Hello Friends, in today's session we all are going to discuss about numbers and one of the most interesting topics of mathematics, equivalent fractions which is usually studied in grade IV of gujarat board. Here I am going to tell you the best way to understand this topic and you can get more information about this from various Tutor sites available.
In equivalent fractions, we will discuss what equivalent fractions are, way to determine two fractions are equivalent or not. How to convert a fraction into equivalent fractions and also way to reduce fraction and reduce rational expressions to lowest terms.
Numbers represented as numerator and denominator form, called fractional number. An equivalent fraction can be defined as the two different objects with different names but same relationship, they represents the same part of an object. The equivalent fractions are the fraction which have same overall value but are different in look. for more about it click here.
Example: 1/2 = 2/4
1/2 is the two equal parts of one and 2/4 is the 4 equal parts.
To check whether two fractions are equivalent or not, there is a rule which can be express as:
a / b = c / d
or a x d = b x c
This rule say that two fractions will be equal if the product of the numerator of the first fraction i.e. ‘a’ and the denominator of the second fraction i.e. ‘d’ is equal to the product of denominator of first fraction i.e. ‘b’ is and numerator of the second fraction i.e. ‘c’. Let’s understand it by taking an numerical example:
2 / 4 = 8 / 16
Only if ………
2 x 16 = 4 x 8
Check ……..
32 = 32
In this example we can say that these fractions will be equal only if the product of the numerator of the first fraction i.e. ‘2’ and the denominator of the second fraction i.e. ‘16’ is equal to the product of denominator of first fraction i.e. ‘4’ is and numerator of the second fraction i.e. ‘8’.So we know that 2/4 is equivalent to 8/16, because
2 x 16 = 32 and 4 x 8 = 36.
A simple and best way to check for equivalent fractions is "cross - multiplication", which say that multiplication of the numerator of one fraction by the denominator of the second fraction and the multiplication of the denominator of the first fraction by numerator of the second fraction.
Now coming to our next topic, where we learn how to convert a fraction into equivalent fractions. Suppose we have 4/3 = ?/24. We have to find the values missing.
Now to make denominator equals to 24 we have to multiply 3 with 8,
4 ?
------- = -------
3 x 8 24
To make it equivalent fraction, we have multiply both denominator and numerator with same number. So now
4 x 8 32
-------- = -------
3 x 8 24
Now suppose a fact when the one denominator can’t be divided by other side denominator so what would we do now?
Example: 2/5 and 4/3
Just multiply both denominator with the same digit an convert them into same digit
Now we have
2/5 = 6/15 and 4/3 = 20/15
Now in our last topic we will see reduce a fraction into lowest term.
Taking an example:
Reduce 20/28 in lowest term. Both have a common divisor 4 so we divide both by 4.
20 5
------ = -----
28 7
These are some basics of Equivalent fractions. As a student of grade IV, you have to practice it harder to get master in this. As it is not an easy topic of mathematics and if you want to know about Equivalent Fractions in Grade III
then you can refer Internet.
In equivalent fractions, we will discuss what equivalent fractions are, way to determine two fractions are equivalent or not. How to convert a fraction into equivalent fractions and also way to reduce fraction and reduce rational expressions to lowest terms.
Numbers represented as numerator and denominator form, called fractional number. An equivalent fraction can be defined as the two different objects with different names but same relationship, they represents the same part of an object. The equivalent fractions are the fraction which have same overall value but are different in look. for more about it click here.
Example: 1/2 = 2/4
1/2 is the two equal parts of one and 2/4 is the 4 equal parts.
To check whether two fractions are equivalent or not, there is a rule which can be express as:
a / b = c / d
or a x d = b x c
This rule say that two fractions will be equal if the product of the numerator of the first fraction i.e. ‘a’ and the denominator of the second fraction i.e. ‘d’ is equal to the product of denominator of first fraction i.e. ‘b’ is and numerator of the second fraction i.e. ‘c’. Let’s understand it by taking an numerical example:
2 / 4 = 8 / 16
Only if ………
2 x 16 = 4 x 8
Check ……..
32 = 32
In this example we can say that these fractions will be equal only if the product of the numerator of the first fraction i.e. ‘2’ and the denominator of the second fraction i.e. ‘16’ is equal to the product of denominator of first fraction i.e. ‘4’ is and numerator of the second fraction i.e. ‘8’.So we know that 2/4 is equivalent to 8/16, because
2 x 16 = 32 and 4 x 8 = 36.
A simple and best way to check for equivalent fractions is "cross - multiplication", which say that multiplication of the numerator of one fraction by the denominator of the second fraction and the multiplication of the denominator of the first fraction by numerator of the second fraction.
Now coming to our next topic, where we learn how to convert a fraction into equivalent fractions. Suppose we have 4/3 = ?/24. We have to find the values missing.
Now to make denominator equals to 24 we have to multiply 3 with 8,
4 ?
------- = -------
3 x 8 24
To make it equivalent fraction, we have multiply both denominator and numerator with same number. So now
4 x 8 32
-------- = -------
3 x 8 24
Now suppose a fact when the one denominator can’t be divided by other side denominator so what would we do now?
Example: 2/5 and 4/3
Just multiply both denominator with the same digit an convert them into same digit
Now we have
2/5 = 6/15 and 4/3 = 20/15
Now in our last topic we will see reduce a fraction into lowest term.
Taking an example:
Reduce 20/28 in lowest term. Both have a common divisor 4 so we divide both by 4.
20 5
------ = -----
28 7
then you can refer Internet.
No comments:
Post a Comment