Properties of Fractional Division
We are already learnt division of fractional numbers. It is basically multiplication of the first fraction with the reciprocal or multiplicative inverse of another fractional number. In case of finding the multiplicative inverse we actually interchange the numerator and denominators, where a proper fraction is converted into an improper fraction and an improper fraction is converted into a proper fraction. However, this topic deals with the properties of division. The understanding of the properties of division will help the students in better understanding of the concept of division and would lead to more in-depth knowledge along with the properties of multiplication learnt in previous topic as both the properties of division and multiplication are related.
The properties of division of fractional numbers are discussed below:
Property I:
When a fractional number is divided by itself the result is always 1.
Here are few examples to justify property 1:
1. 9/5 ÷ 9/5
= 9/5 × 5/9
= (9 ×5)/(9 ×5)
= 45/45
= 1
2. 15/7 ÷ 15/7
= 15/7 × 7/15
= (15 ×7)/(7 ×15)
= 105/105
= 1
Explanation:
From the examples we can see that any fraction divided by itself is 1. As the fraction is divided by the multiplicative inverse of itself when both the numerator and denominator gets reduced to lowest terms the answer is 1.
Property II:
If a non- zero fractional number is divided by 1 the result is the fractional number itself
Here are few examples to justify property 2:
1. 9/7 ÷ 1
= 9/7 × 1
= 9/7
2. 11/9 ÷ 1
= 11/9 ×1
= 11/9
Explanation:
From the example it is clear that fractional number divided by 1 is the fractional number itself. As the multiplicative inverse of 1 is 1 only. According to the rule of division,
Division = 1st fraction multiplied by the multiplicative inverse of the second fraction/ whole number.
Here the second number is 1 whose multiplicative inverse is also 1. Again according to the properties of multiplication anything multiplied by 1 is the number itself. Hence, fractional number divided by 1 is the fractional number itself.
Property III:
If zero is divided by a non-zero fractional number then the result is zero.
Here are few examples to justify property 3:
1. 0 ÷ 9/5
= 0 × 5/9
= 0
2. 0 ÷ 15/7
= 0 × 7/15
= 0
Explanation:
In the above two examples we can see that when zero is divided by a non-zero fractional number the result is always zero. As we can see that we are finding out the multiplicative inverse of the second fraction. After finding the multiplicative inverse of the second fraction it is actually multiplied with 0 any we know from the properties of multiplication that anything multiplied by zero is zero.
Hence in example (i)
0 ÷ 9/5 = 0
And in example (ii)
0 ÷ 15/7
= 0
Property IV:
As, fractional number cannot be divided by zero hence multiplicative inverse of 0 does not exists.
You might like these
-
Word Problems on H.C.F. and L.C.M. | Highest Common Factor | Lowest Co
We have already learnt H.C.F, L.C.M and the relationship between the two and now we will learn on how to do word problems on H.C.F. and L.C.M. Note: In word problems on H.C.F. and L.C.M we have to remember two points: • When we are asked to find out maximum, highest
-
Worksheet on H.C.F. and L.C.M. | HCF × LCM = 1st Number × 2nd Number
This topic will provide worksheet to students on H.C.F and L.C.M which will help to judge themselves their level of understanding of the topic and the areas where they need more careful study and analysis. This worksheet will serve as a yardstick for measuring the level of
-
Relationship between H.C.F. and L.C.M. |HCF× LCM=1st Number×2nd Number
This topic discusses about the relationship between H.C.F and L.C.M in case of two numbers. The relationship between H.C.F and L.C. M of two number states that: H.C.F × L.C.M = First number × Second number Hence from this relationship we can find the following: H.C.F
-
Examples to Find Least Common Multiple of Three Numbers by using Divis
This topic would provide examples on how to find least common multiple of three numbers. Various examples on finding L.C.M would help the learners in understanding the topic better. Here are few examples illustrated on finding the least common multiple of three numbers using
-
To Find Lowest Common Multiple by using Division Method | Examples
This topic discusses about finding the lowest common multiple using division method. Steps to find the loqest common multiple using the division method: Step 1: Write the numbers in a row separating by commas Step 2: Then divide the given numbers (if possible both the
-
Examples to Find Least Common Multiple of Two Numbers |Division Method
This topic would provide examples to find least common factor by using division method. This topic will help learners to clear their doubts and improve their understanding and knowledge on how to find out least common multiple (L.C.M) by division method.
-
Examples to find Least Common Multiple by using Prime Factorization
This topic would provide various examples on finding the least common multiple using the method of prime factorization. Here are few examples illustrated on finding the least common multiple using the prime factorization method. 1. Find the least common multiple (L.C.M) of
-
To Find Least Common Multiple by using Prime Factorization Method
This topic would discuss about how to find the least common multiple by using prime factorization method. Steps to find out the least common multiple by using prime factorization method: •First find all the prime factors of the given number .Then write all the prime factors
-
Least Common Multiple (L.C.M.) | Lowest Common Multiple | Examples
In the last topic we have discussed about common multiples that is same multiples of two or more numbers. Now here we will discuss about the least common multiple that is the smallest common multiple of two or more numbers. Here are few examples illustrated on least common
-
Common Multiples | What is Common Multiples? | Three Common Multiples
This topic would deal with common multiples. If some of the multiples of two or more number are same then those same multiples are termed as common multiples. Here are few examples illustrating common multiples: List the two common multiples of 5 and 6
-
Multiples | Important Facts about Multiple | Even and Odd Multiples
This topic would deal with multiples. Multiples of a number are actually the tables of a certain number. If we are talking about multiple of 2 then it is actually the tables of 2. When we have learnt table we have learnt the tables till 10 or 12 that is till 2 multiplied
-
Highest Common Factor of Three Numbers by using Division Method
This topic would discuss about finding highest common factor using the division method. We have already learnt finding the highest common factor by prime factorization method but it is not suitable when we are dealing with large numbers. Division method is quite convenient
-
Find Highest Common Factor of Two Numbers by using Division Method
We have already learnt the method of finding highest common factor using division method. Here are few more examples given to clear your understanding, concepts and improve your knowledge on how to find H.C.F. this topic would provide a wide range of examples will help the
-
To Find Highest Common Factor by using Division Method | Examples
This topic would discuss about finding the highest common factor of three numbers using the division method. We have learnt in our last topic about finding the highest common factor of two numbers. While doing with three numbers first we will find the highest common factor
From Properties of Fractional Division to HOME PAGE
New! Comments
Have your say about what you just read! Leave me a comment in the box below.