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Verify commutativity of addition of rational numbers for each of the following pairs of rational numbers.
Commutativity of the addition of rational numbers means that if ab and cd are two rational numbers, then ab + cd = cd + ab.
(i) We have:
Hence, verified.
(ii) We have:
Hence, Verified.
(iii) We have:
(iv) We have:
(v) We have:
(vi) We have:
Verify associativity of addition of the rational numbers i.e.,
(x + y) + z = x + (y + z), when:
We have to verify that:
Write the additive inverse of each of the following rational numbers:
(i) Additive inverse is the negative of the given number.
So, additive inverse of -2/17 = 2/17
(ii) Additive inverse is the negative of the given number.
So, additive inverse of 3/-11 = 3/11
(iii) Additive inverse is the negative of the given number.
So, additive inverse of -17/5 = 17/5
(iv) Additive inverse is the negative of the given number.
So, additive inverse of -11/-25 = 11/25
Write the negative (additive inverse) of each of the following:
(i) -25
(ii) 7-9
(iii) -1613
(iv) -51
(v) 0
(vi) 1
(vii) -1
(i) Additive inverse of −2/5 = 2/5
(ii) Additive inverse of −7/9 = 7/9
(iii) Additive inverse of −16/13 = 16/13
(iv) Additive inverse of −5/1 = 5/1
(v) Negative value of 0 is 0
(vi) Negative value of 1 is -1
(vii) Negative value of -1 is 1
Using commutativity and associativity of addition of rational numbers, express each of the following as a rational number:
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