# RATIONAL NUMBERS AND THEIR PROPERTIES

The numbers of the form a/b, where a and b are integers and b is not equal to 0 are called rational numbers. Checkout the article for details. #### WHAT ARE RATIONAL NUMBERS?

The numbers of the form a/b, where a and b are integers and b is not equal to 0 are called rational numbers. Some examples of rational numbers: 2/3, 4/1, 6/9, -1/2, etc.

Is 3 a rational number? yes, because it can be written in the form of a/b as such= 3/1

#### PROPERTIES OF RATIONAL NUMBERS

##### 1) Closure Property-

i) Addition- When a rational number is added to another rational number, the sum is a rational number. Ex. 2/3+5/3=7/3, here 7/3 is also a rational number.

ii) Subtraction- When we subtract a rational number from another rational number, the difference between them is a rational number. Ex. 5/2-1/2=4/2, here 4/2 is a rational number. We can further divide 4/2 and the answer will be 2 which is another rational number as it can also be written in the form of a/b.

iii) Multiplication- When we multiply a rational number with another rational number, the product is also a rational number. ex. 6/2 x 3/5= 18/10, here 18/ 10 is a rational number.

iv) Division- When we divide a rational number by another rational number, the answer may or may not be a rational number.

##### 2) COMMUTATIVE PROPERTY-

i) Addition- According to the commutative property, a/b + c/d = c/d=a/b. The order of numbers doesn’t affect the results here, therefore we can say that addition is commutative.

Ex. 3/2 + 5/2= 5/2 + 3/2 =8/2

ii) Subtraction- Subtraction is not commutative. Here, the order of numbers affects the results. Ex. 5/3-4/3=1/3 whereas 4/3-5/3=-1/3. Here the difference is not the same if we change the order.

iii) Multiplication- Multiplication is commutative. The order of numbers doesn’t affect the answer. ex. 2/3 x 5/3= 10/9 and 5/3 x 2/3=10/9.

iv) Division- Division is not cumulative. Here, the order of numbers does affect the answer. Ex. 6/2 divided by 4/2 is 3/2, whereas if we change the order and divide 4/2 by 6/2 the answer will be 2/3.

##### 3)ASSOCIATIVE PROPERTY-

The associative property states that changer the grouping of three numbers will not change the answer. This property is applicable only on addition and multiplication

i)Addition- Addition is associative. Even if we change the sequence of three or more rational numbers, their sum will remain the same. Ex. 2/3 + 5/3 + 7/3=14/3 and 2/3 + 7/3 + 5/3= 14/3.

ii) Subtraction- Subtraction is not associative. If we change the sequence of three or more rational numbers, the differences between them will also change. ex. 9/2- 5/2- 3/2 = 1/2 and 5/2 – 9/2 -3/2 = -7/2

iii) Multiplication- Multiplication is associative. If we change the sequence of three or more rational numbers, the product will not change. ex. 6/5 x 4/5 x 2/5= 48/125 and even if we change the sequence, 4/5 x 6/5 x 2/5= 48/125, the product did not change.

iv) Division- Division is not associative. If we change the sequence of three or more rational numbers, the answer will also change. Ex. ( 2/3 ÷ 4/3) ÷ 5/3= 18/60 and if we change the expression to 2/3 ÷ (4/3 ÷ 5/3)= 12/10 the answer also changes.

##### 4) DISTRIBUTIVE PROPERTY-

i)Multiplication over Addition- Multiplication over addition is distributive. It means that an equation like this= a (b+c)can be written as=ab +ac.

ii) Multiplication over subtraction- Multiplication over subtraction is distributive. It means that an equation like this: a(b-c) can be written like this: ab-ac.

iii) Distributive property is not applicable on multiplication over division.

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