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