Rational Numbers(7th Grade > Mathematics ) Questions and answers for exam Preparation

7th Grade > Mathematics

RATIONAL NUMBERS MCQs

Total Questions : 120 | Page 2 of 12 pages

Question 11. (a) An investor invested 20 cr in a company for the development of a mobile application. The company distributed this money among various departments to cover up the needs. One-fourth of invested money is allocated to advertisement team. Two third of the remaining money was given to development team. In development team, there are two sub-teams namely Graphics and content team. Among them, it is distributed in such a way that content team will get

\frac{3}{2}

times more money than that of graphics team. Find the money allocated to each team separately.
(b) Sean is helping his dad build a tiled walkway in their backyard. The walkway will be 60 feet long and 2 feet wide. The local hardware store sells tiles which are 2 by 2 feet and come in boxes of 6.
How many boxes of tiles do they need?
[4 MARKS]

Discuss Question

:
Each part: 2 Marks
(a) Total money invested = 20cr
Amount allocated to advertisement team =

20 \times \frac{1}{4}

= 5 cr.
Remaining amount: 20 - 5 = 15cr; Two third of15 cr is allocated for development team

= 15 \times \frac{2}{3} = 10 c r

Let graphics team got

x

,then content team got

\frac{3}{2}

x

.
By solving,

x

\frac{3}{2}

x

=10;

x

=4
Hence, amount allocated for graphics and content team were 4cr and 6cr respectively.
(b) Area of the walkway = (60

\times

2)feet

^{2}

=120feet

^{2}

Area of 1 tile =(2

\times

2)feet

^{2}

= 4feet

^{2}

Total tiles required =

\frac{120}{4} = 30

1 box contains 6 tiles.

∴

No. of boxes for 30 tiles

= \frac{30}{6} = 5

Question 12. Arrange the following rational number in increasing order. [4 MARKS]
(i)

\frac{4}{3}

\frac{3}{2}

\frac{7}{9}

\frac{5}{4}

.
(ii)

\frac{8}{5}

\frac{12}{7}

\frac{9}{2}

\frac{23}{20}

Discuss Question

:
Each part: 2 Marks
(i) Find the LCM of denominators, i.e. the LCM of 3, 2, 9 and 4 = 36.
Nowmake the denominatorscommon to theabove fraction.
So,

\frac{4 \times 12}{3 \times 12}

\frac{48}{36}

;

\frac{3 \times 18}{2 \times 18}

\frac{54}{36}

;

\frac{7 \times 4}{9 \times 4}

\frac{28}{36}

;

\frac{5 \times 9}{4 \times 9}

\frac{45}{36}

;
Now arrange the fractions according to their numerator, fraction having large magnitude of numerator will be of greater magnitude.
So, correct sequence is

\frac{28}{36}

\frac{45}{36}

\frac{48}{36}

\frac{54}{36}

\Rightarrow \frac{7}{9} < \frac{5}{4} < \frac{4}{3} < \frac{3}{2}

(ii) Find the LCM of denominators, i.e. the LCM of 5, 7, 2 and 20 = 140.
Nowmake the denominatorscommon to theabove fraction.
So,

\frac{8 \times 28}{5 \times 28}

\frac{224}{140}

;

\frac{12 \times 20}{7 \times 20}

\frac{240}{140}

;

\frac{9 \times 70}{2 \times 70}

\frac{630}{140}

;

\frac{23 \times 7}{20 \times 7}

\frac{161}{140}

;
Now arrange the fractions according to their numerator, fraction having large magnitude of numerator will be of greater magnitude.
So, correct sequence is

\frac{161}{140}

\frac{224}{140}

\frac{240}{140}

\frac{630}{140}

\Rightarrow \frac{23}{20} < \frac{8}{5} < \frac{12}{7} < \frac{9}{2}

Question 13.

The diagram shows a circle with radius 3 and centre at O.
The circumference and the area of this circle are rational or irrational? [2 MARKS]

Discuss Question

:
Formula: 1 Mark
Answer: 1 Mark
The circumference is given by the formula

C = 2 \times π \times r

So,

C = 2 \times π \times 3 = 6 π

The area is given by the formula

A = π \times r^{2}

So,

A = π \times 3^{2} = 9 \times π

As,

π

is irrational, so the circumference and area are both irrational.

Question 14.

The sum of three rational numbers is \frac{- 1}{5} . If two numbers are \frac{- 2}{5} and \frac{3}{10}, then find the third number.

810
110
−110
−210

Discuss Question

Answer: Option C. -> −110
:
C

Let the unknown number be x .

\frac{- 1}{5} = \frac{3}{10} + \frac{- 2}{5} + x x = \frac{- 1}{5} - \frac{3}{10} + \frac{2}{5}

Taking LCM, we get, x = \frac{- 2}{10} - \frac{3}{10} + \frac{4}{10} x = \frac{- 1}{10}

Question 15. Which of the following forms a pair of equivalent rational numbers?

2440 and 3550
−2535 and 55−77
−815 and −2448
972 and −321

Discuss Question

Answer: Option B. -> −2535 and 55−77
:
B
When we have to compare two rational numbers, we first make their denominators equal and then comparetheir 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 16. Compare the rational numbers and choose the correct option.

\frac{2}{5}

___

\frac{3}{4}

>
=
Cannot be determined

Discuss Question

Answer: Option B. -> −2535 and 55−77
:
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 17.

\frac{- 4}{3} > 0

True
False
67
−67

Discuss Question

Answer: Option B. -> False
:
B
Any negative number is less than 0. So,

\frac{- 4}{3} < 0

Question 18. Find the value of

\frac{- 16}{21} \div \frac{- 4}{3} .

−310
47
−721
−76

Discuss Question

Answer: Option B. -> 47
:
B

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

= \frac{4}{7}

Question 19. Which of the following is a rational number that lies between 0 and 1?

3913
2420
1314
1513

Discuss Question

Answer: Option C. -> 1314
:
C

\frac{13}{14}

is less than 1 as the numerator ofthe fraction is smallerthan 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 20. Which of the following is a rational number equal to