CBSE Class 8

On this page, you will find Simple Equations Class 7 Notes Maths Chapter 4 Pdf free download. CBSE NCERT Class 7 Maths Notes Chapter 4 Simple Equations will seemingly help them to revise the important concepts in less time.

CBSE Class 7 Maths Chapter 4 Notes Simple Equations

Simple Equations Class 7 Notes Conceptual Facts

1. An equation having only one variable with highest power 1 is called linear equation.
For example:
3x – 5 = 11 with 1 variable x
5 – 2y = 0 with 1 variable y

2. A number which satisfies the given linear equation is called its solutions.
For example: 3x – 2 = 4 requires a particular value of x which satisfies this equation and that value of x will be the solution of the equation.

3. Rules for finding the solution of linear equations:
(i) Trial and error method:
Let us take an equation, 3x-2 = 4
Put x = 1 inLHS, 3 x 1-2=3 – 2 ≠ 4 RHS
Put x = 2 in LHS, 3 x 2 – 2=6-2=4 RHS
Thus, by putting x = 2, we get RHS
Hence, x = 2 is the solution of the given equation.

(ii) Transposition method: A term may be transposed from one side of the equation to the other side with the change its sign.
For example:
(a) 3x – 6 = 9 ⇒ 3x = 6 + 9 (Transposing -6 from LHS to RHS by changing its sign)

(b) 3x-5=x ⇒ 3x-x = 5 (Transposingx from RHS to LHS and 5 from LHS to RHS by changing their signs)
multiplying or dividing on both sides

(iii) Adding, subtracting, multiplying or dividing on both sides
For example:
(a) 3x – 10 – 5 ⇒ 3x – 10+ 10 = 5 + 10 ⇒ 3x = 15 (Adding 10 to both sides)
(b) 5x + 12 = 27 ⇒ 5x + 12- 12 = 27 – 12 ⇒ 5x = 15 (Subtracting 12 from both sidés)
(c) \(\frac{x}{5}\) = 10 ⇒ \(\frac{x}{5}\) x 5 =10 x 5 ⇒ x=50 (Multiplyingbothsidesby5)
(d) 3x = 18 ⇒ 3x + 3 = 18÷ 3 (Dividing both sides by 3)
⇒ x = 6

On this page, you will find Fractions and Decimals Class 7 Notes Maths Chapter 2 Pdf free download. CBSE NCERT Class 7 Maths Notes Chapter 2 Integers will seemingly help them to revise the important concepts in less time.

CBSE Class 7 Maths Chapter 2 Notes Fractions and Decimals

Fractions and Decimals Class 7 Notes Conceptual Facts

Fraction \(=\frac{\text { Numerator }}{\text { Denominator }}\)

1. Types of fraction:

• Proper fractions = Representing a part of a whole, e.g\(\frac{1}{2}, \frac{3}{4} \text { and } \frac{1}{4}\)
• Improper fraction: Numerator is always greater than the denominator, \(\text { e.g. } \frac{6}{5}, \frac{7}{4} \text { and } \frac{3}{2}\)
• Mixed fraction: Combination of a whole number and a proper fraction.\(\text { -e.g. } 1 \frac{2}{3}, 2 \frac{5}{6} \text { and } 3 \frac{1}{2}\)

2. Multiplication of two fractions: \(\frac{\text { Product of numerators }}{\text { Product of denominators }} \text { e.g. } \frac{2}{5} \times \frac{3}{4}=\frac{2 \times 3}{5 \times 4}=\frac{6}{20}\)

3. Reciprocal of a non-zero fraction is obtained by interchanging its numerator and the denominator e.g. reciprocal of  \(\frac{3}{4} \text { is } \frac{4}{3}\)

4. While dividing a whole number by a fraction, we multiply the whole number with the reciprocal of that
\(\text { e.g. } 5 \div \frac{3}{2}=5 \times \frac{2}{3}=\frac{10}{3}\)

5. While dividing a fraction by a whole number, we multiply the fractions by the reciprocal of the whole
\(\text { e.g. } \frac{1}{4} \div 2=\frac{1}{4} \times \frac{1}{2}=\frac{1}{8}\)

6. Division of a fraction by another fractions.

7. Multiplication of two decimal numbers: 2.25 x 1.2 = 2.700

8. Number obtained by dividing a non-zero integer by 0, is not defined, e.g. \(\text { e.g. } \frac{2}{0}, \frac{\frac{3}{2}}{0} \text { and } \frac{-5}{0}\)

On this page, you will find Integers Class 7 Notes Maths Chapter 1 Pdf free download. CBSE NCERT Class 7 Maths Notes Chapter 1 Integers will seemingly help them to revise the important concepts in less time.

CBSE Class 7 Maths Chapter 1 Notes Integers

Integers Class 7 Notes Conceptual Facts

1. Number line

For a positive integer on number line, we move towards right of zero and for a negative integer, we move towards the left of the zero.

2. Integers are closed under addition, subtraction and multiplication.
For example:

• a + b = integer
• a – b = integer
• a x b = integer

3. Addition and multiplication are cumulative for integers.
For example:

• a + b = b + a
• a x b = b x a

4. Addition and multiplication are associative for integers.
For example:

• (a + b) + c = a + (b + c)
• (a x b) x c = a x (b x c)

5. Zero (0) is an additive identity for integers.
For example: a + 0 = 0 + a = a

6. One (1) is a multiplicative identity for integers.
For example: a x 1 = 1 x a = a

7. Algebra of integers,

• a x (-b) = -ab
• (-a) xb = -ab
• (-a) x (-b) = ab
• a xb = ab

8. Product of even number of negative integers is positive whereas the product of odd number of negative integers is negative. For example:

• (-a) x (-b) x (-c) x (-d) (-e) -a x b x c x d x e …. even number times
• (-a) x (-b) x (-c) x (-d) (-e) = -(a x b x c x d x e) odd number times

9. Division on integers:
(i) \(\frac{(-a)}{(b)}=-\left(\frac{a}{b}\right)\)
(ii) \(\frac{(-a)}{(-b)}=\left(\frac{a}{b}\right)\)
(iii) \(\frac{(a)}{(-b)}=-\left(\frac{a}{b}\right)\)
(iv) \(\left(\frac{+a}{+b}\right)=\left(\frac{a}{b}\right)\)

On this page, you will find Pollution of Air and Water Class 8 Notes Science Chapter 18 Pdf free download. CBSE NCERT Class 8 Science Notes Chapter 18 Pollution of Air and Water will seemingly help them to revise the important concepts in less time.

CBSE Class 8 Science Notes Chapter 18 Pollution of Air and Water

Pollution of Air and Water Class 8 Notes Understanding the Lesson

1. Agents or substances that pollute water, air or soil are called pollutants.

2. The term air pollution is defined as the accumulation of harmful substances or increase in the quantity of any gas in the air above the normal level.

3. Air pollution is harmful for human beings also.

4. In the earth’s atmosphere there is about 78% of nitrogen, 21% of oxygen and the rest are other gases like CO₂, methane, ozone and water vapour.

5. The substances which contaminate the air are called air pollutants.

6. There are natural as well as man-made sources of air pollution.

7. Smoke and fog combines to form smog. Smoke may contain oxides of nitrogen which combine with other pollutants and fog to form smog.

8. Smog causes breathing difficulties.

9. Chlorofluorocarbons (CFCs) which are used in refrigerators, air conditioners and aerosol sprays damages ozone layer of the atmosphere.

10. Some pollutants like SO₂ and NO₂ react with water vapour present in the air to form sulphuric acid and nitric acid. These acids come down with rain as acid rain.

11. A part of the radiation of the sun that falls on the earth is absorbed by it, whereas a part is reflected back into space. A part of the reflected radiation is trapped by the atmosphere. This trapping of radiations by the earth’s atmosphere causes warming of the earth and this is known as greenhouse effect.

12. Human activities contribute to the accumulation of CO₂ in the atmosphere. CO₂ traps heat and does not allow it to escape into space. As a result of this, the average temperature of the earth’s atmosphere increases gradually and this is called global warming.

13. Gases which contribute to global warming, like CO₂, methane, nitrous oxide and water vapour are called greenh’ouse gases.

14. The substances that pollute water are called water pollutants.

15. The harmful substances such as sewage, toxic chemicals, silt, etc., get mixed with water and this leads to water pollution.

16. Water which is suitable for drinking is called potable water.

17. Chlorination is a commonly used chemical method for purifying water. It is done by adding chlorine tablets ‘ or bleaching powder to the water.

18. We must conserve water as it is a precious natural resource.

Class 8 Science Chapter 18 Notes Important Terms

Air pollution: When some unwanted substances get mixed with air and have harmful effect on both living and non-living things, is known as air pollution.

Chemical contamination: Presence of harmful chemicals in air, water and soil causing pollution of water is called chemical contamination.

Global warming: Due to the increasing levels of greenhouse gases, like CO₂, the average temperature of earth’s atmosphere is gradually increasing. This is called global warming.

Greenhouse effect: The process of trapping of radiations by the Earth’s atmosphere due to increasing levels of gases like CO₂ is called greenhouse effect.

Pollutants: The substances which causes pollution are known as pollutants.

Potable water: Water which is purified and is also fit for drinking is known as potable water.

Water pollution: The contamination of clean water by substances which are harmful to life is called water pollution.

On this page, you will find Stars and the Solar System Class 8 Notes Science Chapter 17 Pdf free download. CBSE NCERT Class 8 Science Notes Chapter 17 Stars and the Solar System will seemingly help them to revise the important concepts in less time.

CBSE Class 8 Science Notes Chapter 17 Stars and the Solar System

Stars and the Solar System Class 8 Notes Understanding the Lesson

1. The science dealing with the study of the universe is called astronomy.

2. The scientist who study the universe are called astronomers.

3. The stars, the planets, the moon and many other objects in the sky are called celestial objects.

4. The various shapes of the bright part of the moon as seen during a month are called phases of the moon.

5. The phases of the moon occur because we can see only that part of the moon which reflects the light of the sun towards us.

6. The stars are hot glowing spheres that continuously emit their own heat and light, that is they are self luminous objects.

7. Stars appear to move from east to west.

8. The group of stars that move together and form a characteristic pattern in the sky is called constellation.

9. There are many types of constellations like Ursa Major, Ursa Minor, Orion.

10. The sun and the celestial bodies which revolve around it form the solar system. It consists of large number of bodies such as planets, comets, asteroids and meteors.

11. The sun is the nearest star from us. It continuously emits huge amounts of heat and light.

12. A planet has a definite path in which it revolves around the sun. This path is called orbit.

13. There are total eight planets in our solar system.

14. There is a large gap in between the orbits of Mars and Jupiter. This gap is occupied by a large number of small objects that revolve around the sun. These are called asteroids.

15. Comets are also members of our solar system. They revolve around the sun, in highly elliptical orbits. A comet appears generally as a bright head with a long tail.

16. Meteors are the pieces made of stones or metals or both that move very fast in space. They are also called as ‘shooting stars’.

17. Some meteors are so big in size that they do not burn up completely in the atmosphere and reach the earth’s surface. They are called meteorites.

18. A satellite is defined as a heavenly body that moves around another heavenly body along its own orbit.

19. There are two types of satellites:

• Natural satellite
• Artificial satellite

20. Aryabhatta was the first Indian satellite. Some other Indian satellites are INSAT, IRS, Kalpana, EDUSAT, etc.

21. Artificial satellites have many practical applications. They are used for forecasting weather, transmitting television and radio signals. They are used for telecommunication and remote sensing.

Class 8 Science Chapter 17 Notes Important Terms

Artificial satellite: The satellites other than natural satellites are known as artificial satellites. They are used for forecasting weather, transmitting television and radio signals.

Asteroids: Asteroids are small bodies revolving around the sun mostly between the orbits of Mars and Jupiter.

Cassiopeia: Cassiopeia is another prominent constellation in the northern sky. It is visible during winter in the early part on the night.

Celestial objects: Objects such as stars, the planets, the moon and many other objects in the sky are called celestial objects.

Comets: Comets are small, icy objects that orbits the sun and has a long tail of gas. They revolve around the sun in highly elliptical orbits.

Constellations: The group of stars that move together and form a characteristic pattern in the sky are called constellations.

Light year: The distance travelled by light in one year is known as light year.

Meteorites: Some meteors are so large that a part of them reaches the surface of the Earth before they evaporate completely. These are called meteorites.

Meteors: A meteor is a small heavenly object moving around the sun. When a meteor occasionally enters the Earth’s atmosphere it gets heated up because of friction and glows but evaporates in a very short period of time.

Natural satellites: A natural celestial body revolving around another celestial body is called natural satellites.

Orbit: A planet revolves around the sun in a definite path. This path is known as orbit of the planet.

Orion: Orion is a constellation which contain 7 or 8 stars. It looks like a hunter.

Phases of Moon: The various shapes of the bright part of the moon as it is seen during a month are called phases of moon.

Planets: The celestial bodies that revolve around the sun in a well defined orbit are known as planets.

Pole star: The only star which always appears to remain at the same position in the sky is known as pole star.

Remote sensing: It is scanning of the earth by artificial satellite for collecting information from distance.

Solar system: The sun and the celestial bodies which revolve in the space form the solar system.

Stars: Stars are the celestial bodies which emit light of their own. The sun is also a star.

Ursa Major: Ursa major is a constellation which constitutes seven stars and is also known as ‘SaptarishV.