Question

what rational number is between 7 2/3 and √60

Answer 1

Answer:

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Question 1:

Identify the property in the following statements:

(i) 2 + (3 + 4) = (2 + 3) + 4; (ii) 2.8 = 8.2; (iii) 8. (6 + 5) = (8.6) + (8.5).

ANSWER:

(i) 2 + (3 + 4) = (2 + 3) + 4

This is the associative property under addition.

(ii) 2·8 = 8·2

This is the commutative property under multiplication.

(iii) 8· (6 + 5) = 8·6 + 8·5

This is the distributive property of multiplication over addition

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Question 2:

Find the additive inverses of the following integers:

6, 9, 123, −76, −85, 1000

ANSWER:

Here, 6 + (−6) = 6 − 6 = 0

Thus, − 6 is the additive inverse of 6.

9 + (−9) = 9 − 9 = 0

Thus, −9 is the additive inverse of 9.

123 + (−123) = 123 − 123 = 0

Thus, −123 is the additive inverse of 123.

(−76) + 76 = −76 + 76 = 0

Thus, 76 is the additive inverse of −76.

(−85) + 85 = −85 + 85 = 0

Thus, 85 is the additive inverse of −85.

1000 + (−1000) = 1000 − 1000 = 0

Thus, −1000 is the additive inverse of 1000.