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Operations on Rational Numbers | Operations on Rational Numbers Exercise 5.1

Question 4
  1. Add the following rational numbers:

(i) (3/4) and (-3/5)

(ii) -3 and (3/5)

(iii) (-7/27) and (11/18)

(iv) (31/-4) and (-5/8)

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  • Solution

  • Transcript

(i) Given (3/4) and (-3/5)

If p/q and r/s are two rational numbers such that q and s do not have a common factor other than one, then

(p/q) + (r/s) = (p × s + r × q)/ (q × s) (3/4) + (-3/5) = (3 × 5 + (-3) × 4)/ (4 × 5)

= (15 – 12)/ 20

= (3/20)

(ii) Given -3 and (3/5)

If p/q and r/s are two rational numbers such that q and s do not have a common factor other than one, then

(p/q) + (r/s) = (p × s + r × q)/ (q × s)

(-3/1) + (3/5) = (-3 × 5 + 3 × 1)/ (1 × 5)

= (-15 + 3)/ 5

= (-12/5)

(iii) Given (-7/27) and (11/18)

LCM of 27 and 18 is 54

(-7/27) = (-7/27) × (2/2) = (-14/54) (11/18) = (11/18) × (3/3) = (33/54) (-7/27) + (11/18) = (-14 + 33)/54

= (19/54)

(iv) Given (31/-4) and (-5/8)

LCM of -4 and 8 is 8

(31/-4) = (31/-4) × (2/2) = (62/-8)

(31/-4) + (-5/8) = (-62 - 5)/8

= (-67/8

"Welcome to yet another video Q&A video and we need and I'm going to tutor and today we are going to solve the question on your screen add the following rational numbers. These are the numbers we are going to look at them one by one again when we add fractions if they are like fractions, we add the numerators if they are not like fractions. We convert them into the night fractions by taking the LCM and converting the denominator of each one of them into sem and multiplying the numerator with the same number and then we add the denominators that the numerators and keep the genome. Yes. Okay. Let's start with the first 3 by 4 plus minus 3 by 5. Okay, the most common mistake they make is we had the add the numerators and then add the denominator. We never do that with fractions. The sem is 20. So we turn the denominator into 24 both the sections so Oh this one we have to multiply by 5. So the numerator also multiplies by 5 similarly this one we multiply by 4 and by 4. Okay, then we get 15 by 20 plus minus 12 by 20. So this is equal to 15 plus minus 12 by 20 so addition of integers you act different signs. Subtract the smaller one from the bigger one you get three. And keep the sign of the bigger one that is positive. So 3 by 2. Let's look at number 2 - 3 + 3 bye-bye. Again. We have a whole number. So what we do is very simple we multiply this by the denominator of the fraction because the denominator here is one. Okay, and then we get minus 15 plus 3 by 5. So this is equal. - 2 L by 3 okay addition of integers, you know the rule right? Okay. Now let's look at number 3 - 7 by 20 7 plus 11 by 15. Okay. So the LCM is 18 and 27. So 369 again 3 2 3 so 2 into 3 6 3 is ID pleasure 54 So 54 is the LCM making the denominator common, you multiply this by 2. So this numerator also multiplies by 2 again this by 3. So this by 3s by now we get minus 40 plus 33 by 50. So this is equal to 1095 50 right guys. Okay now This one is five. Sorry, I wrote it as 3 it now again the last one. Last one is 31 by -4 + -5 V. So this can be written as minus 30 1 by 4 plus -5 by a if now clearly 87 CM so we multiply this by two making the fractions like so - 62 + -5 by key, okay. So this is minus 62 minus 5 plus minus 5, we add them and keep the sign so - 67 by ache is our answer. Yeah, that was easy guys, right. So if you still have a doubt these leave a comment and we'll get back to you do like the video and subscribe to our Channel and take your leave now and see you in our next video until then. Take Care by KX Keep practicing "

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Question 4

  1. Add the following rational numbers:

(i) (3/4) and (-3/5)

(ii) -3 and (3/5)

(iii) (-7/27) and (11/18)

(iv) (31/-4) and (-5/8)

  • Solution

  • Transcript

(i) Given (3/4) and (-3/5)

If p/q and r/s are two rational numbers such that q and s do not have a common factor other than one, then

(p/q) + (r/s) = (p × s + r × q)/ (q × s) (3/4) + (-3/5) = (3 × 5 + (-3) × 4)/ (4 × 5)

= (15 – 12)/ 20

= (3/20)

(ii) Given -3 and (3/5)

If p/q and r/s are two rational numbers such that q and s do not have a common factor other than one, then

(p/q) + (r/s) = (p × s + r × q)/ (q × s)

(-3/1) + (3/5) = (-3 × 5 + 3 × 1)/ (1 × 5)

= (-15 + 3)/ 5

= (-12/5)

(iii) Given (-7/27) and (11/18)

LCM of 27 and 18 is 54

(-7/27) = (-7/27) × (2/2) = (-14/54) (11/18) = (11/18) × (3/3) = (33/54) (-7/27) + (11/18) = (-14 + 33)/54

= (19/54)

(iv) Given (31/-4) and (-5/8)

LCM of -4 and 8 is 8

(31/-4) = (31/-4) × (2/2) = (62/-8)

(31/-4) + (-5/8) = (-62 - 5)/8

= (-67/8

"Welcome to yet another video Q&A video and we need and I'm going to tutor and today we are going to solve the question on your screen add the following rational numbers. These are the numbers we are going to look at them one by one again when we add fractions if they are like fractions, we add the numerators if they are not like fractions. We convert them into the night fractions by taking the LCM and converting the denominator of each one of them into sem and multiplying the numerator with the same number and then we add the denominators that the numerators and keep the genome. Yes. Okay. Let's start with the first 3 by 4 plus minus 3 by 5. Okay, the most common mistake they make is we had the add the numerators and then add the denominator. We never do that with fractions. The sem is 20. So we turn the denominator into 24 both the sections so Oh this one we have to multiply by 5. So the numerator also multiplies by 5 similarly this one we multiply by 4 and by 4. Okay, then we get 15 by 20 plus minus 12 by 20. So this is equal to 15 plus minus 12 by 20 so addition of integers you act different signs. Subtract the smaller one from the bigger one you get three. And keep the sign of the bigger one that is positive. So 3 by 2. Let's look at number 2 - 3 + 3 bye-bye. Again. We have a whole number. So what we do is very simple we multiply this by the denominator of the fraction because the denominator here is one. Okay, and then we get minus 15 plus 3 by 5. So this is equal. - 2 L by 3 okay addition of integers, you know the rule right? Okay. Now let's look at number 3 - 7 by 20 7 plus 11 by 15. Okay. So the LCM is 18 and 27. So 369 again 3 2 3 so 2 into 3 6 3 is ID pleasure 54 So 54 is the LCM making the denominator common, you multiply this by 2. So this numerator also multiplies by 2 again this by 3. So this by 3s by now we get minus 40 plus 33 by 50. So this is equal to 1095 50 right guys. Okay now This one is five. Sorry, I wrote it as 3 it now again the last one. Last one is 31 by -4 + -5 V. So this can be written as minus 30 1 by 4 plus -5 by a if now clearly 87 CM so we multiply this by two making the fractions like so - 62 + -5 by key, okay. So this is minus 62 minus 5 plus minus 5, we add them and keep the sign so - 67 by ache is our answer. Yeah, that was easy guys, right. So if you still have a doubt these leave a comment and we'll get back to you do like the video and subscribe to our Channel and take your leave now and see you in our next video until then. Take Care by KX Keep practicing "

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