Multiplying Rational Numbers Multiplying Rational Numbers Any number which can be expressed in form of p/q, where ‘p’ and ‘q’ are integers, and q > 0, then it is called a rational number. All numbers namely - natural numbers, whole numbers, integers and fractions are written in the form of p/q, where q > 0, so they all belong to the set of rational numbers. If there exist any number ‘n’, which does not have any denominator, we look at it carefully and observe that , n can be written as n/1, thus ‘n’ is also in form of p/q and thus it is a rational number. As we know that integers , natural numbers and whole numbers are endless and goes up to infinite. We must remember that between any two integers, there exist infinite number of rational numbers. So we say that rational numbers are uncountable. All mathematical and logical operators can be performed on the rational numbers. Thus we say that we can add, subtract, multiply and even find the quotient of any two rational numbers. We can compare rational numbers and so they can be arranged in ascending or descending order. There are different properties of rational numbers. Some of them are closure property, Commutative property, associative property, Density property and many others. To do addition or subtraction of two rational numbers we need to make the denominators same and then proceed for the calculations. But to find the product of two rational numbers, we only have to multiply the numerator with the numerator and the denominator with the denominator. When we have to divide any one rational number by another, Know More About :- Definition of Difference
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we find the multiplicative inverse of the number and change the operation of division to multiplication. Here we are going to learn, how to find the Multiplicative Inverse of the Number. To find the Multiplicative inverse of any rational number we simply need to write the numerator of the rational number as the denominator and the denominator of the rational number as the numerator. It is also called the reciprocal of the given number. Here is an example to understand the multiplicative inverse of any number. Multiplicative Inverse of 3/7 is 7/3. Here we observe that the denominator 7 becomes the numerator and the numerator 3 becomes the denominator. Let us take any whole number say 4, this 4 can be written as 4 / 1. So we observe that 4 is the numerator and 1 is the denominator. When we write its reciprocal, it becomes ¼. Now let us try to divide one rational number by another, Say 2/7 divided by 2/9. It can be written as 2 / 7 multiplies by the multiplicative inverse of (2/9) i.e. 9/2.= ( 2/7 ) * (9 /2). Here by changing 9/2 to its reciprocal, it becomes a simple product problem = 2 cancels from numerator and the denominator and we get 9/7. If we write any number which can be expressed in form of p/q, where ‘p’ and ‘q’ are integers, and q <> 0, then it is called a rational number. We observe that all natural numbers, whole numbers, integers, and fractions can be expressed in the form of p/q, where q <> 0, so they all form the elements of set of rational numbers. It is observed that any number ‘n’, does not have any denominator, but if we look carefully, ‘n’ can be written as ‘n/1’, thus ‘n’ is also in form of ‘p/q’ and thus it is a rational number. There are infinite number of integers, natural numbers and whole numbers. Very interesting thing to be observe is that between any two integers, there exist infinite number of rational numbers. So we say that rational numbers are uncountable. Thus we say that we can add, subtract, multiply and even find the quotient of any two rational numbers. Any two rational numbers can also be compares and thus they can be arranged in ascending or descending order. There are any properties of rational numbers. Some of them are closure property, Commutative property, associative property, Density property and many others. To do addition or subtraction of two rational numbers we need to make the denominators same and then proceed for the calculations. But to find the product of two rational numbers, we only have to multiply the numerator with the numerator and the denominator with the denominator. When we have to divide any one rational number by another, we simply find the reciprocal of the divisor and change the operation of division to multiplication. Here we are going to learn, how to find the Reciprocal of Rational Numbers. Read More About :- 2 Digit by 1 Digit Multiplication
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