Question

Add the following, \[\dfrac{-9}{10},\dfrac{22}{15},\dfrac{13}{-20}\] .

Answer 1

Hint: The first number, second number, and third number are \[\dfrac{-9}{10}\] , \[\dfrac{22}{15}\] , and \[\dfrac{-13}{20}\] . Multiply the first number by 6, second number by 4, third number by 3. Now, add the numbers directly and get the answer.

 Complete step by step answer:
According to the question, we are given three fractional numbers and we have to calculate the value when all these numbers are added.
The first number = \[\dfrac{-9}{10}\] ……………………………………(1)
The second number = \[\dfrac{22}{15}\] ……………………………………(2)
The third number = \[\dfrac{13}{-20}=\dfrac{-13}{20}\] ……………………………………(3)
We can observe that the above three numbers don’t have an equal denominator. That is, we have 10, 15, and 20 in the denominator.
The LCM of 10, 15, and 20 is 60 ……………………………………. (4)
The denominator of the first number is 10 so, we can say that LCM is 6 times the denominator of the first number.
On multiplying by 6 in numerator and denominator in equation (1), we get
The first number = \[\dfrac{-9\times 60}{10\times 60}=\dfrac{-54}{60}\] ………………………………………………(5)
The denominator of the second number is 15 so, we can say that LCM is 4 times the denominator of the second number.
On multiplying by 4 in numerator and denominator in equation (2), we get
The second number = \[\dfrac{22\times 4}{15\times 4}=\dfrac{88}{60}\] ………………………………………….(6)
The denominator of the second number is 20 so, we can say that LCM is 3 times the denominator of the second number.
On multiplying by 3 in numerator and denominator in equation (2), we get
The third number = \[\dfrac{-13\times 3}{20\times 3}=\dfrac{-39}{60}\] ………………………………………….(7)
Now, on adding equation (5), equation (6), and equation (7), we get
The first number + The second number + The third number = \[\dfrac{-54}{60}+\dfrac{88}{60}+\dfrac{-39}{60}\] = \[\dfrac{-54+88-39}{60}\] \[=\dfrac{-93+88}{60}=\dfrac{-5}{60}=\dfrac{-1}{12}\] .
So, addition = \[\dfrac{-1}{12}\] .
Hence, the addition of the numbers \[\dfrac{-9}{10},\dfrac{22}{15},\dfrac{13}{-20}\] is \[\dfrac{-1}{12}\] .

Note:
For this of questions where we have to add the fractional numbers and the denominator of each fractional number is different. Always approach this type of question by obtaining the LCM of the denominators and then make the denominator of each number equal by multiplying the numerator and denominator by a factor where factor = \[\dfrac{\text{LCM}}{\text{Denominator}}\].