1. Fill in the blanks and write the name of the property in brackets used in the following:
(i) [tex]\frac{8}{15} + 0 =[/tex]
(ii) [tex]\frac{-17}{23} + \frac{13}{42} = \frac{13}{42} +[/tex]
(iii) [tex]\frac{-18}{29} + \frac{18}{29} =[/tex]
(iv) [tex]\frac{5}{6} + (\frac{-2}{9} + \frac{1}{4}) = (\_ + \_) + \frac{1}{4}[/tex]
Answer (1)
Let's fill in the blanks for each expression and identify the property used.
(i) 15 8 + 0 = 15 8
Here the number is added to 0, and the result is the same number. This uses the Additive Identity Property . According to this property, adding 0 to any number does not change the number.
(ii) 23 − 17 + 42 13 = 42 13 + 23 − 17
This expression shows that the order of addition does not change the sum. This is known as the Commutative Property of Addition . This property states that changing the order of addends does not change the sum.
(iii) 29 − 18 + 29 18 = 0
When a number is added to its opposite, the result is 0. This is known as the Additive Inverse Property . The property states that for every number a , there is a number − a such that a + ( − a ) = 0 .
(iv) 6 5 + ( 9 − 2 + 4 1 ) = ( 6 5 + 9 − 2 ) + 4 1
This uses the Associative Property of Addition . This property states that the way in which numbers are grouped does not change their sum. Changing the grouping of the addends does not affect the sum.
