give examples of any two rational number. Also find their sum, subtraction, multiplication and division and check if the result is again a rational number or not
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Answer:
Addition of Rational Numbers
Addition of Rational Numbers with Same Denominators: Consider two rational numbers, say 2/9 and 3/9. In this case, the denominators of both numbers are the same. (i.e., 9). So, keep the denominators as common, and add the numerators of the rational number. Thus, the addition of two rational numbers with the same denominators is given by:
29+39=2+39=59
Addition of Rational Numbers with Different Denominators: Consider two rational numbers, say 4/3 and 5/2. In this case, the denominators of the rational numbers are different, and hence, the addition of two rational numbers directly is not possible. So, first, convert the rational numbers with different denominators into the same denominator by taking the L.C.M of the denominator values. The procedure to add rational numbers with different denominators is given below:
Step 1: Take the LCM of the denominator value
Step 2: Now, find the equivalent fractional value for the given rational numbers, by using the LCM value, and make the denominators of the two rational numbers are the same.
Step 3: Now, add the two rational numbers.
Consider an example given above, 4/3 and 5/2. Now, let us find the sum of two given rational numbers:
Step 1: The LCM of 2 and 3 is 6
Step 2: 43+52=4(2)+5(3)6
Step 3: 43+52=8+156=236
Subtraction of Rational Numbers
Like addition, the subtraction of two rational numbers has two different cases.
Subtraction of Rational Numbers with Same Denominators: Consider two numbers, say 7/3 and 5/3. The subtraction of two rational numbers is given by:
73−53=7−53=23
Subtraction of Rational Numbers with Different Denominators: Assume two rational numbers, say 4/3 and 5/2. Here, the denominators are different. Like the addition of rational numbers, make the denominator value same by finding the LCM of the denominator values.
Step 1: LCM of 3 and 2 is 6.
Step 2: 43−52=4(2)−5(3)6
Step 3: 43−52=8−156=−76
Multiplication of Rational Numbers
The multiplication of rational numbers is similar to the multiplication of the integers. The product of any two rational numbers is equal to the product of the numerator divided by the product of the denominator. Thus, the formula to multiply the rational numbers is given by
Product of Rational Numbers = product of Numerator / Product of Denominator
Assume that the rational numbers are 6/5 and 4/3, the product of the given rational numbers is:
65×43=6×45×3=2415
Division of Rational Numbers
The division of rational numbers is similar to the division of fractions. The reciprocal of a rational number is nothing but the swapping of the numerator and denominator of the given rational number.
Also, check: Dividing Fractions
The procedure to perform the division of the rational number is given as follows:
Step 1: Take the reciprocal of the divisor value
Step 2: Find the product of the numerator and the product of the denominator to get the result
Assume that, 6/5 and 9/7 are the two rational numbers.
Step 1: The reciprocal of 9/7 is 7/9
Step 2: Division of two rational numbers is:
65×79=6×75×9=4245