# Free Rational Numbers Subjective Test 02 Practice Test - 7th grade

### Question 1

Find out the numbers of rational number skipped by the frog. [1 MARK]

#### SOLUTION

Solution :

There are infinite rational numbers between two points hence we cannot practically calculate the number of rational numbers skipped by the frog.

### Question 2

(a) Write four irrational numbers.

(b) The product of two rational numbers is 34. If one of them is 56, find the other number.

[2 MARKS]

#### SOLUTION

Solution :Each part: 1 Mark

(a) Four irrational numbers are √2,√3,√5 and π

(b) Let the other number be x.

⇒34=56×x

⇒x=3×64×5=910

### Question 3

Are the following expressions true:

(a) 713<38

(b) The rational number −18−13 lies to the left of 0 on the number line.

[2 MARKS]

#### SOLUTION

Solution :Each part: 1 Mark

(a) Converting both numbers with common denominator: 7×813×8 and 3×138×13

The numbers are 56104 and 39104.

Hence, the expression is false.

(b) −18−13=1813, which is a positive number. Therefore the number lies to the right of 0 on the number line.

Hence the given statement was not true.

### Question 4

(a) Give the additive inverse of:

314,−519

(b) Give the multiplicative inverse of −34

[2 MARKS]

#### SOLUTION

Solution :Each part: 1 Mark

(a) Additive inverse of 314=−314

Additive inverse of −519=519

(b) Multiplicative inverse of −34=4−3

### Question 5

Find the sum of:

(a) −311,−14 and 58

(b) −59,−712 and 1118

[2 MARKS]

#### SOLUTION

Solution :Each part: 1 Mark

(a) −311+−14+58

−3×888−1×2288+5×1188

−24−22+5588

−46+5588=988

(b) −59+−712+1118

−5×436−7×336+11×236

−20−21+2236=−1936

### Question 6

(a) Find the sum of 916 + 924.

(b) Arun walks 13km from a place A towards East and then from there 123km towards west, where will he be now from A.

[3 MARKS]

#### SOLUTION

Solution :(a) Solution: 1 Mark

(b) Steps: 1 Mark

Result: 1 Mark

(a) Firstly we simplify the fraction 924 = 38

Now the LCM of denominator 8 and 16 is 16.

916+38=9+616=1516

(b)

Arun walks 13km towards East from place A

Then he walks 123=53km towards West, ie. in the opposite direction.

Arun's new position is 53−13=43=113

Arun is 113km towards West from place A.

### Question 7

(a) Which of these is a rational number between 2 and 3:

1827,73,103,52

(b) Find one rational number that lies between 78 and 12. What is its reciprocal?

[3 MARKS]

#### SOLUTION

Solution :(a) Steps: 1 Mark

Result: 1 Mark

(b) Answer: 1 Mark

(a) Simplified form of the numbers:

1827=23

73=213

103=313

52=212

The rational numbers between 2 and 3 are 73 and 52.

(b) Rational number that will lie between 78 and 12 is their average.

78+122=1182=1116

Its reciprocal is 1611.

### Question 8

(a) 227 is a rational number but π is an irrational number. Comment on this.

(b) Do the numbers 13 and −52 lie on the opposite sides of 0 on the number line?

[3 MARKS]

#### SOLUTION

Solution :(a) Explanation: 2 Marks

(b) Answer: 1 Mark

(a) 227 is a rational number because we can write it in a form of pq.The actual value of π is 3.141516........which implies that there is no end to the values after the decimal, the decimal goes on forever without repeating.

Hence we are not able to find the actual value of π therefore we can't represent it on a number line and moreover, we can't represent it in the form of pq, that's why it is an irrational number.

(b) Yes, the numbers 13 and −52 lie on the opposite sides of 0 on the number line as one of them is positive and the other is negative.

### Question 9

(a) How many right angles are there in a cubical room?

(b) What should be subtracted from (512+32) to get 2?

[3 MARKS]

#### SOLUTION

Solution :(a) Answer: 1 Mark

(b) Steps: 1 Mark

Result: 1 Mark

(a) Each corner has three mutually perpendicular edges, hence forming three right angles in each corner. A room has 8 corners. Hence, there are 24 right angles in the room.

(b) Let the number to be subtracted be x.

⇒512+32−x=2

⇒5+1812−x=2

⇒2312−x=2

⇒x=2312−2

⇒x=23−2412

⇒x=−112

⇒x=−112

### Question 10

(a) Arrange the rational numbers −710, 5−8, 2−3 in ascending order.

(b) Arrange the rational numbers 43, 172, 518 in ascending order.

[4 MARKS]

#### SOLUTION

Solution :Each part: 2 Marks

(a) First write the rational numbers with positive denominator = −710, 5−8, 2−3.LCM of denominators (LCM of 10, 8, 3 is 120)

−710 = (−7×12)(10×12)=−84120

−58 = (−5×15)(8×15)=−75120

−23 = (2×40)(3×40)=−80120

Comparing the numerators of these numbers, we get:

- 84 < - 80 < - 75

∴ −84120 < −80120 < −75120;

−710 < −23 < −58.

(b) 43, 172, 518LCM of denominators (LCM of 3, 2, 18 is 18)

43 = (4×6)(3×6)=2418

172 = (17×9)(2×9)=15318

518 = (5×1)(18×1)=518

Comparing the numerators of these numbers, we get:

5 < 24 < 153

∴ 518 < 2418 < 15318;

518 < 43 < 172.

### Question 11

(a) You are going on a road trip over a distance of 3000 kilometres with three friends. The car consumes 6 litres of gas per 100 kilometres and gas costs Rs1.20 per litre. If you want to split the cost of gas evenly between the four of you, how much should each of you contribute?

(b) Find 8 rational numbers between −13 and 69.

[4 MARKS]

#### SOLUTION

Solution :Each part: 2 Marks

(a) Distance of trip = 3000km

Rate at which car consumes gas = 6 litres per 100 km

Total amount of gas consumed in the trip =6100×3000 km=180 litres

Cost of gas = 1.20 Rs per litre.

Total cost = 1.20 × 180 = 216 Rs

∴ Contribution from each =2164=Rs 54

(b) Upper limit =69

Lower limit =−13 or −39

Rational numbers between these are:

−29,−19,0,19,29,39,49,59

### Question 12

(a) Candy bars were distributed equally among students of a class. The number of candy bars each student got was one-eighth of the number of students. Had the number of students been half, each student would have got 16 candy bars. What is the total number of candy bars that were distributed?

(b) Reduce to simplest form.

(i) 63+(−16)

(ii) −32−38

(iii) −96+(−35)

(iv) −13−(−35)

[4 MARKS]

#### SOLUTION

Solution :a) Steps: 1 Mark

Answer: 1 Mark

b) Each sub-part: 0.5 Marks

(a) Let the total number of students =x.Then, number of candy bars each student has =x8

Now, no. of student has been half =x2,

Number of candies each student would have got = 16

x2×16=x×x8

Or No. of initial students = 64 ; x2=32.

So, number of candies distributed = 32 x 16 = 512

(b)

(i) 63+−16=2−16=116

(ii) −32−38=−12−38=−158

(iii) −96+−35=−32−35

−15−610=−2110

(iv) −13−(−35)=−13+35

−5+915=415

### Question 13

(a) In a number line, there are eight points.They are lying on number line such that US = SR = RT and AP = PQ = QB. Find the rational numbers represented by P, Q, R, S.

(b) Ashley recently opened a store that sells only natural ingredients. She wants to advertise her products by distributing bags of samples in her neighbourhood. It takes one person 2 minutes to prepare one bag.

How many hours will it take to prepare 900 bags of samples if Ashley and 5 of her friends do the work?

[4 MARKS]

#### SOLUTION

Solution :Each part: 2 Marks

(a) As given in the question AP = PQ = QB = 13, because interval of one between AB is divided by into three equal parts.

Similarly, US = SR = RT = 13, since the interval of one between U and T is divided into three equal parts.So, value of P =2+13=73;

Q =73+13=83

Similarly for R =−1−13=−43;

S =−43−13=−53

(b) Time taken by 1 person to prepare 1 bag = 2 minutes

Time taken by 6 people to prepare 1 bag = 26minutes

Time taken by 6 people (Ashley and her 5 friends) to prepare 900 bags

= 26×900=300 minutes=5 hrs

### Question 14

(a) In the figure given below, normally in two jumps frog covers the distance of 9m. One day on seeing the snake frog jumped 15 times more than his normal jump and again he jumped with full strength and covered 12 times more distance than he normally covers in the second jump. Find the distance covered by frog in the second jump and in total.

(b) Are the statements below correct?

(i) The rational numbers −215 and 7−31 are on the opposite sides of 0 on the number line.

(ii) The rational number −3−5 is on the right of −47 on the number line.

[4 MARKS]

#### SOLUTION

Solution :Each part: 2 Marks

(a) In normal jump frog covers 5m in first jump but this time his jump covered =5+(5×15)=6mIn the second jump it covered =4+(4×12)=6m.

So, distance covered in second jump = 6m.

Total distance covered by frog = 6m + 6m = 12m

(b) (i) The statement is false as −215 and 7−31 both are negative numbers and lie to the left side of 0 on the number line i.e. they are at the same side to that of 0 which is left.

(ii) This statement is true as the number −3−5 is actually positive 35 and −47 is negative. Therefore, 35 is is on the right of −47 on the number line.

### Question 15

(a) Find ten rational number between -25 and 12.

(b) Insert 5 rational numbers and 2 irrational numbers between √2 and √3.

[4 MARKS]

#### SOLUTION

Solution :Each part: 2 Marks

(a) The LCM of denominator -5 and 2 = -10. Converting these rational numbers to equivalent rational numbers having common denominator.−2×25×2=−410=−4×210×2=−820

1×52×5=510=5×210×2=1020

Clearly -7, -6, -5.............8, 9 are integers between numerators -8 and 10 of these equivalent rational number. Thus we can take any 10 rational numbers and the numbers are −720, −620, −520,−320,−120, 0,120, 320, 420, 520.

(b) √2 = 1.414 (approx)

√3 = 1.732 (approx)

5 rational numbers between √2 and √3 are 1.42, 1.43, 1.44, 1.45, 1.50. (there are many more)

2 irrational numbers between √2 and √3 are √2.1 and √2.9 (there are many more)