Which of the following is not true?

1

(a)

\(\frac{10}{11}+\frac{11}{12}=\frac{11}{12}+\frac{10}{11}\)

(b)

\(\frac{10}{11}\times \frac{11}{12}=\frac{11}{12}\times \frac{10}{11}\)

(c)

\(\frac{10}{11}+ \frac{11}{12}=\frac{11}{12}\div \frac{10}{11}\)

(d)

\(\frac{10}{11}\div \frac{11}{12}=\frac{11}{12}\times \frac{10}{11}\)

The reciprocal of \({-3\over8 } \times {-24\over 13}\) is

1

(a)

\(9\over 13\)

(b)

\(-9\over 13\)

(c)

\(-13 \over 9\)

(d)

\(13\over9\)

Which of the following is the identity element?

1

(a)

1

(b)

-1

(c)

0

(d)

None of these

Which of the following is the multiplicative identity for rational numbers?

1

(a)

1

(b)

-1

(c)

0

(d)

None of these

Which of the following is the product of \(\frac { 7 }{ 8 } \) and \(\frac { -2 }{ 21 } ?\)

1

(a)

\(\frac { -1 }{ 12 } \)

(b)

\(\frac { 1 }{ 12 } \)

(c)

\(\frac { -16 }{ 63 } \)

(d)

\(\frac { -147 }{ 16 } \)

Numbers	Closed under
	Addition	Subtraction	Multiplication	Division
Whole numbers	___________	___________	Yes	__________

1

(a)

Numbers	Closed under
	Addition	Subtraction	Multiplication	Division
Whole numbers	yes e.g (0+5=5)Whole numbers	No e.g (5-7=-2)Not a Whole numbers	Yes e.g (3x7=21)Whole numbers	No e.g (5\(\div\)8) Not a Whole numbers

Numbers	Associative for
	Addition	Subtraction	Multiplication	Division
Whole numbers	yes	________	_________	________

1

(a)

Numbers	Associative for
	Addition	Subtraction	Multiplication	Division
Whole numbers	Yes, e.g. 2 +(0+5) =(2 +0)+5 \(\Rightarrow\)7=7, which is true	\(No \ e.g \\ 2-(0-5)\\ \neq (2-0)-5\\ \Rightarrow 7 \neq -3\) which is not true	Yes, e.g.2 x[3 x (-5)] =(2 x3)x(-5) \(\Rightarrow\)2 x[-15]=(6)x(-5) \(\Rightarrow\)-30=- 30, which is true.	No eg  \((2\div 3)\div 5\neq 2 \div (3\div5) \\ \Rightarrow ({2\over 3})\div 5\neq2 \div ({3\over 5}) \\ \Rightarrow {2\over 3}\times {1\over 5} \neq 2 \times {5\over 3}\\ \Rightarrow {2\over 15} \neq {10\over 3}\) which is not true

\({1\over15}\times[{27\over31}+{32\over37}]=[{1\over15}\times{27\over31}]+\) ______________________

1

(a)

\([{1\over15}\times{32\over37}]\)[using distributive property over addition]

The rational number ______________has no reciprocal.

1

(a)

0

The reciprocal of the reciprocal of a number is __________.

1

(a)

The number itself

Write the additive inverse of the following  \(19\over-6\)

2

(a)

Verify that -(-x) = x, for x = \(11\over15\)

2

(a)

Simplify : \({7\over8}+{1\over16}-{1\over12}\)

2

(a)

Multiply the reciprocal of \(\frac { 7 }{ 8 } \) by the reciprocal of  \(\frac { -2 }{ 21 } \) 

2

(a)

The product of two rational numbers is \(\frac { -28 }{ 75 } \) if one of the numbers is \(\frac { 14 }{ 25 } \) find the other

2

(a)

Find using distributivity. \( \{{7\over5}\times ({-3\over12}) \}+ \{{7\over16}\times {5\over12} \}\)

3

(a)

Write any five non-negative rational numbers less than 1

3

(a)

Find three rational numbers between -3 and - 4

3

(a)

Take some more rational numbers, add them as above and see if the two sums are equal.

3

(a)

\((-\frac{2}{3})+\frac{2}{3}=0\).How?

3

(a)

Rearrange suitably and find the sum in each of the following:
\({2\over 3}+{9\over2}+{7\over4}+{-6\over3}+{-3\over2}\)

5

(a)

Find three rational numbers between \(\frac { 1 }{ 2 } \) and (-2)

5

(a)

Recall the associativity of the four operations for whole numbers through this table:

Operation	Numbers	Remarks
Addition	_________	Addition is associative.
Subtraction	_________	Subtraction is not associative.
Multiplication	Is \(7 \times (2 \times 5)=(7 \times 2) \times 5 ?\) Is \(4 \times (6 \times 0)=(4 \times 6) \times 0?\) For any three whole numbers a, b and c \(a \times (b \times c)=(a \times b) \times c?\)	Multiplication is associative.
Division	_________	Division is not associative.

Fill in this table and verify the remarks given in the last column.
Check for yourself the associativity of different operations for natural numbers.

5

(a)