Free Rational Numbers 02 Practice Test - 8th Grade

Question 1

The ___ property states that we can add rational numbers in any order.

commutative

B. associative

C. closure

D. distributive

SOLUTION

Solution : A

The addition of rational numbers can be done in any order and the result remains the same. This is called commutative property.
E.g: 2 + 3 = 3 + 2

Question 2

Choose the rational numbers whose numerator is $(- 5) \times 6$ , and the denominator is $(34 - 23) \times (7 - 5)$ .

$\frac{20}{11}$

$\frac{40}{22}$

$\frac{- 15}{11}$

$\frac{- 30}{22}$

SOLUTION

Solution : C and D

Rational numbers are the numbers which can be expressed in the form of $\frac{p}{q}$ , given $q \neq 0$ , p and q are integers.

$\frac{p}{q} = \frac{- 5 \times 6}{(34 - 23) \times (7 - 5)}$

$= \frac{- 30}{11 \times 2}$

$= \frac{- 30}{22}$

$= \frac{- 15}{11}$

Question 3

Write down the rational number whose numerator is the smallest four digit number and denominator is the largest five digit number.

$\frac{1000}{99999}$

$\frac{1000}{99900}$

$\frac{9999}{99999}$

$\frac{1000}{10000}$

SOLUTION

Solution : A

The smallest four digit number is 1000 and largest five digit number is 99999.

Therefore, the required rational number is $\frac{smallest four digit number}{largest five digit number} = \frac{1000}{99999}$ .

Question 4

Which of the following pair of rational numbers are smaller than -5?

$\frac{- 12}{2}$ & $\frac{- 20}{2}$

$\frac{- 10}{5}$ & $\frac{- 32}{4}$

$\frac{- 27}{3}$ & $\frac{- 18}{3}$

$\frac{- 100}{5}$ & $\frac{- 200}{5}$

SOLUTION

Solution : A, C, and D

a) $\frac{- 12}{2} = - 6$ & $\frac{- 20}{2} = - 10$
-6 and -10 are smaller than -5.

b) $\frac{- 10}{5} = - 2$ & $\frac{- 32}{4} = - 8$
-2 is greater than -5.

c) $\frac{- 27}{3} = - 9$ & $\frac{- 18}{3} = - 6$
-9 and -6 are smaller than -5.

d) $\frac{- 100}{5} = - 20$ & $\frac{- 200}{5} = - 40$
-20 and -40 are smaller than -5.

Question 5

Arrange the following rational numbers in the ascending order
$\frac{5}{4}, \frac{2}{3}, \frac{6}{8}, \frac{8}{5}, \frac{9}{2} .$

$\frac{2}{3} < \frac{6}{8} < \frac{5}{4} < \frac{8}{5} < \frac{9}{2}$

$\frac{5}{4} < \frac{6}{8} < \frac{2}{3} < \frac{8}{5} < \frac{9}{2}$

$\frac{9}{2} < \frac{8}{5} < \frac{5}{4} < \frac{6}{8}$ < $\frac{2}{3}$

$\frac{9}{2} < \frac{2}{3} < \frac{5}{4} < \frac{8}{5} < \frac{6}{8}$

SOLUTION

Solution : A

To compare the rational numbers, we first make the denominators equal.

L.C.M of the denominators 4, 3, 8, 5, 2 is 120.

Equivalent fractions with the denominator 120 are

$\frac{5}{4} \times \frac{30}{30} = \frac{150}{120}$

$\frac{2}{3} \times \frac{40}{40} = \frac{80}{120}$

$\frac{6}{8} \times \frac{15}{15} = \frac{90}{120}$

$\frac{8}{5} \times \frac{24}{24} = \frac{192}{120}$

$\frac{9}{2} \times \frac{60}{60} = \frac{540}{120}$

Since the denominator is same in the above equivalent fractions, we can decide the ascending order based on the numerator values.

Ascending order :
$\frac{2}{3} < \frac{6}{8} < \frac{5}{4} < \frac{8}{5} < \frac{9}{2}$

Question 6

Product of $\frac{7}{6}$ and reciprocal of $\frac{11}{66}$ is __________.

$\frac{1}{6}$

$\frac{7}{6}$

$7$

$\frac{7}{11}$

SOLUTION

Solution : C

Reciprocal of $\frac{11}{66} = \frac{66}{11}$

$\Rightarrow \frac{7}{6} \times \frac{66}{11} = 7 \times \frac{11}{11} = 7$

Question 7

$\frac{- 15}{51}$ is a multiplicative inverse of $\frac{- 17}{5}$ .

True

False

SOLUTION

Solution : A

Multiplicative inverse of $\frac{a}{b}$ is $\frac{c}{d}$ if $\frac{a}{b} \times \frac{c}{d} = 1$ .

Now, $\frac{- 15}{51} \times \frac{- 17}{5} = \frac{3}{3} = 1$

Question 8

Which of the following rational numbers are equivalent to $\frac{9}{4}$ ?

$\frac{12}{3}$

$\frac{81}{25}$

$\frac{63}{28}$

$\frac{36}{16}$

SOLUTION

Solution : C and D

When we multiply and divide a rational number by the same number, the value of rational number remains unchanged. Therefore,

$\frac{9}{4} \times \frac{7}{7} = \frac{63}{28} \frac{9}{4} \times \frac{4}{4} = \frac{36}{16}$

Question 9

Which of the following statements is incorrect?

Every whole number is a rational number

Every integer is a rational number

Zero is a whole number and it is rational number too

Every rational number is not an integer

SOLUTION

Solution : C

Zero is a whole number as well as the rational number. Zero can be expressed in the form of $\frac{p}{q}$ as $\frac{0}{1}$ . Hence zero is a rational number since it satisfies the definition of rational number where p = 0 and q $\neq$ 0.

Question 10

Which of the following rational numbers lie betwen $\frac{3}{7}$ and $\frac{4}{8}$ ?

$\frac{9}{2}$

$\frac{26}{56}$

-2

$\frac{13}{28}$

SOLUTION

Solution : B and D

L.C.M of 7 and 8 is 56.

$\frac{3}{7}$ and $\frac{4}{8}$ can be written as $\frac{24}{56}$ and $\frac{28}{56}$ .

Check for numbers which lie between $\frac{24}{56}$ and $\frac{28}{56}$ .

Now, $\frac{13}{28}$ = $\frac{26}{56}$ lies between $\frac{3}{7}$ and $\frac{4}{8}$ .

Free Rational Numbers 02 Practice Test - 8th Grade

Question 1

SOLUTION

Question 2

SOLUTION

Question 3

SOLUTION

Question 4

SOLUTION

Question 5

SOLUTION

Question 6

SOLUTION

Question 7

SOLUTION

Question 8

SOLUTION

Question 9

SOLUTION

Question 10

SOLUTION

Related ExamsCubes and Cube Roots 02Direct and Inverse Proportions 02Introduction to Graphs 02

Related Exams
Cubes and Cube Roots 02
Direct and Inverse Proportions 02
Introduction to Graphs 02