Rational Numbers Test

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Rational Numbers Test - 4

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Weekly Quiz Competition

Question 1
1 / -0

Which of the following statements is incorrect?

A
A rational number is of the form x/y, where x and y are integers and y≠0.

B
The product of two negative rational number is negative rational number.

C
There are infinite rational numbers between any two rational numbers.

D
All fractions greater than 1 are rational numbers.

Solution

Product of two negative number is always positive.
Question 2
1 / -0

Which of the following statements is incorrect?

A
The number $\frac{5}{2}$ lies between 2 and 3

B
The number $\frac{11}{12}$ lies between $\frac{5}{6}$ and $\frac{23}{24}$

C
The number $\frac{3}{4}$ lies between $\frac{2}{3}$ and $\frac{6}{7}$

D
The number $\frac{5}{9}$ lies between $\frac{2}{3}$ and $\frac{3}{4}$

Solution

Take LCM of $\frac{5}{9}, \frac{2}{3}, \frac{3}{4}\Rightarrow$$\frac{20}{36}, \frac{24}{36}, \frac{27}{36}$ and compare;
we can see that $\frac{20}{36}$ does not lie between $\frac{24}{36}$ and $\frac{27}{36}$
Question 3
1 / -0

p: All integers are rational numbers.
q: Every rational number is an integer.
Which of the following statements is correct?

A
p is false and q is true.

B
p is true and q is false.

C
Both p and q are true.

D
Both p and q are false.

Solution

Since, every integer can have a denominator 1,
so it can be expressed in p/q form.
Hence statement 'p' is true.
But every rational number, say −6/7, is not an integer.
Question 4
1 / -0

If $\frac{-4}{9}=\frac{-16}{x},$ what is the value of $x ?$

A
36

B
-36

C
42

D
-42

Solution

$\frac{-4}{9}=\frac{-16}{x}$ Cross multiply $\Rightarrow-4 x=-9 \times 16$
Question 5
1 / -0

Meena's height is $3 \frac{5}{6}$ feet. If her sister Gita is $4 \frac{6}{7}$ feet tall, then what is the difference between their heights?

A
$\frac{10}{11}$ feet

B
$1 \frac{1}{6}$ feet

C
$\frac{2}{7}$ feet

D
$1 \frac{1}{42} \mathrm{feet}$

Solution

$4 \frac{6}{7}-3 \frac{5}{6}$
Question 6
1 / -0

Which of the following pairs of numbers is not a pair of equivalent rational numbers?

A
$\frac{13}{2}$ and $\frac{65}{10}$

B
$\frac{15}{36}$ and $\frac{63}{108}$

C
$\frac{4}{5}$ and $\frac{16}{20}$

D
None of these

Solution

$\frac{15}{36}=\frac{5}{12}$ where as $\frac{63}{109}=\frac{7}{12}$
Question 7
1 / -0

p: Every fraction is a rational number.
q: Every rational number is a fraction.
Which of the following is correct?

A
p is true and q is false.

B
p is false and q is true.

C
Both p and q are true.

D
Both p and q are false.

Solution

Let us consider a fraction 27; this is also a rational number.
However a rational number say, 6 is not a fraction
∴ 'p' is true, 'q' is false.
Question 8
1 / -0

Which of the following statements is true?

A
$\frac{5}{-8}>\frac{-20}{32}$

B
$\frac{5}{-8}=\frac{-20}{32}$

C
$\frac{5}{-8}<\frac{-20}{32}$

D
$\frac{5}{6}<\frac{11}{12}$

Solution

$\frac{5}{-8}=\frac{5 \times 4}{-8 \times 4}=\frac{20}{-32}=\frac{-20}{32}$
Question 9
1 / -0

What type of a numerator does $\frac{0}{9}$ have?

A
Positive

B
Negative

C
Either positive or negative

D
Neither positive nor negative

Solution

Neither positive nor negative
Question 10
1 / -0

Which row is incorrectly matched?
Row Rational Number Standard Form
A. $22/ - 42$ $1/ 2$
B. $- 12/ - 21$ $4/ 7$
C. $27/ 30$ $9/ 10$
D. $- 32/ 56$ $- 4/ 7$

A
Row A

B
Row B

C
Row C

D
Row D

Solution

$\frac{22}{-42}=\frac{-22}{42}=\frac{-11}{21} \neq \frac{1}{2}$
Question 11
1 / -0

What is the value of the expression $\left[-\frac{17}{18} \times(-3) \times \frac{108}{30}\right]$

A
$\frac{-108}{10}$

B
$\frac{62}{5}$

C
$\frac{51}{5}$

D
$\frac{17}{33}$

Solution

$\frac{-17}{18} \times-3 \times \frac{108}{30}=\frac{-17}{18} \times(-1) \times \frac{108}{10}=17 \times \frac{6}{10}=\frac{51}{5}$
Question 12
1 / -0

Which of the following is not a rational number(s)?

A
$\frac{-2}{19}$

B
$\frac{2}{-8}$

C
$\frac{-3}{-13}$

D
$\frac{\sqrt{2}}{6}$

Solution

$\frac{\sqrt{2}}{3}$ is not a rational number as $\sqrt{2}$ is not an integer
Question 13
1 / -0

Which among the following is a rational number equivalent to $\frac{-13}{3}$ ?

A
$\frac{-100}{27}$

B
$\frac{26}{6}$

C
$\frac{-117}{27}$

D
$\frac{15}{25}$

Solution

$\frac{-117}{27}=\frac{-13 \times 9}{3 \times 9}=\frac{-13}{3}$
Question 14
1 / -0

How can the rational numbers $\frac{11}{15}, \frac{-11}{12}, \frac{-4}{9}$ and $\frac{7}{12}$ be written in ascending order?

A
$\frac{-11}{12}<\frac{-4}{9}<\frac{11}{15}<\frac{7}{12}$

B
$\frac{-11}{12}<\frac{-4}{9}<\frac{7}{12}<\frac{11}{15}$

C
$\frac{-4}{9}<\frac{-11}{12}<\frac{7}{12}<\frac{11}{15}$

D
$\frac{-4}{9}<\frac{-11}{12}<\frac{11}{15}<\frac{7}{12}$

Solution

Take LCM of all fraction and compare.
Question 15
1 / -0

What type of a number is −6/0?

A
A positive rational number

B
A negative rational number

C
Either a positive or a negative rational number

D
Neither a positive nor a negative rational number

Solution

Since, denominator is 0, it is not a rational number.

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Re-Attempt Weekly Quiz Competition

Row	Rational Number	Standard Form
A.	$22/ - 42$	$1/ 2$
B.	$- 12/ - 21$	$4/ 7$
C.	$27/ 30$	$9/ 10$
D.	$- 32/ 56$	$- 4/ 7$

Rational Numbers Test - 4

Result

Rational Numbers Test - 4

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SHARING IS CARING

Question 1

A rational number is of the form x/y, where x and y are integers and y≠0.

The product of two negative rational number is negative rational number.

There are infinite rational numbers between any two rational numbers.

All fractions greater than 1 are rational numbers.

Solution

Question 2

The number \(\frac{5}{2}\) lies between 2 and 3

The number \(\frac{11}{12}\) lies between \(\frac{5}{6}\) and \(\frac{23}{24}\)

The number \(\frac{3}{4}\) lies between \(\frac{2}{3}\) and \(\frac{6}{7}\)

The number \(\frac{5}{9}\) lies between \(\frac{2}{3}\) and \(\frac{3}{4}\)

Solution

Question 3

p is false and q is true.

p is true and q is false.

Both p and q are true.

Both p and q are false.

Solution

Question 4

36

-36

42

-42

Solution

Question 5

\(\frac{10}{11}\) feet

\(1 \frac{1}{6}\) feet

\(\frac{2}{7}\) feet

\(1 \frac{1}{42} \mathrm{feet}\)

Solution

Question 6

\(\frac{13}{2}\) and \(\frac{65}{10}\)

\(\frac{15}{36}\) and \(\frac{63}{108}\)

\(\frac{4}{5}\) and \(\frac{16}{20}\)

None of these

Solution

Question 7

p is true and q is false.

p is false and q is true.

Both p and q are true.

Both p and q are false.

Solution

Question 8

\(\frac{5}{-8}>\frac{-20}{32}\)

\(\frac{5}{-8}=\frac{-20}{32}\)

\(\frac{5}{-8}<\frac{-20}{32}\)

\(\frac{5}{6}<\frac{11}{12}\)

Solution

Question 9

Positive

Negative

Either positive or negative

Neither positive nor negative

Solution

Question 10

Row A

Row B

Row C

Row D

Solution

Question 11

\(\frac{-108}{10}\)

\(\frac{62}{5}\)

\(\frac{51}{5}\)

\(\frac{17}{33}\)

Solution

Question 12

\(\frac{-2}{19}\)

\(\frac{2}{-8}\)

\(\frac{-3}{-13}\)

\(\frac{\sqrt{2}}{6}\)

Solution