Equivalent fractions

This unit is for grade IV. In this unit we are going to define equivalent fractions. By Equivalent fractions we mean that the two fractions are equal if when we convert them to the lowest terms, results in  the same fraction. Let us take some example. If we want to check if 3/12 and 6/24 are equivalent fractions or not, then we first convert each of them in their lowest form, by dividing the numerator and the denominator by the same number,(  which is their GCF ). Now we check if the two resultant fractions are same, the given fractions (how to do fractions) are equivalent.
So we first find the GCF of (3 and 12 ), which is 3. Now in 3/12, we divide both numerator and the denominator by 3 and get
(3÷3) /( 12÷3)
= ¼
Now we take the fraction 6/24 and find the GCF of (6 and 24 ), which is 6. Now in 6/24, we divide both numerator and the denominator by 6 and get
(4÷4) /( 24÷6)
= ¼
Thus in both the cases, the result is ¼. Thus the two fractions are equivalent.
Now let us learn  How to find the equivalent fractions for the given fraction?
Let the given fraction is 3/5, we first multiply both the numerator and the denominator by  any number say 2, we get
= (3 * 2) / ( 5 * 2)
=6/10
In the same way  we go on multiplying the numerator and the denominator by the same number, we  will get the series of the equivalent fractions for the given fraction number. We proceed as follows :
= (3 * 3) / ( 5 * 3)
= 9/15
Or = (3 * 4) / ( 5 * 4)
= 12/20
So 6/10, 12/20,  . . . .  are all equivalent  fractions of  3/5

In upcoming posts we will discuss about Multiplication facts and tables and How to tackle Decimals and Percentage problems? Visit our website for information on syllabus of economics for ICSE class 12

Negative numbers

Hello students, in this session we are going to discuss the negative numbers for Grade IV. Numbers are helpful to count anything. And in mathematics we used so many types of numbers; for example real, positive, negative, whole, prime, odd and even and many more. We cannot imagine the calculation in mathematics without the help of numbers. In mathematics we also use the negative numbers, now the question is that how to define negative numbers, let’s take a look. They are the numbers that are less than the zero.
For example : - -1, -4, -5, -9, -75 these are the negative numbers. (Also improve your skills by reading Negative Correlation Coefficient)
In the negative numbers we do not include the 0. The negative numbers are denoted by this ' - ' symbol. This symbol is called the Minus sign or symbol and we used this symbol when we need to show that we have negative numbers for example -7, -85, -124, -5543, if you want to show the negative numbers then it is necessary to apply the sign or put this sign just before the number. (also play adding and subtracting positive and negative numbers worksheet)
Negative numbers are the just opposite of the positive numbers. We can express the negative numbers by taking an example : - -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
In above number line the numbers that are left to the zero are known as the negative numbers. And those numbers that are right to the zero are said to be the positive numbers.
In negative numbers we can also perform any binary operation such as addition, subtraction, multiplication and division. Mainly negative numbers are used in the accounting and science to show the less than zero values.


In upcoming posts we will discuss about Positive numbers and Estimates of Measurements in Grade V. Visit our website for information on West Bengal council of higher secondary education syllabus

Understand Negative Numbers and their Operations

Children, Earlier we have studied about 3 digit subtraction with regrouping and today i am going to tell you the most simplest and a bit complex topic- Numbers which comes under Gujarat Board Syllabus. When we start studying math we will first introduced with number. Numbers can be positive or negative.  Positive numbers are 1, 2, 3, 4, 5, and so on. Positive sign (+) or no sign means the number is positive. A grade IV student is aware of zero’s concept and can solve math problems related to it, Whole numbers starts with 0, 1, 2, 3, 4, 5, and so on. Numbers lesser than zero (0) are called negative numbers. A negative sign (-) implies that the number is negative. Negative numbers are -5, -4, -3, -2, -1, and so on.
In case of negative numbers -5 is less then -4 and so as -4 is less then -3.
It is always easy for a grade IV student to perform some operation on positive numbers. Because it is easy to add, subtract, multiply or divide them. But in case of negative numbers those operations causes some problems for them. Because of the negative sign attached with them and it is always important to take extra care of them. Because while performing operations if we unknowingly change the sign than the complete answer is wrong.(want to Learn more about Negative Numbers ,click here),

Now we will discuss operations that can be performed on negative numbers.

Addition:
Adding a negative number is not easy as adding a positive number. While we add positive number we simply plus them for example: 5 + 6 = 10 but in case of negative numbers we couldn’t do this thing.
Let’s take an example to understand this:
Add 5 to -3.
We can do this by just putting + sign between them. It is good practice to use parentheses  That is
5 + (-3) = 2
Suppose if we -5 + 3 then. This time our answer we be changed. Now we have answer -2 instead of 2.

Subtraction:
When we perform subtraction operations the sign of the number after the operation sign (-) gets changed.
Example:
            Subtract 3 from 6.
                        +6 – (+3)
Now the sign of +3 will be changed into – sign. Se the answer will be positive 3.
Now suppose we have -6 and +3 and then the result will be
                        (-6) – (+3)
                        -6 -3 = -9


Multiplication:
While multiplying negative numbers we need to always remember few points:

1. If negative numbers are even in sign then the result will be a positive number.
2. If negative numbers are odd in sign then the result will be a negative number.

Example:
            -3 x -4 = 12
            -5 x  2 = -10

Division:
Similarly like multiplication we need to remember some issues while performing division operation. There are four points listed below:

1. If we divide positive number from a positive number result will be positive.

                  Example: 6/2 = 3

2. If we divide negative number from a positive number result will be negative.

                  Example: -8/4 = -2

3. If we divide positive number from a negative number result will be negative.

                  Example: 12/-3 = -6

4. If we divide negative number from a negative number result will be positive.

                        Example: -25/-5 = 3


Now you all are aware of the concept of negative numbers and their operations. Do practice this with interest and I am very much sure you will find it very easy and if anyone want to know about Properties of odd/even numbers then they can refer to internet and text books for understanding it more precisely. Read more maths topics of different grades such as Steps in problem solving in the next session here.

Numbers in Grade IV

Hello friends, in today's session we are going to learn about the number sense – positive numbers and negative numbers. And of course we are going to do some addition and subtraction on these numbers. So let's start without wasting any time.

What is a number?

A Number is just a mathematical term used for counting and measuring. The definition of number has been long extended from so many years to include various new topics in it.

Mathematical operations are some steps that we follow which include one or more numbers (read this for more information) as input and give a number as an output. The most simple and basic operations that we perform are addition, subtraction, multiplication and division. Every number is either positive or negative, and has a sign in front of it. The sign before the number decides whether it is positive or not.

A positive number in general is a number greater than zero.

For Example – 1, 2, 3, 10, 100, 1000, 2.9, 3.14, 0.5 etc.

What we have studied in mathematics in our previous grades, we were considering the positive numbers.

A natural number which is not positive is negative. In a more proper way we can say that any real number which is less than zero is known as a negative number.

For Example – -1, -2, -3, -10, -100, -1000, -2.9, -3.14, - 0.5 etc. In general it is used to represent the absence or loss of something. The Negative number is written with a minus sign “-” in front of it.

To understand it more properly we can use a number line.

like in this number you can see that at the center we have a zero and the same numbers on both sides of it, but with different signs. The numbers which are right to the number line without any sign are known as the positive numbers while the numbers to the left of the zero with minus sign are known as the negative numbers.

We should also know that the numbers which are farther to the right are greater than each of the number to its left and similarly the one farther to the left is smaller to the one from the right.

For positive numbers the number with with large magnitude is greater, but for the negative number the number higher in magnitude is less than the one lower in magnitude.

Like if we take example for positive number the number 8 is greater than 5, we represent it as 8 > 5.

For negative numbers minus 8 is considered less than minus 5, and we represent it as – 8 < - 5.

But when we take a positive and a negative number, we should remember that we do not take the magnitude into consideration, the positive number is always greater than the negative number.

Like if we take -8 and 5 into consideration, then 5 will be greater than – 8, for second example we take -5 and 8, then 8 will be greater than -5. and we represent these two situations as 5 > - 8 and 8 > - 5.

Now we have compared both the numbers, so we know which one is greater and which one is smaller. So we move forward to the absolute values of these numbers. The absolute value in general means how far the number is from zero on the number line. The absolute value of any number is always positive. Like in general if we have to see the absolute value of n, then we represent it by putting two vertical bars across it : |n|.

you will better understand it with the help of an example.

|6| = 6

|-0.004| = 0.004

|0| = 0

|3.44| = 3.44

|-3.44| = 3.44

|-10000.9| = 10000.9

So, now it would be very much clear what an absolute value is.

Now we are going to perform some simple arithmetic operations on positive numbers and negative numbers.

For Example -

2 + 5.7 = 7.7

4 + 8 = 12

14 + 32 = 46

80 -12 = 68

42 – 4 = 38.

This is what you have already learnt, so let's now move to the arithmetic operations on negative numbers. which is of more importance as this topic is new for you. Let's start with the addition process.

The addition of two positive numbers is similar to the addition of the two negative numbers like

-4 + -5 = -9

(-$420) + (-$200) = -$620

The concept is like when two profits are added together to make bigger profit same way two losses are added to together to represent the whole loss. While adding a positive number and a negative number we should take the problem like two positive quantities being subtracted.

For Example –

8 + (-3) = 8 – 3 = 5.

$420 + (-$200) = $220

So for understanding it practically we can say it as the loss being subtracted from the profit. In this case the profit was higher so our total was also a profit.

Now what if the loss is greater than the profit. Then our result will also be a loss.

For Example -

-8 + 3 = -5, as said above it is negative.

(-$420) + $200 = -$220

Now we move over to Subtraction

For Example -

5 – 8 = 5 + ( -8 ) = -3

In general we can say that subtraction of positive number is the same thing as the addition of two negative terms.

And

( -3 ) – 5 = ( -3 ) + ( -5 ) = -8

For subtracting a positive number, it could be considered as the addition of positive numbers.

3 - (-5) = 3 + 5 = 8

and (-5) - (-8) = (-5) + 8 = 3.

(-$420) - (-$200) = -$220

(-$200) - (-$420) = $220

Now you will be able to perform some basic operations on it.

So let's now move towards the another topic which is negation.

A negation in general is a referred to as a reverse of our positive number. If we take 3 as our given number then -3 will be its negation. What we you should keep in mind while negation is that the sum of the given number and its negation term is always equal to zero. In general algebra we write it as

x + -x = 0.

It has two properties -

1. the negation of 0 is always 0
2. the negation of any number will be its corresponding positive number.

Let's move to the reciprocal of negative numbers.

Reciprocal of a positive or negative number is obtained by switching the numerator and denominator, but the sign of the new fraction that is formed always remains same.

For Example -

What is the reciprocal of -2/7?

We just switch the numerator and denominator, and keep the same sign then our answer is -7/2.

Now after solving them you will be very much capable of doing the math word problem help.

1. Steve has taken $27 from his pocket from the total of $100 which he was having, so now what is left with him?

Total is $100, from which he has taken $27, so now the left money is $100 - $27 = $73.

2. Find the difference in height between the top of a hill 973 feet high and a crack caused by an earthquake 79 feet from the ground.

The total height is 973 feet, from which we have reduced the 79, so now it becomes 973 – 79 = 894.

3. The given data shows the temperature of a city for 5 different days, find the lowest temperature.

-12°, -8°, -3°, 6°, -15° among these.

The lowest among the following is -15°.

4. Solve y = 5 - (3.750 - 0.500) - 2.375 ?

by doing simple subtraction we get y = 4.125.

5. In Buffalo, New York, the temperature was -14°F in the morning. If the temperature dropped 7°F, what is the temperature now?

So the temperature now will be (-14) + (-7) = -21. so the temperature would be -21°F.

6. In the Sahara Desert one day it was 136°F. In the Gobi Desert a temperature of -50°F was recorded. What is the difference between these two temperatures?

The temperature would be 136 - (-50) = 186, which is the answer.

7. John has $36.00 to spend. He bought a CD player for $26.75. How much money does John have left?

The left money would be $36.00 - $26.75 = $ 3.25.

8. Mary overspent this month and her bank account has a negative balance of $27.00. The bank charged her $25.00 for overspending. What is the new balance in her account?

She already has a balance of - $27, with this the bank reduced it by -$25, so the remaining balance would be (-27) + (-25) = -52.

Now I can say that you would be able to understand what Numbers are and how to perform some simple operations on Negative Numbers and Positive Numbers.

In upcoming posts we will discuss about Fractions and Decimals in Grade IV and Tools to record observations. Visit our website for information on CBSE board fashion studies syllabus for class 11