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NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Ex 9.1 are part of NCERT Solutions for Class 7 Maths. Here we have given NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Ex 9.1.

• Rational Numbers Class 7 Ex 9.2
• Rational Numbers Class 7 MCQ

NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Ex 9.1

Question 1.
List five rational numbers between

1. -1 and 0
2. -2 and -1
3. –\(\frac { 4 }{ 5 } \) and – \(\frac { 2 }{ 3 } \)
4. –\(\frac { 1 }{ 2 } \) and \(\frac { 2 }{ 3 } \)

Solution:

Question 2.
Write four more rational numbers in each of the following patterns :

Solution:

Question 3.
Give four rational numbers equivalent to:
(i) \(\frac { -2 }{ 7 } \)
(ii) \(\frac { 5 }{ -3 } \)
(iii) \(\frac { 4 }{ 9 } \)

Solution:
(i) Four rational numbers equivalent to \(\frac { -2 }{ 7 } \) are

(ii) Four rational numbers equivalent to \(\frac { 5 }{ -3 } \) are

(iii) Four rational numbers equivalent to \(\frac { 4 }{ 9 } \) are

Question 4.
Draw the number line and represent the following rational numbers on it:

1. \(\frac { 3 }{ 4 } \)
2. \(\frac { -5 }{ 8 } \)
3. \(\frac { -7 }{ 4 } \)
4. \(\frac { 7 }{ 8 } \)

Solution:

Question 5.
The points P, Q, R, S, T, U, A, and B on this number line are such that, TR = RS = SU and AP = PQ = QB. Name the rational numbers represented by P, Q, R, and S.

Solution:
The rational number represented by P is 2 \(\frac { 1 }{ 3 } \) = \(\frac { 7 }{ 3 } \)
The rational number represented by Q is 2 \(\frac { 2 }{ 3 } \) = \(\frac { 8 }{ 3 } \)
The rational number represented by R is -1 \(\frac { 1 }{ 3 } \) = \(\frac { -4 }{ 3 } \)
The rational number represented by S is -1 \(\frac { 2 }{ 3 } \) = \(\frac { -5 }{ 3 } \)
The rational numbers represented by P, Q, R and S are 2 \(\frac { 1 }{ 3 } \), 2 \(\frac { 2 }{ 3 } \), -1 \(\frac { 1 }{ 3 } \) and – 1 \(\frac { 2 }{ 3 } \) respectively

Question 6.
Which of the following pairs represent the same rational number?

Solution:
(i) \(\frac { -7 }{ 21 } \) is a negative rational number and \(\frac { 3 }{ 9 } \) is a positive rational number. So, the given pair does not represent the same rational number.

So, the given pair represents the same rational number.

So, the given pair represents the same rational number.

So, the given pair represents the same rational number.

So, the given pair represents the same rational number.
(vi) \(\frac { 1 }{ 3 } \) is a positive rational number and \(\frac { -1 }{ 9 } \) is a negative rational number. So, the given pair does not present the same rational number.

Thus, \(\frac { -5 }{ -9 } \) is a positive rational number and \(\frac { 5 }{ -9 } \) is a negative rational number. So, the given pair does not represent the same rational number.

Question 7.
Rewrite the following rational numbers in the simplest form :

Solution:

Question 8.
Fill in the boxes with the correct symbol out of >, < and =

Solution:

Question 9.
Which is greater in each of the following?


Solution:

Question 10.
Write the following rational numbers in ascending order :

Solution:

We hope the NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Ex 9.1 help you. If you have any query regarding NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Ex 9.1, drop a comment below and we will get back to you at the earliest.

NCERT Solutions for Class 7 Maths Chapter 8 Comparing Quantities Ex 8.1 are part of NCERT Solutions for Class 7 Maths. Here we have given NCERT Solutions for Class 7 Maths Chapter 8 Comparing Quantities Ex 8.1.

• Comparing Quantities Class 7 Ex 8.2
• Comparing Quantities Class 7 Ex 8.3
• Comparing Quantities Class 7 MCQ

NCERT Solutions for Class 7 Maths Chapter 8 Comparing Quantities Ex 8.1

Question 1.
Find the ratio of:
(a) ₹ 5 to 50 paise
(b) 15 kg to 210 g
(c) 9 m to 27 cm
(d) 30 days to 36 hour

Solution:
(a) ₹ 5 : 50 paise
= ₹ 5 : 50 paise
= 5 × 100 paise : 50 paise
= 500 paise : 50 paise
= 10 : 1.

(b) 15 kg to 210g
= 15 kg : 210g
= 15 × 1000 g : 210g
= 15000 g : 210g = 500:7.

(c) 9 m to 27 cm
= 9m : 27 cm = 9 × 100 cm : 27 cm
= 900 cm : 27 cm
900 : 27 = 100 : 3.

(d) 30 days to 36 hours
= 30 days : 36 hours
30 × 24 hours : 36 hours
= 720 hours : 36 hours
= 720 : 36 = 20 : 1.

Question 2.
In a computer lab, there are 3 computers for every 6 students. How many computers will be needed for 24 students?
Solution:
Let x computers be needed for 24 students.

Hence, 12 computers will be needed for
24 students.
Aliter:
In a computer lab,
Every 6 students need 3 computers.
∴ Every 1 student needs \(\frac { 3 }{ 6 } \) computers.
∴ Every 24 students need \(\frac { 3 }{ 6 } \) × 24 = 3 × 4 = 12 computers

Question 3.
Population of Rajasthan = 570 lakhs
and population of UP = 1660 lakhs.
Area of Rajasthan =3 lakh km2
and area of UP = 2 lakh km2.
(i) How many people are there per km2 in both these States?
(ii) Which State is less populated?
Solution:
(i) Number of people per sq. km. in Rajasthan state

(ii) The Rajasthan State is less populated.

We hope the NCERT Solutions for Class 7 Maths Chapter 8 Comparing Quantities Ex 8.1 helps you. If you have any query regarding NCERT Solutions for Class 7 Maths Chapter 8 Comparing Quantities Ex 8.1, drop a comment below and we will get back to you at the earliest.

NCERT Solutions for Class 7 Maths Chapter 7 Congruence of Triangles Ex 7.1 are part of NCERT Solutions for Class 7 Maths. Here we have given NCERT Solutions for Class 7 Maths Chapter 7 Congruence of Triangles Ex 7.1.

• Congruence of Triangles Class 7 Ex 7.2
• Congruence of Triangles Class 7 MCQ

NCERT Solutions for Class 7 Maths Chapter 7 Congruence of Triangles Ex 7.1

Question 1.
Complete the following statements:
(a) Two line segments are congruent if……..
(b) Among two congruent angles, one has a measure of 70°; the measure of the other angle is…….
(c) When we write ∠A = ∠B, we actually mean….
Solution:
(a) they have the same length
(b) 70°
(c) m∠A = m∠B

Question 2.
Give any two real-life examples for congruent shapes.
Solution:

1. Two coins or notes of the same denomination.
2. Two keys of the same lock.

Question 3.
If ∆ ABC = ∆ FED under the correspondence ABC ↔ FED, write all the corresponding congruent parts of the triangles.
Solution:
Corresponding vertices: A and F; B and E; C and D.
Corresponding sides : \(\overline { AB } \) and \(\overline { FE } \) ; \(\overline { BC } \) and \(\overline { ED } \); \(\overline { CA } \) and \(\overline { DF } \).
Corresponding angles: ∠A and ∠F; ∠B and ∠E; ∠C and ∠D.

Question 4.
If ∆ DEF = ∆ BCA, write the part(s) of ∆ BCA that correspond to

1. ∠E
2. \(\overline { EF } \)
3. ∠F
4. \(\overline { DF } \)

Solution:

1. ∠C
2. \(\overline { CA } \)
3. ∠A
4. \(\overline { BA } \)

We hope the NCERT Solutions for Class 7 Maths Chapter 7 Congruence of Triangles Ex 7.1 help you. If you have any query regarding NCERT Solutions for Class 7 Maths Chapter 7 Congruence of Triangles Ex 7.1, drop a comment below and we will get back to you at the earliest.

NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and its Properties Ex 6.1 are part of NCERT Solutions for Class 7 Maths. Here we have given NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and its Properties Ex 6.1.

• The Triangle and its Properties Class 7 Ex 6.2
• The Triangle and its Properties Class 7 Ex 6.3
• The Triangle and its Properties Class 7 Ex 6.4
• The Triangle and its Properties Class 7 Ex 6.5
• The Triangle and its Properties Class 7 MCQ

NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and its Properties Ex 6.1

Question 1.
In ∆PQR, D is the mid-point of \(\overline { QR } \).

Solution:
\(\overline { PM } \) is the altitude.
PD is the median.
No! QM ≠ MR.

Question 2.
Draw rough sketches for the following:

(a) In ∆ ABC, BE is a median.
(b) In ∆ PQR, PQ and PR are altitudes of the triangle.
(c) In ∆ XYZ, YL is an altitude in the exterior of the triangle.

Solution:

Question 3.
Verify by drawing a diagram if the median and altitude of an isosceles triangle can be the same.
Solution:
AD is the median.
AL is the altitude.

Draw a line segment BC. By paper folding, locate the perpendicular bisector of BC. The folded crease meets BC at D, its mid-point.
Take any point A on this perpendicular bisector. Join AB and AC. The triangle thus obtained is an isosceles ∆ABC in which AB = AC.
Since D is the mid-point of BC, so AD is its median. Also, AD is the perpendicular bisector of BC. So, AD is the altitude of ∆ABC.
Thus, it is verified that the median and altitude of an isosceles triangle are the same.

We hope the NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and it’s Properties Ex 6.1 help you. If you have any query regarding NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and its Properties Ex 6.1, drop a comment below and we will get back to you at the earliest.

NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Ex 5.1 are part of NCERT Solutions for Class 7 Maths. Here we have given NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Ex 5.1.

• Lines and Angles Class  7 Ex 5.2
• Lines and Angles Class  7 MCQ

NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Ex 5.1

Question 1.
Find the complement of each of the following angles:

Solution:
Since, the sum of the measures of an angle and its complement is 90°, therefore,

1. The complement of an angle of measure 20° is the angle of (90° – 20°), f.e., 70°.
2. The complement of an angle of measure 63° is the angle of (90° – 63°), i.e., 27°.
3. The complement of an angle of measure 57° is the angle of (90° – 57°), i.e., 33°.

Question 2.
Find the supplement of each of the following angles:

Solution:

1. Supplement of the angle 105° = 180° – 105° = 75°
2. Supplement of the angle 87° = 180° – 87° = 93°
3. Supplement of the angle 154° = 180° – 154° = 26°

Question 3.
Identify which of the following pairs of angles are complementary and which are supplementary.

1. 65°, 115°
2. 63°, 27°
3. 112°, 68°
4. 130°, 50°
5. 45°,45°
6. 80°, 10°.

Solution:

1. Since, 65°+ 115° = 180°
   So, this pair of angles are supplementary.
2. Since, 63°+ 27° = 90°
   So, this pair of angles are complementary.
3. Since, 112° + 68° = 180°
   So, this pair of angles are supplementary.
4. Since, 130°+50° = 180°
   So, this pair of angles are supplementary.
5. Since, 45°+ 45° = 90°
   So, this pair of angles are complementary.
6. Since, 80°+ 10° = 90°
   So, this pair of angles are complementary.

Question 4.
Find the angle which is equal to its complement.
Solution:
Let the measure of the angle be x°. Then, the measure of its complement is given to be x°.
Since, the sum of the measures of an angle and its complement is 90°, therefore,
x° + x° = 90°
⇒ 2x° = 90°
⇒ x° = 45°
Thus, the required angle is 45°.

Question 5.
Find the angle which is equal to its supplement.
Solution:
Let the measure of the angle be x°. Then,
a measure of its supplement = x°
Since, the sum of the measures of an angle and its supplement is 180°, therefore,
x° + x° = 180°
⇒ 2x° =180°
⇒ x° = 90°
Hence, the required angle is 90°.

Question 6.
In the given figure, ∠ 1 and ∠ 2 are supplementary angles.

If ∠1 is decreased, what changes should take place in ∠ 2 so that both the angles still remain supplementary?
Solution:
∠ 2 will increase as much as ∠ 1 decreases.

Question 7.
Can two angles be supplementary if both of them are:

1. acute?
2. obtuse?
3. right?

Solution:

1. No! two acute angles cannot be a supplement.
2. No! Two obtuse angles cannot be supplementary.
3. Yes! Two right angles are always supplementary.

Question 8.
An angle is greater than 45°. Is its complementary angle greater than 45° or equal to 45° or less than 45°.
Solution:
Since the sum of the measure of ah angle and its complement is 90°.
∴ The complement of an angle of measures 45° + x°,
where x > 0 is the angle of [90° – (45° + x°)] = 90° – 45° – x°= 45° – x°.
Clearly, 45° + x° > 45° – x°
Hence, the complement of an angle > 45° is less than 45°.

Question 9.
In the adjoining figure:

1. Is ∠1 adjacent to ∠2 ?
2. Is ∠ AOC adjacent to ∠ AOE?
3. Do ∠ COE and ∠ EOD form a linear pair?
4. Are ∠ BOD and ∠ DOA supplementary?
5. Is ∠ 1 vertically opposite to ∠ 4?
6. What is the vertically opposite angle of ∠ 5?

Solution:

1. Yes ! ∠ 1 is adjacent to ∠ 2.
2. No ! ∠ AOC is not adjacent to ∠ AOE.
3. Yes! ∠ COE and ∠ EOD form a linear pair.
4. Yes ! ∠ BOD and ∠ DOA are supplementary.
5. Yes ! ∠ 1 is vertically opposite to ∠ 4.
6. The vertically opposite angle of ∠ 5 is ∠ 2 + ∠ 3, i.e., ∠ COB.

Question 10.
Indicate which pairs of angles are:

1. Vertically opposite angles.
2. Linear pairs.

Solution:

1. The pair of vertically opposite angles are ∠1, ∠4; ∠5, ∠2 + ∠3.
2. The pair of linear angles are ∠1, ∠5; ∠4, ∠5.

Question 11.
In the following figure, is ∠ 1 adjacent to ∠ 2? Give reasons.

Solution:
∠1 is not adjacent to ∠2 because they have no common vertex.

Question 12.
Find the values of the angles x, y, and z in each of the following:

Solution:

Question 13.
Fill in the blanks:

1. If two angles are complementary, then the sum of their measures is
2. If two angles are supplementary, then the sum of their measures is
3. Two angles forming a linear pair are
4. If two adjacent angles are supplementary, they form a
5. If two lines intersect at a point, then the vertically opposite angles are always
6. If two lines intersect at a point, and if one pair of vertically opposite angles are acute angles, then the other pair of vertically opposite angles are

Solution:

1. 90°
2. 180°
3. supplementary
4. linear pair
5. equal
6. obtuse angles

Question 14.
In the adjoining figure, name the following pairs of angles.

1. Obtuse vertically opposite angles
2. Adjacent complementary angles
3. Equal supplementary angles
4. Unequal supplementary angles
5. Adjacent angles that do not form a linear pair.

Solution:

1. Obtuse vertically opposite angles are ∠AOD and ∠BOC.
2. Adjacent complementary angles are ∠BOA and ∠AOE.
3. Equal supplementary angles are ∠BOE and ∠EOD.
4. Unequal supplementary angles are ∠BOA and ∠AOD, ∠BOC and ∠COD, ∠EOA, and ∠EOC.
5. Adjacent angles that do not form a linear pair are ∠AOB and ∠AOE, ∠AOE and ∠EOD; ∠EOD and ∠COD.

We hope the NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Ex 5.1 help you. If you have any query regarding NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Ex 5.1, drop a comment below and we will get back to you at the earliest.