Finding the Cuberoot of a perfect cube – An easy way

Earlier in our posts I had written about how to find the Square root of a perfect square number in an easy way. Today we are going to show how to find the cube root of the perfect cube easily without any stress. However to find the cube roots really fast you need to remember the Cube Roots of numbers from 1 to 9 as given in the below slide

Do try this method at home and let us know what you think about it..download the free worksheets to practice the method from our free download section

Send us your views on the article. write to us on a2yacademy@outlook.com and let us know what you would like to learn through our blog…

Multiply any Number using this method

Earlier we have written and shown how you can easily multiply the algebraic expressions..We can use the same method for solving the multiplication problems of any two or three digits number..This method will come in handy when children are trying to solve the questions which contain 3 ,4  or more digits numbers..though this works for 2 digits as well..

Here is another example

Try the free worksheets and see whether this method works for you. You can download the worksheets from our free download section.

Do write to us and let us know whether this blog has been helpful for you. Our email id is a2yacademy@outlook.com..

How to multiply quickly – few tricks to remember

In our last post we have learnt how to make the multiplication tables from 1 to 100 in an easy manner. How ever  as our kids go to higher grades they need to multiply bigger numbers. In this post today we are going to see how we can do  the  multiplication quickly and without using the calculator. This becomes extremely useful for children when they have to go for the competitive examination.

Multiplication by 5

Lets see how we can easily multiply any number with 5. Example 28×5

Step 1 – divide the number by 2 i.e  make 28/2 = 14

Step 2 – Multiply it with 10 so your answer will be 140

Explanation – 5 is half of 10 so when we multiply a number by 5 we are actually multiplying it by 10/2

Lets take another number  25

Step1 – half of the number is ( it will not be a whole number )  25/2 = 12.5

Step 2 – multiply it with 10 so your answer will be 125

This can be extremely useful when we have to multiply slightly bigger numbers as well.

For example : 122×5 = 122/2= 61×10 =610

Multiplication by 25

Lets see how we can multiply a number by 25 quickly

Step 1 : divide the number by 4

Step 2- multiply the number by 100

Explanation: 25 is nothing but  1/4 th of 100 or it can be written as 100/4

lets take couple of examples :

28×25 

divide 28 by 4 which is 7

multiply 7 by 100

Answer is 700

Lets take another example

35×100

35/4 =8.75 ( 35 when divided by 4 will give answer in decimals)

8.75×100= 875

Lets take one more example

432×25

432/4 = 108

108×100= 10800

Multiplication by 50

Step 1 : divide the number by 2

Step 2- multiply the number by 100

Explanation: 50 is nothing but  1/2  of 100 or it can be written as 100/2

lets take couple of examples :

88×50

88/2=44 ( divide 88 by 2)

44×100 =4400  is the answer

another example : 762×50

762/2 = 381

381×100

lets take an example where we can not divide the number by 2 and we get the answer in decimal

lets take   35×50

35/2= 17.5

17.5 x 100= 1750

Try out these with few numbers yourself and let us know whether you found this useful. Mail your queries to us on a2yacademy@outlook.com or just leave a comment for us and we will try and bring to you more such  tricks to make your life a bit easier.

 

 

Think out of box – Learn to solve multiplication in Algebra

I remember the time when I was taught Algebra in school..it was so confusing that during my midterm exam I flunked.. It was X did this so find  Y..I just couldn’t relate to these X’s and Y’s which used to zoom in on the black board ..however the midterm exam debacle woke me up to the fact that I need to find a way to understand these X’s and Y’s that seem to be related to each other but somehow I never could see that relation. I am sure a lot of children even today might be finding it difficult to solve these equations. Addition and subtraction will be easy enough process however when we have to do the multiplication  of the Algebraic terms  it becomes difficult..To solve the multiplication please check the below 2 illustration. This clearly shows the easy way of dealing with the multiplication in Algebra

Another Example:

Download the two free practice sheets from our download section or take out your algebra book and try out this method for solving the questions..Post your comments in our comment section or write to us on  a2yacademy@outlook.com

Finding the Square Root of a number which is a perfect square

Mathematics can be an amazing subject if we can observe and find some relationships between numbers and find a solution. Today I am going to write about finding the square root of the number..

What is the square of any number?

The answer to this question is when we multiply the number by itself we get the square  of the number. For example if we multiply 4 with 4 itself we get 16.  This is nothing but creating  4 groups of 4 objects and putting these together.

so 4×4 =16 and this can be written as 42.

The square root is just the reverse of  finding the square. to find the square root of any number we need to find the number which multiplies by itself to give us that big number. In this post I am going to show how to calculate the square root of any perfect square if you remember the squares between 1 to 9. To help memorize I am giving you the squares of the numbers between 1 to 9

12 =1, 22 =4, 32 =9, 42 =16, 52 =25, 62 =36, 72 =49

82 =64, 92 =81, 102 =100

Once we know this we can start our calculations of finding the square root of any perfect square.

Lets take an example of 3969.

The first thing to do is to divide the number in 2 parts. Keep the right most two digits ( here that will be 69) and keep the remaining digits in one group.

In the next step find out the squares that end with 9. Here we have two such squares

32 =9

72 =49

so for the unit place of our answer we have two choices 3 and 7.

Now take the other portion which is 39. Find out the number that is a perfect square and is nearer to 39. From our table we see that such number is 62 =36 as 72 =49 is bigger that 39.

So we have the answer as 6 for this. However for the unit place we still have the 2 choices 3 and 7. To find which one is the correct choice take the answer that we just got i.e 6 and multiply it with the next number which is 7

6×7 =42  and 42> 39 so for our unit place we will go for the smaller number which is 3 and we have the answer as 63

The below flow chart makes it more clear

now we will take another example 7396

 

Few things to remember 

  • when you multiply a number it has to be the number you got as an answer for the ten’s place
  • The number needs to be multiplied by the next number i.e if you have found the number for the right group as 7 then it needs to be multiplied by 8.
  • You should remember your tables from 2 to 10 perfectly. ( to practice on the tables you can buy my practice sheets from the shop)
  • While comparing the number that you have found through multiplication compare it always to the group that you have formed on the left side
  • If the number after the multiplication is bigger than the number on the left then select the smaller number if it is smaller then select the bigger number.

Download the free practice sheets from our download section  and try to find the answers… Do write to us on a2yacademy@outlook.com.

 

 

 

 

 

 

 

 

Multiplication and making tables upto 100 – an easy way

Most of the children find the multiplication daunting and remembering the tables till 20 is always a challenge. However we can make the tables up to 100 by using a very simple method of place value. It can be really easy and a child only has to remember the tables upto 9 to do this.

Lets take an example of number 12

12 x8 =

12 can be broken into 10+2

so we are actually multiplying 10+2 by 8.

now it will become

10×8+2×8 = 80 + 16 = 96

Lets take a bigger number and try to do the same. Lets take an example of 47

47×7 =

Now  47 = 40+7

40×7+7×7

we know 4×7 =28 so write for 40×7  28 and then put a zero before it so the answer for 40×7  becomes 280 and we know 7×7 is 49

so our answer is

40×7+7×7 = 280+49

to add these together see how much you will need to make 280 to 300 in this case it is 29. We take that away from 49 and so it will be

280+20+29 = 300+29 =329

Easy to do isn’t it?

Practice it and you will be able to do these multiplications in under 30 seconds..

I will soon be posting the worksheets for the same.

Learning Multiplication- making a table to understand

All of us have to struggle with the multiplication tables..specially young kids who have to solve the questions based on the concepts of multiplications.. How nice it will be to do an activity and learn the tables at least the basic ones. I struggled with the tables as a child and wanted to make it really simple for my children and I landed on this idea of making the tables with the blocks so that they can see what it means when I say 2 times 2 is 4. You can see in the below pictures my sons enjoying themselves making the tables.

 

Once we had done with making the tables till 10 we were able to move to the colouring and making the table method on the paper..you can download the two free worksheets for the same from our free download section.

 

I found that this method worked really well with my children and I have been successful in teaching them tables upto 10.

There are various shortcuts for teaching the multiplication tables but I feel that once the concept sinks in by actually building it in 3 Dimensional way then learning the tables becomes very easy.

Another way of making them to memorize the same is teaching them skip counting and repeated addition method.However for the bigger numbers these can be slightly difficult for the kids..

Let me know whether this method helped your child learn the multiplication tables faster..

 

 

 

Science Fun : Lets learn Density

Let me first introduce myself. I am a mother of 6 year old very energetic twin boys and started this as an attempt to make kids interested in science. To make them understand density I made a simple coloured rainbow with liquids in a small glass with the materials available in my kitchen. The result was as shown below and the kids loved it

Lets first do the experiment and then talk about the physics behind it. here is the list of the materials that I used

Honey

Oil ( any cooking oil can be used)

water + food colour

dishwashing soap

Rubbing alcohol

If you don’t want to use these the same experiment can be done making the sugar solutions with different food colours.

The sequence was

Pour honey first, then liquid soap, after that I poured coloured water, then pour oil and finally the rubbing alcohol.

you can pour in different order as well but the liquids will settle down as shown below. Enjoy your colourful creation without disturbing it.

The end result is the picture that I posted on top. Now let’s understand why it happens? However before we do so lets also see what happens when we throw a straw in the bucket of water and when we throw a stone in the bucket of water. The stone sinks because it is heavier than water but straw floats because it is lighter than water. The same principle applies here..Honey is heavy so it settles in the bottom whereas alcohol is the lightest so it comes to the top.

Another concept that is very closely related to the concept of density is the concept of mass and weight.

Do you know what is the difference between Mass and Weight?

If you ask this question to people the common answer that you will get is that they are the same. However they are not..though these are closely related with each other.Weight is a  force which is felt as we experience the gravitational pull and will change if we go to the moon or to the outer space  whereas the  Mass is something that will remain constant wherever you go.

Density

Which is heavier 1 Kg of iron or 1kg of feathers?

Did you fall for that and said Iron? Both are 1 Kg and hence weigh the same but you will need a lot of feathers to make it as equal to 1 Kg of iron. 

Lets also find out what happens if we put 1kg of  iron bars and 1 kg of feathers in two boxes?  which box will be heavy to lift? Of course the one with the iron bars in it.  The same volume of feathers will be much lighter as feathers are not as dense as iron . Mass is actually how much stuff is actually there in a thing.  So now we can define density as the amount of mass in a specified space.

The unit of density is Rho and is arrived at dividing the mass of an object by the volume

Density = Mass/Volume

ρ=m/V

The standard measuring unit for the same is kilogram per cubic meter. This is so that when scientists are talking to each other they can understand and relate to each others discoveries.

If you have any questions you can post it as comment and we will try to answer it to the best of our abilities or you can mail us your queries a2yacademu@outlook.com