Free Rational Numbers 01 Practice Test - 7th grade

Question 1

The sum of the rational numbers $\frac{- 8}{19}$ and $\frac{- 4}{57}$ is _____.

$\frac{- 28}{57}$

$\frac{- 12}{57}$

$\frac{- 42}{47}$

$\frac{- 32}{47}$

SOLUTION

Solution : A

$\frac{- 8}{19} + \frac{- 4}{57} = \frac{(- 8 \times 3)}{(19 \times 3)} + \frac{- 4}{57}$

$= \frac{- 24}{57} + \frac{- 4}{57}$

$= \frac{- 28}{57}$

Question 2

Find the greatest rational number among the given options.

$- \frac{4}{9}$

$- \frac{5}{12}$

$- \frac{7}{18}$

$- \frac{2}{3}$

SOLUTION

Solution : C

Note that LCM of 9, 12, 18, 3 is 36.

Using LCM to convert each of the given rational numbers to equivalent forms,

$- \frac{4}{9}$ = $- \frac{16}{36}$

$- \frac{5}{12}$ = $- \frac{15}{36}$

$- \frac{7}{18}$ = $- \frac{14}{36}$

$- \frac{2}{3}$ = $- \frac{24}{36}$
Since the denominators are equal, we now compare the rational numbers using its numerators.
Thus, $- \frac{24}{36} < - \frac{16}{36} < - \frac{15}{36} < - \frac{14}{36}$
i.e., $- \frac{2}{3} < - \frac{4}{9} < - \frac{5}{12} < - \frac{7}{18}$
$∴ - \frac{7}{18}$ is the greatest among the given options.

Question 3

Which of the following forms a pair of equivalent rational numbers?

$\frac{24}{40}$ and $\frac{35}{50}$

$\frac{- 25}{35}$ and $\frac{55}{- 77}$

$\frac{- 8}{15}$ and $\frac{- 24}{48}$

$\frac{9}{72}$ and $\frac{- 3}{21}$

SOLUTION

Solution : B

When we have to compare two rational numbers, we first make their denominators equal and then compare their numerators.
Consider $\frac{24}{40}$ and $\frac{35}{50} .$ LCM of 40 and 50 is 200.
$⟹ \frac{(24 \times 5)}{(40 \times 5)} = \frac{120}{200}$
and $\frac{(35 \times 4)}{(50 \times 4)} = \frac{140}{200} \neq \frac{120}{200}$ .
Thus, $\frac{24}{40}$ and $\frac{35}{50}$ are not equivalent.
Considering $\frac{- 25}{35}$ and $\frac{55}{- 77},$ LCM of 35 and 77 is 385.
$⟹ \frac{(- 25 \times 11)}{(35 \times 11)} = \frac{- 275}{385}$
and $\frac{(55 \times 5)}{(- 77 \times 5)} = \frac{- 275}{385} .$
Thus, $\frac{- 25}{35}$ and $\frac{55}{- 77}$ are equivalent rational numbers.

Similarly, on checking the remaining options we find that $\frac{- 25}{35}$ and $\frac{55}{- 77}$ is the only pair of equivalent rational numbers.

Question 4

Find the value of
$\frac{- 16}{21} \div \frac{- 4}{3} .$

$\frac{- 3}{10}$

$\frac{4}{7}$

$\frac{- 7}{21}$

$\frac{- 7}{6}$

SOLUTION

Solution : B

$- \frac{16}{21} \div - \frac{4}{3} = - \frac{16}{21} \times - \frac{3}{4}$

$= \frac{4}{7}$

Question 5

Compare the rational numbers and choose the correct option.

$\frac{2}{5}$ ___ $\frac{3}{4}$ .

Cannot be determined

SOLUTION

Solution : B

To compare two rational numbers we make their denominators equal and then compare their numerators.
LCM of the denominator 4 and 5 is 20.

$\frac{2 \times 4}{5 \times 4} = \frac{8}{20}$

$\frac{3 \times 5}{4 \times 5} = \frac{15}{20}$

$Comparing \frac{8}{20} and \frac{15}{20},$

$we see that \frac{8}{20} < \frac{15}{20}$

$Hence, \frac{2}{5} < \frac{3}{4}$ .

Question 6

Write a rational number equal to $\frac{4}{7}$ with 63 as the denominator.

$\frac{12}{63}$

$\frac{20}{63}$

$\frac{36}{63}$

$\frac{60}{63}$

SOLUTION

Solution : C

Consider given rational number $\frac{4}{7}$ .

To make the denominator as 63, we have to multiply it with 9.

Multiplying both numerator and denominator by 9, we get

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

Therefore, $\frac{36}{63}$ is an equivalent rational number of $\frac{4}{7}$ with denominator equal to 63.

Question 7

Which of the following is a rational number that lies between 0 and 1?

$\frac{39}{13}$

$\frac{24}{20}$

$\frac{13}{14}$

$\frac{15}{13}$

SOLUTION

Solution : C

$\frac{13}{14}$
is less than 1 as the numerator of the fraction is smaller than the denominator.
While on the other hand, the other fractions are greater than 1 as all the numbers are positive and their numerator is greater than the denominator.

Question 8

Find the result obained by the addition of
$\frac{2}{3} to the reciprocal of \frac{- 2}{3} .$

$\frac{5}{6}$

$\frac{- 5}{6}$

$\frac{6}{7}$

$\frac{- 6}{7}$

SOLUTION

Solution : B

$Reciprocal of \frac{- 2}{3} is \frac{- 3}{2} .$

$\frac{2}{3} - \frac{3}{2} = \frac{4}{6} - \frac{9}{6} = \frac{(4 - 9)}{6} = \frac{- 5}{6}$

[LCM of 2 and 3 is 6]

Question 9

Simplified form of $\frac{108}{12}$ is 8.

True

False

SOLUTION

Solution : B

12 $\times$ 9 = 108

$\Rightarrow \frac{108}{12} = \frac{(12 \times 9)}{12}$

= 9

Question 10

$\frac{- 4}{3} > 0$

True

False

SOLUTION

Solution : B

Any negative number is less than 0. So, $\frac{- 4}{3} < 0$

Free Rational Numbers 01 Practice Test - 7th 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 ExamsSimple Equations 01Exponents and Powers 02Algebraic Expressions 02

Related Exams
Simple Equations 01
Exponents and Powers 02
Algebraic Expressions 02