Rational Numbers Test

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Rational Numbers Test - 16

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Weekly Quiz Competition

Question 1
1 / -0

$\displaystyle \frac{-7}{5} + \left(\displaystyle \frac{2}{-11} + \frac{-13}{25} \right) = \left(\displaystyle \dfrac{-7}{5} + \frac{2}{-11} \right) + \frac{-13}{25}$
This property is

A
closure

B
commutative

C
associative

D
identity

Solution

Since a + (b + c) = (a + b) + C is associative property.
Question 2
1 / -0

Which of the following order is correct for rational numbers between $\displaystyle \frac{4}{11}$ and $\displaystyle \frac{9}{16}?$

A
$\dfrac{4}{11}$ , $\dfrac{67}{176}$ , $\dfrac{79}{176}$ , $\dfrac{9}{16}$

B
$\dfrac{4}{11}$ , $\dfrac{67}{276}$ , $\dfrac{79}{176}$ , $\dfrac{9}{16}$

C
$\displaystyle \frac{4}{11}, \frac{17}{38}, \frac{13}{27}, \frac{22}{43}, \frac{9}{16}$

D
$\displaystyle \frac{4}{11}, \frac{27}{38}, \frac{13}{27}, \frac{22}{43}, \frac{9}{16}$

Solution

$L.C.M$ of $11$ and $16$ is $11\times 16 =176$

$\dfrac{4}{11}=\dfrac{4\times 16}{11\times 16}=\dfrac{64}{176}$

$\dfrac{9}{16}=\dfrac{9\times 11}{16\times 11}=\dfrac{99}{176}$

rational numbers between $\dfrac{4}{11}$ and $\dfrac{9}{16}$ are

$\dfrac{67}{176}$ , $\dfrac{79}{176}$
Question 3
1 / -0

The additive inverse of $\displaystyle \frac{-a}{b}$ is

A
$\displaystyle \frac{a}{b}$

B
$\displaystyle \frac{b}{a}$

C
$\displaystyle \frac{-b}{a}$

D
$\displaystyle \frac{-a}{b}$

Solution

$\therefore$ p + (-P) = (-P) + P = 0 is the additive inverse property.
So additive inverse of $\displaystyle \frac{-a}{b}$ is $\displaystyle \frac{a}{b}$
Question 4
1 / -0

Which one of the following is the rational number lying between $\displaystyle \frac{6}{7} \ and \ \frac{7}{8}?$

A
$\displaystyle \frac{3}{4}$

B
$\displaystyle \frac{99}{122}$

C
$\displaystyle \frac{95}{112}$

D
$\displaystyle \frac{97}{112}$

Solution

Required rational number $\displaystyle =\frac{1}{2}\left ( \frac{6}{7}+\frac{7}{8} \right )=\frac{1}{2}\left ( \frac{48+49}{56} \right )=\frac{97}{112}$
Hence option (d) is correct
Question 5
1 / -0

Which of the following statements is correct?

A
0 is called the additive identity for rational numbers.

B
1 is called the multiplicative identity for rational numbers.

C
The additive inverse of 0 is zero itself.

D
All the above

Solution

Option A.
For any rational number, additive element is an element which when added to the rational number, gives the same number as its sum. Like if $\dfrac{p}{q}$ is a rational number, where $p$ and $q$ are integers, $q$ not equal to zero. The above mentioned equation is additive identity and $0$ is an additive element.

Option B.
The multiplicative identity property states that any time you multiply a number by $1$ , the result, or product, is that original number. This is why $1$ is called the multiplicative identity for rational numbers.

Option C.
$0$ being neutral, has no sense of being written as $+0$ or $-0$ , hence, it is additive inverse of itself.

All the statements are correct.
Question 6
1 / -0

Multiplicative inverse of '0' is

A
$\displaystyle \frac{1}{0}$

B
0

C
Does not exist

D
$\displaystyle \frac{0}{0}$

Solution

Does not exist since division by zero is not defined.
Question 7
1 / -0

$x$ is additive identity of rational numbers.Then the value of x is

A
0

B
1

C
-1

D
None

Solution

Since $5 + 0 = 5$
$\therefore$ 0 is the additive identity of rational numbers.
Question 8
1 / -0

Rational numbers are closed under substraction.

A
True

B
False

C
Cannot be determined

D
None

Solution

Rational numbers are closed under subtraction.Because if we subtract a rational number with another rational number we will get rational number. For example $45 - 35 = 10$ , which is also a rational number.
Question 9
1 / -0

What is the additive inverse of $\displaystyle\frac{a}{b}$ ?

A
$\dfrac{-a}{b}$

B
$\dfrac{b}{a}$

C
$\dfrac{-b}{a}$

D
$\dfrac{a}{b}$

Solution

The additive inverse of a number is what you add to a number to create the sum of zero.

So in other words, the additive inverse of $x$ is another number, $y$ , as long as the sum of $x + y$ equals zero.

The additive inverse of $x$ is equal and opposite in sign to it (so, $y = -x$ or vice versa).

Let the additive inverse of $\cfrac{a}{b}$ be $z$ . Then,
$\cfrac{a}{b}+z=0$
$=>z=-\cfrac{a}{b}$
Question 10
1 / -0

Write the additive inverse of each of the following: $\dfrac{2}{8}$ and $-\dfrac{5}{9}$

A
$-\dfrac{2}{8}\;;\; \dfrac{5}{9}$ .

B
$-\dfrac{1}{5};\dfrac{3}{5}$

C
$\dfrac{1}{8};\dfrac{5}{9}$

D
$\dfrac17;\dfrac89$

Solution

The additive inverse of $\displaystyle\frac{2}{8}$ is $\begin{pmatrix}\displaystyle\frac{-2}{8}\end{pmatrix}=\displaystyle\frac{-2}{8}$ .

The additive inverse of $\displaystyle\frac{-5}{9}$ is $-\begin{pmatrix}\displaystyle\frac{-5}{9}\end{pmatrix}=\displaystyle\frac{5}{9}$ .

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Rational Numbers Test - 16

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Rational Numbers Test - 16

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Question 1

closure

commutative

associative

identity

Solution

Question 2

411\dfrac{4}{11}114​, 67176\dfrac{67}{176}17667​, 79176\dfrac{79}{176}17679​, 916\dfrac{9}{16}169​

411\dfrac{4}{11}114​, 67276\dfrac{67}{276}27667​, 79176\dfrac{79}{176}17679​, 916\dfrac{9}{16}169​

411,1738,1327,2243, 916\displaystyle \frac{4}{11}, \frac{17}{38}, \frac{13}{27}, \frac{22}{43}, \frac{9}{16}114​,3817​,2713​,4322​, 169​

411,2738,1327,2243, 916\displaystyle \frac{4}{11}, \frac{27}{38}, \frac{13}{27}, \frac{22}{43}, \frac{9}{16}114​,3827​,2713​,4322​, 169​

Solution

Question 3

ab\displaystyle \frac{a}{b}ba​

ba\displaystyle \frac{b}{a}ab​

−ba\displaystyle \frac{-b}{a}a−b​

−ab\displaystyle \frac{-a}{b}b−a​

Solution

Question 4

34\displaystyle \frac{3}{4}43​

99122\displaystyle \frac{99}{122}12299​

95112\displaystyle \frac{95}{112}11295​

97112\displaystyle \frac{97}{112}11297​

Solution

Question 5

0 is called the additive identity for rational numbers.

1 is called the multiplicative identity for rational numbers.

The additive inverse of 0 is zero itself.

All the above

Solution

Question 6

10\displaystyle \frac{1}{0}01​

0

Does not exist

00\displaystyle \frac{0}{0}00​

Solution

Question 7

0

1

-1

None

Solution

Question 8

True

False

Cannot be determined

None

Solution

Question 9

−ab\dfrac{-a}{b}b−a​

ba\dfrac{b}{a}ab​

−ba\dfrac{-b}{a}a−b​

ab\dfrac{a}{b}ba​

Solution

Question 10

−28 ; 59-\dfrac{2}{8}\;;\; \dfrac{5}{9}−82​;95​.

−15;35-\dfrac{1}{5};\dfrac{3}{5}−51​;53​

18;59\dfrac{1}{8};\dfrac{5}{9}81​;95​

17;89\dfrac17;\dfrac8971​;98​

Solution

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$\dfrac{4}{11}$ , $\dfrac{67}{176}$ , $\dfrac{79}{176}$ , $\dfrac{9}{16}$

$\dfrac{4}{11}$ , $\dfrac{67}{276}$ , $\dfrac{79}{176}$ , $\dfrac{9}{16}$

$\displaystyle \frac{4}{11}, \frac{17}{38}, \frac{13}{27}, \frac{22}{43}, \frac{9}{16}$

$\displaystyle \frac{4}{11}, \frac{27}{38}, \frac{13}{27}, \frac{22}{43}, \frac{9}{16}$

$\displaystyle \frac{a}{b}$

$\displaystyle \frac{b}{a}$

$\displaystyle \frac{-b}{a}$

$\displaystyle \frac{-a}{b}$

$\displaystyle \frac{3}{4}$

$\displaystyle \frac{99}{122}$

$\displaystyle \frac{95}{112}$

$\displaystyle \frac{97}{112}$

$\displaystyle \frac{1}{0}$

$\displaystyle \frac{0}{0}$

$\dfrac{-a}{b}$

$\dfrac{b}{a}$

$\dfrac{-b}{a}$

$\dfrac{a}{b}$

$-\dfrac{2}{8}\;;\; \dfrac{5}{9}$ .

$-\dfrac{1}{5};\dfrac{3}{5}$

$\dfrac{1}{8};\dfrac{5}{9}$

$\dfrac17;\dfrac89$