Rational Numbers Test

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Rational Numbers Test - 5

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Weekly Quiz Competition

Question 1
1 / -0

Suprabha purchases $3 \frac{1}{2} k g$ of watermelons, $\frac{5}{6} k g$ of apples and $\frac{3}{4} k g$ guavas from a fruit seller. What is the total quantity of fruits purchased by her?

A
$4 \frac{5}{9} k g$

B
$3 \frac{1}{2} k g$

C
$6 \frac{1}{4} k g$

D
$5 \frac{1}{12} \mathrm{kg}$

Solution

$3 \frac{1}{2}+\frac{5}{6}+\frac{3}{4}=\frac{7}{2}+\frac{5}{6}+\frac{3}{4}=\frac{42+10+9}{12}=\frac{61}{12}=5 \frac{1}{12}$
Question 2
1 / -0

Raju, Suraj and Subhash participated in a long jump competition on their school's sports day. Raju jumped $5 \frac{1}{2} m$ Whiie Suraj jumped $\frac{1}{4} m$ less than Raju. On the other hand, Subhash jumped $1 \frac{1}{4} \mathrm{m}$ more than Suraj. How long did Subhash jump?

A
$6 \frac{1}{2} m$

B
7 m

C
$4 \frac{1}{2} m$

D
18 m

Solution

Subhash's jump $=5 \frac{1}{2}-\frac{1}{4}+1 \frac{1}{4}$$=5 \frac{1}{2}+1=6 \frac{1}{2}$
Question 3
1 / -0

$\frac{1}{1+\frac{1}{5+\frac{1}{3}}}=$

A
$\frac{5}{19}$

B
$\frac{7}{9}$

C
$\frac{16}{19}$

D
None of these

Solution

This problem is always solved from below.
$5+\frac{1}{3}=\frac{16}{3}$
then, $1+\frac{3}{16}=\frac{19}{16}$
then, $\frac{1}{19 / 16}=\frac{16}{19}$
Question 4
1 / -0

Name the property of multiplication illustrated by $\frac{-3}{7} \times\left(\frac{-6}{11}+\frac{8}{9}\right)=\left(\frac{-3}{7} \times \frac{-6}{11}\right)+\left(\frac{-3}{7} \times \frac{8}{9}\right)$

A
Associative property

B
Commutative property

C
Distributive property

D
Closure property

Solution

Distributive property means $a \times(b+c)=(a \times b)+(a \times c)$ or
$-a \times(-b+c)=(-a \times-b)+(-a \times c)$
Question 5
1 / -0

For what value of ${ }^{\prime} x^{\prime}$ is $\frac{3}{8}-\left(-\frac{17}{4}\right)+x=-1 \frac{9}{24}$?

A
-6

B
6

C
-1/6

D
+1/6

Solution

$\frac{3}{8}-\left(-\frac{17}{4}\right)+x=-1 \frac{9}{24}$
$\Rightarrow x=\frac{-33}{24}-\frac{37}{8}=\frac{-33-111}{24}=\frac{-144}{24}=-6$
Question 6
1 / -0

of which property is $\frac{-5}{7}+\left(\frac{3}{-11}+\frac{-10}{25}\right)=\left(\frac{-5}{7}+\frac{3}{-11}\right)+\frac{-10}{25}$ an example?

A
Closure property

B
Commutative property

C
Associative property

D
Identity property

Solution

Associative property means: $a+(b+c)=(a+b)+c$
Question 7
1 / -0

For any two rational numbers a and b, which of the following properties may be correct?
(i) a < b
(ii) a=b
(iii) a>b

A
Only (i) and (ii) are correct

B
Only (i) and (iii) are correct

C
Only (ii) and (iii) are correct

D
All (i), (ii) and (iii) are correct

Solution

All possibilities exist: For example if a = 2/3 b = 5/6 then a a < b
If $a=\frac{4}{6}$, $b=\frac{8}{12}$ $\Rightarrow a=b$;
If $a=\frac{13}{12}=\frac{11}{12}$ then $a>b$
Question 8
1 / -0

Which of the following statements is true?

A
The reciprocals of numbers 1 and −1 are numbers themselves.

B
Zero has no reciprocal.

C
The product of two rational numbers is a rational number.

D
All the above

Solution

All the above
Question 9
1 / -0

Which row is correctly matched?
Row Rational Number Standard Form
A. $\frac{-1}{3}$ $\frac{1}{-3}$
B. $\frac{-3}{11}$ $\frac{3}{11}$
C. $\frac{2}{11}$ $\frac{-2}{11}$
D. $\frac{9}{2}$ $\frac{-9}{2}$

A
Row A

B
Row B

C
Row C

D
Row D

Solution

Let additive increase of $\frac{2}{11}$ be 'a' Let then $\frac{2}{11}+a=0 \Rightarrow a=\frac{-2}{11}$
Question 10
1 / -0

Reena is travelling from her village to another town. The distance between the village & town is $45 \frac{3}{4} \mathrm{km}$ She stops to rest after covering a distance of $34 \frac{1}{3} k\m). How much distance does she further need to cover to reach the other town?

A
\(11 \frac{3}{4} k m$

B
$20 \frac{1}{2} k m$

C
$09 \frac{5}{12} \mathrm{km}$

D
$11 \frac{5}{12} \mathrm{km}$

Solution

$34 \frac{1}{3}+x=45 \frac{3}{4} \Rightarrow x=45 \frac{3}{4}-34 \frac{1}{3}=11 \frac{5}{12} \mathrm{km}$
Question 11
1 / -0

Evaluate $\mathrm{p}+\mathrm{q}$ given $P=\left(-6 \frac{1}{6}\right) \mathrm{and} q=\left(-8 \frac{1}{8}\right)$

A
$\left(-14 \frac{13}{24}\right)$

B
$\left(-14 \frac{7}{24}\right)$

C
$\left(-3 \frac{8}{18}\right)$

D
$\left(13 \frac{19}{24}\right)$

Solution

Given $\mathrm{p}+\mathrm{q}=\left(-6 \frac{1}{6}\right)+\left(-8 \frac{1}{8}\right)$
$=\frac{-37}{6}-\frac{65}{8}$$=\frac{-148-125}{24}$
$=\frac{-343}{24}=-14 \frac{7}{24}$
Question 12
1 / -0

The value of A such that $-\frac{5}{8}$ and $\frac{A}{-32}$ are equivalent rational numbers is

A
22

B
-36

C
16

D
20

Solution

$\frac{-5}{8}=\frac{-5 \times 4}{8 \times 4}=\frac{20}{-32} \Rightarrow A=20$
Question 13
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Which of the following statements is correct?

A
0 is called the additive identity for rational number

B
1 is called the multiplicative identity

C
The additive inverse of 0 is zero itself.

D
All the above

Solution

(d) All the given statements are correct.
Consider $\frac{1}{7}$
(a) Since $\frac{1}{7}+0=$ hence $\frac{1}{7}$ is the additive identity of rational numbers.
(b) Since $\frac{1}{7} \times 1=\frac{1}{7}, 1$ is the multiplicative identity of rational number.
(c) Since 0 + 0 = 0, 0 is the additive inverse of 0.
Question 14
1 / -0

The value of $1+\frac{1}{1+\frac{1}{5-\frac{1}{5}}}$ is ...........

A
$\frac{36}{29}$

B
$\frac{53}{29}$

C
$\frac{17}{8}$

D
None of these

Solution

$5-\frac{1}{5}=\frac{24}{5}$ then $\frac{1}{24 / 5}=\frac{5}{24}$ then $1+\frac{5}{24}=\frac{29}{24}$ then, $\frac{1}{29 / 24}=\frac{24}{29}$ then $1+\frac{24}{29}=\frac{53}{29}$
Question 15
1 / -0

If a, b, c be rational numbers such that a > b and c < b then.............

A
c > a

B
c < a

C
b < a

D
b > a

Solution

a > b and c < b
⇒ b > c
Thus, a > b;
b > c ⇒ a > b > c ⇒ a > c or c < a

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Re-Attempt Weekly Quiz Competition

Row	Rational Number	Standard Form
A.	$\frac{-1}{3}$	$\frac{1}{-3}$
B.	$\frac{-3}{11}$	$\frac{3}{11}$
C.	$\frac{2}{11}$	$\frac{-2}{11}$
D.	$\frac{9}{2}$	$\frac{-9}{2}$

Rational Numbers Test - 5

Result

Rational Numbers Test - 5

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SHARING IS CARING

Question 1

\(4 \frac{5}{9} k g\)

\(3 \frac{1}{2} k g\)

\(6 \frac{1}{4} k g\)

\(5 \frac{1}{12} \mathrm{kg}\)

Solution

Question 2

\(6 \frac{1}{2} m\)

7 m

\(4 \frac{1}{2} m\)

18 m

Solution

Question 3

\(\frac{5}{19}\)

\(\frac{7}{9}\)

\(\frac{16}{19}\)

None of these

Solution

Question 4

Associative property

Commutative property

Distributive property

Closure property

Solution

Question 5

-6

6

-1/6

+1/6

Solution

Question 6

Closure property

Commutative property

Associative property

Identity property

Solution

Question 7

Only (i) and (ii) are correct

Only (i) and (iii) are correct

Only (ii) and (iii) are correct

All (i), (ii) and (iii) are correct

Solution

Question 8

The reciprocals of numbers 1 and −1 are numbers themselves.

Zero has no reciprocal.

The product of two rational numbers is a rational number.

All the above

Solution

Question 9

Row A

Row B

Row C

Row D

Solution

Question 10

\(11 \frac{3}{4} k m\)

\(20 \frac{1}{2} k m\)

\(09 \frac{5}{12} \mathrm{km}\)

\(11 \frac{5}{12} \mathrm{km}\)

Solution

Question 11

\(\left(-14 \frac{13}{24}\right)\)

\(\left(-14 \frac{7}{24}\right)\)

\(\left(-3 \frac{8}{18}\right)\)

\(\left(13 \frac{19}{24}\right)\)

Solution

Question 12

22

-36

16

20

Solution