Fractions

Math Fractions are the numbers expressed in form of p/q where p and q are the whole numbers such that q <> 0.  Fractions are the part of a whole. It is expressed in form of numerator/denominator. If we write 3/5, here 3 is the numerator and 5 is the denominator. It means that a complete object is equally divided into 5 equal parts and 3, which is in the numerator represents that we are taking only 3 parts out of total 5 parts
If the fractions are written such that the denominators are same are called like fractions .In grade IV we as free math tutor online, will learn about solving fraction with same denominator.
Among 2/4, 3/6, 1/6, 3/7, and 1/9 which of them are like fractions?
   3/6  and 1/6 have the  same denominator , so they are like fractions.
Similarly the fractions which do not have same denominators are called unlike fractions.
On comparing like fractions, we must remember that fractions with smaller numerator are smaller than the fraction with larger numerator .
E.g.: Compare 3/7 and 2/7
As the denominators are same so  we only check the numerators and see that 3/7 > 2/7
If the numerators are same, then the number with a larger denominator is smaller
E.g. Compare 4/7 and 4/9
We find that thee numerators are same, so
  4/7 <  4/9
Let’s learn to solve fractions:
   Now let’s learn how to add or subtract the two like fractions.
  Add 3/5 and 1/5
Now we write it as
    = 3/5  + 1/5
Here the denominator are same so,
= ( 3 + 1 ) / 5
= 4/5 Ans It means that if 3/5 part of a whole and 1/5 part of a whole are added gives us 4/5 of a whole.

Similarly we can subtract like fractions too
1. Solve 5/9  - 2/9
     as the denominators are same and the fractions are like fractions, so we get
   = ( 5 - 2 ) /9
= 3/9 Ans
2. Subtract 3/5 from 7/5
  = 7/5 - 3/5
  = (7-3) /5
  = 4/5 Ans.

In upcoming posts we will discuss about Percents problems in mathematics and LCM, GCF, ratios and proportions. Visit our website for information on CBSE previous years 11 physics

Solve Decimals

Decimals are very significant in the world of mathematics, with the help of decimals we can solve any fraction up to its last limit, and in finding percentage they play a very important role. Decimal is generally a tenth part of any decimal number (you can also use decimal to fraction calculator). We can perform many operations on decimal numbers like addition, subtraction and division. We can represent fractions in decimals by just dividing the numerator by denominator. Now we will see how we can Solve Decimals problems (refer this for more info on decimals).
Example: Add 12.1 + 13.43
Solution: for addition we need to check the digits after decimal, if number of digits is equal then we can simply add them but if number of digits is not equal then we need to equalize the digit then only we can add. For equalizing the digit we can simply add the zero after decimal, as zero has no importance after decimal but you can put the zero after the digit not before the digit. So we can write the above equation as
12.10+ 13.43
=25.53
In this way we can add decimals. In the same way we can also do subtraction with the decimals.
We will see an example of multiplication of decimal number (improve your skills by finding, is a repeating decimal a rational number).
Example: multiply 12.3 with 3.2
Solution: like addition we don't need to equalize the number after. For the above question we need to firstly multiply 2 with 12.3 and then we will multiply 3 with 12.3, when we will multiply 2 with 12.3 we will get 246 and on multiplying 3 with 12.3 we will get 369 now we will add them like
  246
+369*
So we will get 3936 now we need to put decimal after two digits so required answer will be 39.36.
In the same way we can also perform division operations.

In upcoming posts we will discuss about Multiplication/division - inverse relationship and Order of Operations in Grade V. Visit our website for information on CBSE class 12 home science question bank

Fractions and Decimals in Grade IV

Hello friends, now we are going to learn about some of the chapters of mathematics for grade IV. Today we wil learn about decimals (read how to divide decimals), fractions and percents of the numbers. We will get introduced by composition and decomposition of numbers also.

First introducing with fraction and decimals. Fractions are the numbers which represent the part of a whole number. These are in the form of ratio of numerator to denominator. For example 3/4, 5/6, 2/3 etc. Just taking 5/6 in the consideration, then 5 is the numerator which tells us that the fraction represents 5 equal parts, and the denominator, 6, tells us that 6 parts equals a whole quantity. Fraction number shows the part of a whole number and they are used to represent some ratio and decimal form of numbers. Just like fraction, decimal is the number which also shows some part of the whole number. Decimal numbers are the types of fraction of a whole number and they also come from the fraction number. 

For example any fraction number can be converted into the decimal number and decimal also can be same. Say for example any fractional number is ½ then by simplifying it we can write it as 0.5. The simplification is as that let us multiply by 5 on both numerator and denominator terms and we gets 5/10 which on decomposing in the decimal becomes 0.5. So ½ is equivalent to the 0.5 which is half of any whole number.

Now discussing about percentage of a Number. Percentage is a way of representation of any number as a fraction of 100(per cent stands for per 100). It is denoted by “%” sign, for example 54 %( also read as “fifty four percent”) which is equal to 54/100 in the fraction and 0.54 in decimal. Percentages are used to show the quantity of any number that how large or small quantity is and the decrease & increase in the price. We have to find percentage of any number in this topic.

For example, 10% of 50 is 5 and this can be calculated by some methods. That is:

                10 / 100 * 50         = 10 * 50 / 100

                                                =  5.

The change in quantity is also represented in percentage in the form of how much the change has been detected in the quantity. So we first need to find the fraction of number and then convert that to the percentage. For example, an increase of $0.10 in money value of $ 2.75 is an increase by a fraction of 0.10/2.75 = 0.036. Expressed as a percentage, this is therefore increase of 3% in the money value. The concept of percentage is also applicable on percentage of a number, discounts, taxes, sales  percent of changes, and percent of comparison.

Compose and decompose numbers is also a topic in some of the real life topics. Compose and decompose numbers stands for breaking any number into as many combinations of groups as possible. Let's say 4 can be composed in four groups of one, two groups of three, a group of four or by many more other combinations.

In upcoming posts we will discuss about Number Operations in Grade IV and Problem solving strategies. Visit our website for information on CBSE board home science syllabus for class 11

Fractions in Grade IV

Hello kids, today I am going to tell you the basic overview of what we suppose to study in our IV grade mathematics syllabus. What we need to remember is daily little practice and hard work. The most important thing is that there is no alternative for hard-work. Few of the most important topics of IV grade mathematics are as follows:

1. Fraction
2. Addition and Subtraction
3. Multiplication facts
4. Division Facts
5. Decimals
6. Geometry – Area, circumference and perimeter
7. Arranging a number

Let's start with fractions topic of IV grade mathematics syllabus. Before going towards examples let's discuss about the basic terminologies behind fractions. First question comes in our mind is what is fraction? A number that can be represented as the ratio of two numbers known as fractions. For example : 1/3, here 1 is numerator and 3 is denominator. The condition for fraction is that denominator can never be a zero.

Here the number above the bar is stated as the numerator and the number below the bar is expressed as Denominator. As I mention that denominator value can never be a zero because if we are going to divide any of the value with zero then the loop will go on infinite times. Few of the concepts are:

For simplifying fractions following are some rules to follow:

Adding and Subtracting of a fraction is done by using this property: x/y + a/b = xb + ay / yb.
For Multiplying a fraction this property comes in an account: a/b x c/d = ac/bd

and for dividing a fraction we use this property: a/b divide c/d = ad/bc.

Now I am going to tell you the different types of fractions in mathematics. The three different types of fractions are Proper fractions, improper fractions and mixed fractions. Let's start with proper fractions:

Proper Fractions: In this the numerator value is lower in comparison to denominator.

Numerator < Denominator

For example ¾ is the proper fraction in which 4 > 3.

Improper Fractions : In this numerator is greater then the denominator. Denominator < Numerator

For example 3/2 is the improper fraction in which 3 > 2.

Mixed fraction : A mixed fraction is basically a whole number and a fraction combined into one "mixed" number. Example: 1½ (one and a half) is a mixed fraction

To convert an improper fraction to a mixed fraction, follow these steps:

1. Divide the numerator by the denominator.

2. Write down the whole number answer

3. Then write down any remainder above the denominator.

Another terminology is complex fraction: A complex fraction is a rational expression that has a

fraction in its numerator, denominator or both. Example to show the complex fraction: a/b / c/d. The sign / denotes the division of two numbers or variables. Simplifying complex fractions involves following steps: firstly student need to rewrite the numerator and denominator so that, they each form a single fraction. Now divide the numerator by the denominator by multiplying the numerator by the reciprocal of the denominator. In last step we need to simplify the rational expression.

We can also convert a mixed fraction to an improper fraction. To make this kind of conversion we need to follow these steps:

1. 1. 1. Multiply the whole number part by the fraction's denominator.
      2. Add that to the numerator
      3. Then write the result on top of the denominator

Let's take an example to understand it better :

Problem : Convert 3 2/5 to an improper fraction.

Solution : Let's start with the first step that is multiply the whole number by the denominator:

3 × 5 = 15
then the next step to follow is add the numerator to that:
15 + 2 = 17
Then the final step is to write that down above the denominator, like this:
17/5.


Let's take an example to show how we can add two mixed fractions:
Problem : Solve following problem 3 ⁵/₈ + 1 ³/₄
The first step is to convert following mixed fraction into improper fraction :
3 ⁵/₈ = ²⁹/₈
1 ³/₄ = ⁷/₄
Now we need to make same denominator and add:
²⁹/₈ + ¹⁴/₈ = ⁴³/₈ = 5 ³/₈
In similar fashion, we can subtract two mixed fractions. Let's take an example to understand it :

Problem: Solve 15 3/4 - 8 5/6 ?

Similarly the first step is to convert following mixed fractions into Improper Fractions:

15 ³/₄ = ⁶³/₄

8 ⁵/₆ = ⁵³/₆

Make the common denominator of 12:

⁶³/₄ becomes ¹⁸⁹/₁₂

⁵³/₆ becomes ¹⁰⁶/₁₂

Now we need to perform Subtraction:

¹⁸⁹/₁₂ - ¹⁰⁶/₁₂ = ⁸³/₁₂

Finally we can convert the result back to Mixed Fractions:
⁸³/₁₂ = 6 ¹¹/₁₂


As we already perform addition and subtraction, so I am going to discuss about Multiplication facts in IV grade mathematics. In simple mathematical manner we can say that Multiplication is the mathematical operation of surmounting one number by another. In elementary mathematics it is one of the four basic operations that are addition, subtraction, multiplication and division.
Let's discuss about the four basic properties used in multiplication that will help the us to make its problem easier to solve. The four properties are the commutative, associative, multiplicative identity and distributive properties. Let's discuss each property one by one:

1. Commutative Property: This property states that whenever the two numbers are multiplied with each other, the product is the same regardless of the order of the multiplicands. Let's take an example to understand it better: 4 * 2 = 2 * 4 (also play commutative property worksheets)
   
2. Associative Property: This property tells that whenever two of the given numbers are multiplied together the result is the same regardless of the order of the multiplicands. Let's take an example to understand it better : (2 x 3) x 4 = 2 x (3 x 4)
   
3. Multiplicative Identity Property: In this the product of any number and one is that number. For example 5 x 1 = 5.
   
4. Distributive Property : This property shows that the sum of two numbers times a third number is equal to the sum of each addend times the third number. Let's take an example to understand it better : 4 x (6 + 3) = 4 x 6 + 4 x 3
   
5. Another important property is: Property of Zero states that any of the number when multiplied with zero will result zero, whether the given number is in any of the order. For example 6 x 0 = 0.
   

Now I am going to discuss about decimal facts of IV grade mathematics . Before proceeding further let's talk about basic concept behind decimal. In simplest of mathematical way we can say that a decimal is a number that has a decimal point somewhere in the number. A decimal point is a dot, period, spot, or smudge. For example
1.3
1.34
1.345
1.3456
1.34567890123456789
In the above examples the numbers on the left side represent whole numbers such as ones, tens, hundreds, and thousands. While the numbers on the right hand side of the point are the decimal values. Those numbers represent values called tenths, hundredths, thousandths, and so on.
There is a close relation between fractions and decimals as both describe values that are smaller than one. If we  concentrate at a fraction as one number divided by another, the quotient is the decimal number. Let's take some of the examples to understand it better : 1/4 is one quarter.
Similarly we can explain above example as : 1 divided by 4 is equal to 0.25. or we can say that 0.25 is the decimal equivalent to 1/4.
Now I am going to discuss about free geometry help. Geometry is an important area of mathematics which deals with the shape, size, relative position of figures, and the properties of space. It is all about shapes and their properties. Geometry is of two types : Plane geometry and solid geometry. Plane geometry deals about the shapes on a flat surface like lines, circles and triangles ... shapes that can be drawn on a piece of paper whereas Solid geometry is all about three dimensional objects like cubes, prisms and pyramids.

In upcoming posts we will discuss about Angles in Grade IV and adding decimal calculator. Visit our website for information on CBSE board physics syllabus