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
-
This topic would deal with problems on division of fractional number. We are familiar with the fact that division of fraction with another fraction involves multiplying the fraction with the reciprocal or multiplicative inverse of another fraction. The same concept would be
-
This topic discusses about division of a whole number by a fraction. In this we have to divide the whole number that is positive integers including zero by a fractional number. When dividing a whole number by a fraction we actually multiply the whole number by the
-
This topic would discuss about division of a fractional number with another fractional number. In this case if any one or both of the fractional number are in mixed fraction then we will have to change that mixed fraction into improper fraction.
-
-
This topic would discuss on dividing a fraction by a whole number. Whole numbers are numbers from 0 to infinity i.e. {0, 1, 2, 3, 4, 5, 6, 7, 8, 9……} They are not represented in numerator and denominator form. However, for the purpose of division and multiplication of the
-
Here few problems are illustrated on multiplication of fractional numbers. This will give the learners an outline about how story sums on multiplication of fractions are solved. It will also provide the learners a better understanding of application on multiplication of
-
This worksheet will provide a variety of sums on multiplication of fraction for practice. It will help in clear understanding of the topic multiplication on fraction. It will also develop confidence and better in-depth knowledge on the topic.
-
We know that when a fraction is multiplied by its reciprocal the result is always 1. This reciprocal is also known as multiplicative inverse. In order to find out the multiplicative inverse of a fraction the following points are to be kept in mind.
-
We have previously discussed about multiplication of fractional number. However there are few properties of multiplication of fractional numbers which can be applied in certain cases in order to make calculation easier and faster. These properties are helpful in better
-
This topic deals with multiplication of a fraction by another fraction. For eg : 3/7 by 5/11. Here both the numbers are in numerator and denominator form. Here are few examples to show multiplication of fraction by another fraction
-
This topic deals with multiplication of a whole number i.e. (0, 1, 2, 3, 4, 5, 6, 7…….) by a fraction i.e. a number in p/q form. When we are multiplying a whole number with a fraction or fractional number then first we have to change that whole number into fraction just by
-
This topic discusses about multiplication of a whole number by a fraction. Whole numbers are positive integers starting from zero to infinity. The fractions are always in numerator and denominator form whereas, whole numbers are not.
-
Multiplication is a repeated addition as if we add a group of numbers or a single number again and again then actually we are doing multiplication. Let us understand it with an example: Table of 2 2 × 1 =2 2 × 2 = 4 2 × 3 = 6 2 × 4 = 8 2 × 5 = 10 2 × 6 =12 2 × 7 =14
-
Integers are positive and negative number including zero and does not include the fractional part. We will discuss about the rules for subtracting of integers. There are certain rules which will help us in better understanding of subtraction of integers.
-
Integers are positive, negative numbers including zero and do not include any fractional part. This topic will cover the rules for adding integers. There are certain rules which will help us in understanding how: •Two positive integers are added •Two negative integers are
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.