that all of them can complete the entire distance? (Problem: Playing with numbers)
Ans: 1st boy’s step is = 63 cm,
2nd boy’s step is = 70 cm,
3rd boy’s step measures = 77 cm.
L.C.M. of 63, 70 and 77 using the division method
(Image to be added soon)
∴ L.C.M. = 2*3*3*5*7*11 = 6,930 cm
Therefore, the minimum required distance will be 6,930 cm to cover the entire distance.
3. Suppose there are 3 tankers, containing 50 litres, 45 litres and 60 litres of oil, respectively. Find out the highest capacity that measures the oil of all three tankers (number of times).
Ans: Maximum amount of capacity measures through = H.C.F. of (50, 45, 60)
50 = 2*5*5
45 = 3*3*5
60 = 3*2*2*5
∴ H.C.F. = 5 (because it is the common factor)
So, the maximum capacity of the tanker will be 5 litres.
Tips to Tackle Mathematics Problems Regarding Playing with Number Class 8
You may find yourself under a lot of stress when you face complex math problems. However, you can reduce these problems through the following tips:
Try to finish your chapters along with the class. Leaving things for the last minute can worsen your condition. Solving problems related to numbers daily can help you gain confidence. You can also learn from NCERT Solutions for the class 8 maths chapter playing with numbers to score better!
Also, you should try to memorise all the vital formulas before you finish your studies. Keeping the formulas in mind will help you solve the problems quickly. Try recalling the techniques every day apart from learning Class 6 maths playing with numbers before you call it a day to score well in maths.
Students often assume mathematics as a difficult subject. However, you can score better grades in maths if you understand all the concepts clearly.
If you are facing any problem with difficult topics, try going through NCERT Solutions for Class 8 Maths Chapter 16 Exercise 16.2. You can also visit and learn from our live classes and get detailed solutions for playing with numbers Class 6 CBSE.
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In Mathematics Class 8, playing with numbers is one of the most important concepts. As the name suggests, the topic is all about numbers and their properties. There are 4 different types of numbers in mathematics. These are natural numbers, whole numbers, integers, and rational numbers.
Natural numbers are the numbers that include all positive integers excluding 0. Whole numbers are similar to the natural numbers but they also include 0. Integers include negative numbers, positive numbers and 0 also. And rational numbers are nothing but fractions in the form of a/b where b should not be equal to zero.
Read the full article to know more about playing with numbers. Here we will discuss the definition of play with numbers, the General form of numbers, Games with numbers, tests of divisibility, and solved examples in the sections below.
As it is suggested by the name the chapter is all about numbers. You can play various games with numbers. The names of the game which we are going to play in this article are reversing the digits of a number, the general form of the number, letters for digits, and tests of divisibility. The process in detail is discussed here.
Number in General Form
Any number can be represented in simple form following the simple procedure. The only thing to identify a number is to identify the position of each digit in the given number. Now multiply the position of the digit, i.e tens digit 10 * number and add the remaining digits. If we take it as an example AB, take a two-digit number AB. Its general form will be 10 * A + B. The result after applying simple multiplication and addition will be the original number.
The first step is to reverse the digits of the number. Now add the original number, and reversed number. If you divide the number which you got after sum by 11, the remainder will always be zero. You can play this game with either a two-digit number or a three-digit number. But remember here that for three-digit numbers, the procedure will be different.
Letters for Digits
Here we are going to deal with two or more numbers and have operators among them. Just perform these operations and by trial and error method find out which number suits an expression that satisfies the equation. It is one of the most interesting games to play with numbers.
Tests of Divisibility
The test of divisibility is if the given list of some numbers is divided by the particular number or not.
Number Puzzles
Playing with different types of numbers will increase your problem-solving skills as well as your reasoning skills. Here you just have to fill the given numbers in the grid or magic triangle or any other by satisfying the given conditions.
Solved Examples
1. Write the following list of numbers in the generalized form.
a. 145
b. 79
c. 67
d. 777
Ans: Given numbers are 145, 79, 59, 895
The general form of 145 is as follows:
145 can be expressed as 100 + 40 + 5
1 × 100 + 4 × 10 + 5 is 145.
79 = 70 + 9
= 7 × 10 + 9
67 = 60 + 7
= 6 × 10 + 7
777 = 700 + 70 + 7
= 7 × 100 + 7 × 10 + 7
2. Prove that the following numbers satisfy the method of reversing the digits.
a. 35
b. 99
Ans:
Here Given number is 35. Hence the reverse of 35 would be 53.
Now if we will add these numbers then
35 + 53 = 88
Here 88 is the number that we get by adding the number and the number which we get by reversing its digits. Here we can see that 88 is exactly divisible by 11.
88= 11 × 8
Hence the method for reversing the digits is proved here.
Here Given number is 99.
Hence the reverse of 99 would be 99.
Now if we will add these numbers then
99 + 99 = 198
Here 198 is the number which we get by adding the number and the number which we get by reversing its digits. Here we can see that 88 is exactly divisible by 11.
198= 11× 18
Hence the method for reversing the digits is proved here.
FAQs on Playing with Numbers
1. What Is The Dual-step Addition And Subtraction Method In Playing With Numbers?
You can use double-step addition and subtraction method to tackle complex mathematical problem related to playing with numbers. In this method, you need to first attempt which is easy and go for the difficult ones later on. The subtraction method works similarly, removing at first what’s easy and so on.
It helps you when you struggle to add numbers while counting or reducing more than three digits together. For instance, if you need to find the sum of 392 and 88, let’s learn how to find it using this method.
= (392 + 8) + (88 - 8)
= 400 + 80
= 480
2. How To Use Reduction From 1000 Method To Solve Mathematical Equations Quickly?
A quick and easy way to solve problematic mathematical questions is through reducing a number from 1000. The technique will help you to solve four-digit numbers with ease, its ideal for people learning playing with numbers class 8.
Take a number 1000; subtract the first two numbers from 9, and the last digit from 10. You can use this method with integers of 10,000, 1,00,000 and other going through this pattern.
For instance, suppose you need to solve 1000 – 453, then the steps will be:
= 9 – 4 = 5
= 9 – 5 = 4
= 10 - 3 = 7
= 547
3. What Is L.C.M. And H.C.F. In A Mathematical Problem Dealing With Playing With Numbers Class 8 CBSE?
L.C.M. stands for the least possible number, whereas H.C.F. stands for the highest common factor in the chapter playing with numbers. The least expected digit which completely divides a number is known as L.C.M., whereas the maximum times a number gets divided completely is known as H.C.F.
For example, suppose there are three numbers 3, 11, 66 (11*6) present. Therefore, the L.C.M. of these numbers will be 11*3*6 = 198. Similarly, assume that there are three numbers, 10, 25, and 30, present. Hence, the highest common factor (H.C.F.) will be:
10 = 2*5
25 = 5*5
30 = 2*3*5
∴ H.C.F. = 5
4. How Can You Use Doubling And Halving Method For Multiplication To Solve Problems Quickly?
A method that you can use to solve problems faster is applying doubling and halving method in multiplication. If you are studying playing with numbers, this method will be beneficial.
You need to half the even number at first and double the other one later on. Students can use this method when the equation becomes challenging to solve.
For instance, you need to multiply 10*48; the steps will be:
= 20 * 24 (here the first number gets doubled, and the second one gets halved)
= 40 * 12
= 80 * 6
= 160 * 3
= 480 will be the solution.
5. How to apply the method of reversing the digits on any two-digit number.
Here Given number is AB. Hence the reverse of AB would be BA.
Now if we will add these numbers then,
AB + BA
Here AB+ BA is the number that we get by adding the number and the number which we get by reversing its digits. Here this number will be divisible by the 11. Hence by this method, you can do calculations for reversing the digits.