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)

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

Three rational numbers lying between\(\frac{-5}{4}\) and \(\frac{1}{2}\)are

1

(a)

-1, 0 ,\(\frac{4}{3}\)

(b)

\(\frac{-3}{4},\frac{-1}{2},\frac{1}{4}\)

(c)

\(\frac{-3}{4},\frac{4}{3},\frac{1}{4}\)

(d)

\(\frac{-7}{4},-1,0\)

\(\frac{x+y}{2}\) is a rational number

1

(a)

between x and y

(b)

less than x and y both

(c)

greater than x and y both

(d)

less than x but greater than y

Which of the following is the reciprocal of p?

1

(a)

-p

(b)

p

(c)

\(\frac { 1 }{ p } \)

(d)

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

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
Rational numbers	Yes	Yes	__________	No

1

(a)

Numbers	Closed under
	Addition	Subtraction	Multiplication	Division
Rational numbers	Yes e.g \(({3\over8}+{(-5)\over7})\\=3\times7+(-5)\times8\over56\\ {21+(-40)\over56}={-19\over56},Rational \ number\)	Yes\(({(-5)\over 7}+{2\over3}) \\= (-5)\times3-2\times7\over21 \\{-15-14\over21}={-29\over21}, \\Rational \ number\)	yes \(e.g ({-4\over5}\times{-6\over11})={24\over55} \\ Rational \ number\)	No \(e.g ({4\over5}​​\div0) Not \ defined\)

Numbers	Closed under
	Addition	Subtraction	Multiplication	Division
Integers	___________	Yes	__________	No

1

(a)

Numbers	Closed under
	Addition	Subtraction	Multiplication	Division
Integers	Yes e.g (-6+5=-1) Integers	Yes(7-5=2) Integers	yes (5x8=40) Integers​​​​​​​	No (5\(\div\)8)​​​​​​\(\neq\)Integers​​​​​​​​​​​​​​

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

The rational number _________is neither positive nor negative.

1

(a)

0

______________is the only rational number which is equal to its additive inverse.

1

(a)

0

All the natural numbers are whole numbers.

1

(a) False

(b) True

All the whole numbers are integers

1

(a) False

(b) True

All the integers are rational numbers.

1

(a) False

(b) True

All the fractions are not rational numbers but all the rational numbers are fractions

1

(a) True

(b) False

Zero is a rational number

1

(a) False

(b) True

Is there any rational number which when multiplied by 0 gives 1?

2

(a)

No

Which rational numbers are their own reciprocals?

2

(a)

1 and - 1

Is there a rational number that is equal to its negative? If yes, write it.

2

(a)

Yes, 0

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

2

(a)

Verify that -(-x) = x,for x = \(-13\over17\)

2

(a)

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

2

(a)

Using appropriate properties, find  \({2\over 3}\times{-5\over 7}+{7\over3}+{2\over3}\times{-2\over7}\)

2

(a)

If a property holds for rational number, will it also hold for integers? For whole numbers? Which will? Which will not?

2

(a)

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

2

(a)

Find three rational numbers between -3 and - 4

2

(a)

Find the value of  \({x\over y }+xy\) , using appropriate property and name it \(x={3\over4} \ y=2\)

5

(a)

1. Use the distributivity of multiplication of rational numbers over addition to simplify:
   \({2\over7}\times[{7\over16}-{21\over4}]\)

   5

   (a)

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

   5

   (a)