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The Wonderful World of Science | Assess
CROP PRODUCTION AND MANAGEMENT | Assess
Integers | Assess
Integers | Study
Nutrition in Plants | Study
Rational Numbers | Study
The Wonderful World of Science | Assess
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Integers | Assess
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Integers | Study
Mind Map Overal Idea Content Speed Notes Quick Coverage ntegers are a bigger collection of numbers which is formed by whole numbers and their negatives. You have studied inthe earlier class, about the representation of integers onthe number lineand their addition and subtraction. (Scroll down till end of the page) Study Tools Audio, Visual &… readmore
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ntegers are a bigger collection of numbers which is formed by whole numbers and their negatives. You have studied inthe earlier class, about the representation of integers onthe number lineand their addition and subtraction. (Scroll down till end of the page)
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We now study theproperties satisfied by addition andsubtraction.
(a) Integers are closed for addition and subtraction both. That is, a + b and a – b are again integers, where a andb are anyintegers.
(b) Addition is commutative forintegers, i.e., a + b = b + a for allintegers a andb.
(c) Addition is associative for integers, i.e., (a + b) + c = a + (b + c) for all integers a, b and c.
(d) Integer 0 is the identity under addition. That is, a + 0 = 0 + a = a for every integer a. We studied, how integers could be multiplied, andfound that product of a positive and a negative integer is a negative integer, whereas the product of two negative integers isa positive integer. For example, –2 × 7 = –14 and –3 × – 8 =24.
Product of even number of negative integers is positive, whereas the product of odd number of negative integers is negative. Integers showsome properties under multiplication.
(a) Integers are closed under multiplication. Thatis, a × b isan integer forany two integers a and b.
(b) Multiplication is commutative for integers. Thatis, a × b = b × a forany integers a and b.
(c) The integer 1 is theidentity under multiplication, i.e., 1 × a = a × 1 = a forany integer a.
(d) Multiplication is associative for integers, i.e.,(a × b) × c = a × (b × c) for anythree integers a,b and c.
Under addition and multiplication, integers show a property called distributive property.
That is, a× (b +c) = a × b+ a × c forany three integers a, b andc.
The properties of commutativity, associativity under addition and multiplication, and the distributive property help us to make our calculations easier. We alsolearn how to divide integers. We found that,
(a) When a positive integer is divided by a negative integer, the quotient obtained is a negative integer and vice-versa. (b) Division of a negative integer by another negative integer gives a positive integer as quotient. For any integer a,we have
1) The numbers. . . , —4,—3, —1, 0, 1, 2,3, 4, etc.are integers.
2) 1, 2, 3, 4, 5. . . . are positive integers and —1,-2, —3,.. are negative integers.
3) 0 isan integer which is neither positive nornegative.
4). On an integer number line, all numbers to the right of 0 arepositive integers andall numbers tothe left of0 are negative integers.
5) 0 is less than everypositive integer and greater than everynegative integer.
6) Every positive integer is greater than every negative integer.
7) Two integers thatare at thesame distance from 0, but onopposite sides of it are called opposite numbers.
8. The greater the number, the lesser is its opposite.
9. The sumof an integer and its opposite is zero.
10. The absolute valueof an integer is the numerical value of theinteger without regard to its sign.
The absolute value of an integer a isdenoted by |a| and is given by a,if a is positive or 0 a = -a,if a is negative
11. The sum oftwo integers of the same sign is an integer of the same sign whose absolute value is equal to the sum of the absolute values of the given integers.
12. The sum of two integers of opposite signs is an integer whose absolute value is the difference of the absolute values of addend and whose sign isthe sign ofthe addend having greater absolute value.
13. To subtract an integer b from another integer a, we change the sign ofb and addit to a. Thus, a − b = a + (−b)
14. All properties of operations onwhole numbers aresatisfied by theseoperations on integers.
15. If aand b are two integers, then(a − b) is alsoan integer.
16. −a and aare negative oradditive inverses of each other.
17. To find theproduct of twointegers, we multiply theirabsolute values andgive the result a plus signif both thenumbers have the same sign or a minussign otherwise.
18. To find thequotient of oneinteger divided by another non-zero integer, we divide their absolute values and give the result a plus sign if both the numbers have the same sign or a minus signotherwise.
19. All the properties applicable to wholenumbers are applicable to integers in addition, the subtraction operation has the closure property.
20. Any integer whenmultiplied or divided by 1 gives itself and whenmultiplied or divided by-1 gives its opposite.
21. When expression hasdifferent types ofoperations, some operations haveto be performed before the others. That is, each operation has its own precedence. The order in which operations are performed is division, multiplication, addition and finally subtraction (DMAS).
22. Brackets are usedin an expression when we wanta set of operations to be performed before the others.
23. While simplifying anexpression containing brackets, the operations within the innermost set of brackets are performed first and then those brackets are removed followed by the ones immediately after them tillall the brackets are removed.
24. While simplifying arithmetic expressions involving various brackets and operations, we use BODMAS rule.
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Nutrition in Plants | Study
Mind Map Overal Idea Content Speed Notes Quick Coverage Nutrition: It is the mode of taking food by an organism and its utilization by the body. Nutrients: The components of food that provide nourishment to the body. All organisms take food and utilise it to get energy for the growth and maintenance of their bodies.… readmore
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Nutrition: It is the mode of taking food by an organism and its utilization by the body.
Nutrients: The components of food that provide nourishment to the body.
All organisms take food and utilise it to get energy for the growth and maintenance of their bodies. (Scroll down till end of the page)
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Autotrophs: Autotrophs are the green plants which synthesise their food themselves by the process of photosynthesis.
Photosynthesis: the process of preparation of own food by the Green plants with the help of chlorophyll (found in green plants), carbon dioxide and water taken from the environment in presence of sunlight is known as photosynthesis.
Plants use simple chemical substances like carbon dioxide, water and minerals for the synthesis of food.
Chlorophyll and sunlight are the essential requirements for photosynthesis.
Complex chemical substances such as carbohydrates are the products of photosynthesis.
Solar energy is stored in the form of food in the leaves with the help of chlorophyll.
Oxygen is produced during photosynthesis.
Oxygen released in photosynthesis is utilised by living organisms for their survival.
Fungi derive nutrition from dead, decaying matter.
They are saprotrophs.
Plants like Cuscuta are parasites.
They take food from the host plant.
A few plants and all animals are dependent on others for their nutrition and are called heterotrophs.
Parasitic: Organisms that live on the body of other organisms. All parasitic plants feed on other plants as either:
Partial Parasites: Obtain some of their nutrition from the host,
Example: Painted cup
Total Parasites: Dependent completely on the host for nutrition.
Example: Mistletoe.
Nutrition in plants
Saprophytic: Organisms that obtain nutrition from dead and decaying plant and animal matter.
Mushrooms, moulds and certain types of fungi and bacteria.
Insectivorous Plants: Green plants which obtain their nourishment partly from soil and atmosphere and partly from small insects.
Example: pitcher plant, bladderwort, and venus fly trap.
Symbiosis: Mode of nutrition in which two different individuals associate with each other to fulfil their requirement of food.
Lichens found on tree trunks is the association between algae and fungus.
Algae obtains water from fungus and it in turn obtains food from algae.
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Rational Numbers | Study
Mind Map Overal Idea Content Speed Notes Quick Coverage Rational numbers are closed under the operations of addition, subtraction and multiplication, But not in division. (Scroll down till end of the page) Study Tools Audio, Visual & Digital Content The operations addition and multiplication are(i) commutative for rational numbers. (ii) associative for rational numbers. The… readmore
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Rational numbers are closed under the operations of addition, subtraction and multiplication, But not in division. (Scroll down till end of the page)
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The operations addition and multiplication are
(i) commutative for rational numbers.(ii) associative for rational numbers.
The rational number 0 is the additive identity for rational numbers.
The additive inverse of the rational number a/b is -a/b and vice- versa.
The reciprocal or multiplicative inverse of the rational number
is if a/b is c/d if (a/b)(c/d) =1Distributive property of rational numbers:
For all rational numbers a, b and c, a(b + c) = ab + ac
and a(b – c) = ab – ac.Rational numbers can be represented on a number line.
Between any two given rational numbers there are countless rational numbers.
The idea of mean helps us to find rational numbers between two rational numbers.
Positive Rationals: Numerator and Denominator both are either positive or negative.
Example: 2/3, -4/-5
Positive Rationals: Numerator and Denominator both are either positive or negative.
Example: -2/3, 4/-5
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