Properties of Rational Numbers

Author:Subject Experts

8th CBSE

IMPORTANT

Important Questions on Properties of Rational Numbers

MEDIUM

IMPORTANT

NCERT Practice Workbook Mathematics>Rational Numbers>Properties of Rational Numbers> Q 1

Write the rational numbers from the list which are also the integers.

$\frac{9}{4}, \frac{8}{4}, \frac{7}{4}, \frac{6}{4}, \frac{9}{3}, \frac{8}{3}, \frac{7}{3}, \frac{6}{3}, \frac{5}{2}, \frac{4}{2}, \frac{3}{1}, \frac{3}{2}, \frac{1}{1}, \frac{0}{1}, \frac{- 1}{1}, \frac{- 2}{1}, \frac{- 3}{2}, \frac{- 4}{2}, \frac{- 5}{2}, \frac{- 6}{2}$

EASY

IMPORTANT

NCERT Practice Workbook Mathematics>Rational Numbers>Properties of Rational Numbers> Q 2

What are of the form $\frac{a}{b}$ , where $a$ and $b$ are natural numbers.

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IMPORTANT

NCERT Practice Workbook Mathematics>Rational Numbers>Properties of Rational Numbers> Q 3

$\frac{7}{2}$ is

MEDIUM

IMPORTANT

NCERT Practice Workbook Mathematics>Rational Numbers>Properties of Rational Numbers> Q 4

Name the properties used in the following.

- \frac{2}{9} + 0 = 0 + \frac{- 2}{9} = - \frac{2}{9}

EASY

IMPORTANT

NCERT Practice Workbook Mathematics>Rational Numbers>Properties of Rational Numbers> Q 5

Name the property used in the following.

\frac{1}{2} \times [\frac{1}{5} + (- \frac{1}{7})] = \frac{1}{2} \times \frac{1}{5} + \frac{1}{2} \times (\frac{- 1}{7})

EASY

IMPORTANT

NCERT Practice Workbook Mathematics>Rational Numbers>Properties of Rational Numbers> Q 6

Name the property used in the following.

[\frac{4}{5} \times (\frac{- 3}{5})] \times \frac{1}{2} = \frac{4}{5} \times [(- \frac{3}{5}) \times \frac{1}{2}]

EASY

IMPORTANT

NCERT Practice Workbook Mathematics>Rational Numbers>Properties of Rational Numbers> Q 7

Name the property used in the following.

\frac{2}{3} \times (5 \times \frac{6}{7}) = (\frac{2}{3} \times 5) \times \frac{6}{7}

EASY

IMPORTANT

NCERT Practice Workbook Mathematics>Rational Numbers>Properties of Rational Numbers> Q 8

Is $(\frac{- 13}{5} \times \frac{6}{7}) \times \frac{8}{9} = \frac{- 13}{5} \times \frac{6}{7} \times \frac{8}{9} ?$ Verify.

MEDIUM

IMPORTANT

NCERT Practice Workbook Mathematics>Rational Numbers>Properties of Rational Numbers> Q 9

The table given below shows the distances (in kilometres) between four villages of a state. To find the distance between two villages, locate the square where the row for one village and the column for the other village.

Villages	Sonapur	Ramgarh	Himgaon	Rawalpur
Sonapur	X	$40 \frac{2}{3}$	$100 \frac{5}{6}$	$16 \frac{1}{2}$
Ramgarh	$40 \frac{2}{3}$	X	$210 \frac{3}{8}$	$30 \frac{2}{3}$
Himgaon	$100 \frac{5}{6}$	$210 \frac{3}{8}$	X	$98 \frac{3}{4}$
Rawalpur	$16 \frac{1}{2}$	$30 \frac{2}{3}$	$98 \frac{3}{4}$	X

Ravi and Ajay are two friends. They both want to go Himgaon from Sonapur. "If Ravi first move Sonapur to Ramgarh and then Himgaon. While Ajay first move Sonapur to Rawalpur and then Himgaon."

Who will reach first and which value is depicted here?

HARD

IMPORTANT

NCERT Practice Workbook Mathematics>Rational Numbers>Properties of Rational Numbers> Q 10

Match the column

Column I	Column II
a. The equivalent rational number of $\frac{5}{7}$ , whose numerator is $35$ , is	(i) $\frac{21}{8}$
b. Rational number $\frac{57}{1140}$ is equivalent to	(ii) $\frac{104}{21}$
c. If $a = \frac{1}{4}$ and $b = \frac{3}{2}$ , then $(a + b) + (a - b)$ is equal to	(iii) $\frac{- 7}{6}$
d. The reciprocal of $\frac{- 3}{8} \times (\frac{- 7}{13})$ is	(iv) $\frac{- 15}{4}$
e. The multiplicative inverse of $- 1 \frac{1}{7}$ is	(v) $\frac{35}{49}$
f. To get the product $1$ , we should multiply $\frac{8}{21}$ by	(vi) $\frac{1}{20}$
g. The reciprocal of $\frac{3}{5} \times (\frac{- 4}{9})$ is	(vii) $\frac{1}{2}$

HARD

IMPORTANT

NCERT Practice Workbook Mathematics>Rational Numbers>Properties of Rational Numbers> Q 11

Match the columns

Column I	Column II
$a .$ The rational number which is equal to its negative, is	$(i)$ Subtraction
$b .$ The rational number which does not have a reciprocal, is	$(ii)$ Division
$c .$ The rational numbers which are equal to its reciprocals, are	$(iii)$ Zero
$d .$ If zero is excluded from the collection of rational numbers, then the rational numbers are closed under	$(iv)$ One
$e .$ Both natural numbers and whole numbers are not commutative under	$(v)$ Negative of one

MEDIUM

IMPORTANT

NCERT Practice Workbook Mathematics>Rational Numbers>Properties of Rational Numbers> Q 12

Give an example to show that the rational numbers are closed under addition, subtraction and multiplication. Are rational numbers closed under division? Give two examples to support your answer.

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IMPORTANT

NCERT Practice Workbook Mathematics>Rational Numbers>Properties of Rational Numbers> Q 13

By using which property, the value of $\frac{6}{7} (\frac{1}{3} - 3)$ can be determined. Also, find the value.

MEDIUM

IMPORTANT

NCERT Practice Workbook Mathematics>Rational Numbers>Properties of Rational Numbers> Q 14

If $a, b$ and $c$ are the three rational numbers, where $a = \frac{1}{3}, b = \frac{2}{5}$ and $c = \frac{- 5}{3}$ .

Then, verify $a \times (b \times c) = (a \times b) \times c$ (associative property of multiplication)

MEDIUM

IMPORTANT

NCERT Practice Workbook Mathematics>Rational Numbers>Properties of Rational Numbers> Q 15

If $a, b$ and $c$ are the three rational numbers, where $a = \frac{1}{3}, b = \frac{2}{5}$ and $c = \frac{- 5}{3}$ .
Then, verify $a + (b + c) = (a + b) + c$ (associative property of addition)