Fill in the blanks: (i) -12 + (7/12 + -9/11 ) = (-12 + 7/12 ) + (.......) (ii) 19/-5 + ( -3/11 + -7/8 ) = { 19/-5 + (.....)} + (-7)/8

Question

Fill in the blanks:

(i) \(-12 +(\frac{7}{12}+\frac{-9}{11}) = (-12+\frac{7}{12}) +(....)\)

(ii) \(\frac{19}{-5}+(\frac{-3}{11}+\frac{-7}{8}) = \) \(\{\frac{19}{-5}+(.....)\} + \frac{-7}{8}\)

(iii) \(\frac{-19}{7}+..... = .....+\frac{-16}{7} = \frac{-16}{7}\)

Answer 1

(i) \(\frac{-9}{11}\)

By Associative property, i.e., (a+b)+c=a+(b+c) 

Therefore,

\(-12 +(\frac{7}{12}+\frac{-9}{11}) = (-12 + \frac{7}{12}) + (\frac{-9}{11})\)

(ii) \(\frac{-3}{11}\)

By Associative property, i.e., (a+b)+c=a+(b+c) 

Therefore,

\(\frac{19}{-5}+(\frac{-3}{11}+\frac{-7}{8}) = (\frac{19}{-5}+\frac{-3}{11})+ (\frac{-7}{8})\)

(iii) 0.0

0 is the additive identity that is, if we add 0 to any number the result will be the number itself. 

a+0=0+a

Also, By Commutative property, i.e., a+b=b+a 

We get,

\(\frac{-16}{7}+0=0+\frac{-16}{7}\frac{-16}{7}\)