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Class 8 NCERT Mathematics Guide: Rational Numbers - properties and important points

Class 8, Mathematics - NCERT Guide


Properties of Closure
Whole Numbers
>> Whole Numbers are closed under addition. In general, a + b is a Whole Numbers for any two Whole Numbers a and b.
>> Whole Numbers are not closed under subtraction. 5 - 7 = -2, this is not a Whole Number.
>> Whole Numbers are closed under multiplication. In general, if a and b are any two Whole Numbers, their product ab is Whole Number.
>> Whole Numbers are not closed under division..

>> Integers are closed under addition. In general, a + b is an integer for any two integers a and b.
>> Integers are closed under subtraction. For any two integers a and b, a - b is an integer.
>> Integers are closed under multiplication. For any two integers a and b, a x b is an integer.
>> Integers e not closed under division.

Rational Numbers
>> Sum of two rational numbers is again a rational number. Rational Numbers are closed under addition.
>> The difference of two rational numbers is a rational number. Rational numbers are closed under subtraction
>> Rational numbers are closed under multiplication.
>> Rational numbers are not closed under division.      

Properties of Commutativity
Whole Numbers
>> Addition is commutative.
>> Subtraction is not commutative.
>> Multiplication is commutative.
>> Division is commutative.

>> Addition is commutative.
>> Subtraction is not commutative.
>> Multiplication is commutative.
>> Division is commutative.

Rational Numbers
>> Addition is commutative.
>> Subtraction is not commutative.
>> Multiplication is commutative.
>> Division is not commutative.

Properties of Associativity
Whole Numbers
>> Addition is associative.
>> Subtraction is not associative.
>> Multiplication is associative.
>> Division is not associative.

>> Addition is associative.
>> Subtraction is not associative.
>> Multiplication is associative.
>> Division is not associative.

Rational Numbers
>> Addition is associative.
>> Subtraction is not associative.
>> Multiplication is associative.
>> Division is not associative.

Points to Remember
>> Zero is called the identity for addition of rational numbers. It is additive identity for integers and whole numbers. 
>> 1 is multiplicative identity for rational numbers.
>> The additive inverse of the rational number a / b is (- a / b) and vice-versa.
>> The multiplicative or reciprocal inverse of the rational number a / b  is c / d  if, a / b x c / d = 1
>> Rational numbers can be represented on a number line.
>> Between any two rational numbers there are countless rational numbers.

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Class 11 Hardware Concepts, Informatics Practices (IP) - CBSE Notes | CBSE Guide

Class 11, Hardware Concepts - CBSE Informatics Practices (IP) Guide

Computer is an electronic device which can take data as input, process it, and gives out the information as output.
Terminologies used in Computers
Data: Collection of raw facts and figures is called Data.
Input: The data which is given to a computer.
Process: Work done by the computer according to instruction given.
Information: The processed data is called as Information. It is meaningful.
Output: The information which is given by the computer is called as Output.
Hardware: The physical components or parts of a computer.
Software: A set of programmes are called as a Software.
I-P-O Cycle: The first stage is called as Input stage. The second stage is called as Process stage. The third stage is called as Output stage. After getting output again it can be used as Input, then again after process, we get the Output. The whole process can be rotated like a cycle which is called as Input-Process-Output cycle (I-P-O).
Block Diagram or Basic Structure of a Computer:
www.cbsencertsolution.com - Block Diagram or image of Basic Structure of a Computer
(CPU - Central Processing Unit; MU - Memory Unit; ALU - Arithmetic Logic Unit; CU - Control Unit)
Classification of Computers
CBSE Guide NCERT Solution - Types of Computers chart

Input Unit or Input Devices: The devices which are used to supply the data to the computer are called Input Devices. Examples: keyboard, mouse, joystick, OMR, OR etc.
Key Board: It is one of the most important input devices which are used for typing, giving instructions and many other purposes. Key Boards are available in various formats.

Mouse: Also known as Graphical Input Device. It is a painting device. Mouse is used to used draw diagrams, selecting menus and also to perform other tasks mostly in combination with keyboard &/or Monitor. There are three types of Mouses: (1) Mechanical Mouse (2) Optical Mouse (3) Wireless Mouse.
Light Pen: A pointing device consisting of a photocell mounted in a per-shaped tube. A light pen is a light-sensitive computer input device, basically a stylus that is used in conjunction with a computer's CRT display. It allows the user in a similar way to a touch-screen but with greater positional accuracy to select text, draw pictures and interact with user interface elements on a computer screen or monitor.  
Central Processing Unit (CPU): It is used to perform arithmetic (+, -, ×, /, *) and logical operations such as (>, <, =, <=, =>, <>).
Control Unit (CU): This unit controls the flow of data from input devices to memory and from memory to input devices.
Memory Unit (MU): It is used to store and read data. The data will be stored in small location which are called Memory Cells. It stores data in the form of 0, 1 which is called as bits (Binary Digits). A group of 8 bits is called a byte. One Byte can be used to represent a data term or character. The other units of memory are -
1024 Bytes = 1 Kilo Byte (1 KB)
1024 KB = 1 Mega Byte (1MB)
1024 MB = 1 Giga Byte (1 GB)
1024 GB = 1 Tetra Byte (1 TB)
 There are two types of memory units - 1. Main or Primary Memory, 2. Secondary Memory.
Main Memory or Primary Memory: This type of memory is used to store programs and data which run the computer. Examples of Primary Memory Units are - RAM (Random Access Memory), ROM  (Read Only Memory).
RAM: This memory is responsible for read, write and erase the programs or data in the memory. It is also called volatile memory since this memory is temporary only.
ROM: As its name Read Only Memory denotes this memory is used for read only purpose. We cannot write or erase the programs in ROM. That is why this is called permanent or non-volatile memory.
Firmware: The pre-written program which is permanently stored in ROM is called Firmware.
Secondary Memory Devices: Since the primary memory has a limited storage capacity and is not permanent, the secondary storage devices are used to store large amount of data permanently. The following are the various examples -
(1) Magnetic Media Storage Devices: Magnetic Tapes, Floppy Disk, Hard Disk, Zip Drive.
(2) Optical Storage Devices: CD ROM, DVD.
(3) Flash Drive or USB Drives or Jump Drive: Flash drives, also known as USB drives or jump drives, contain mini circuit boards with memory chips to save and retain your data and information. There are no moving parts, and separate media is not necessary to read or record data. This type of storage media is called solid state memory, and differs from optical and magnetic drives. Example: Pen Drive, SD Cards.

Floppy Disks: It is one of the oldest types of portable storage device used to store small amount of data. A floppy disk stores data in the Tracks and Sectors. The first 8-inch floppy disk had a storage capacity of about 80 KB. By 1986, IBM introduced the 3-1/2 inch floppy disk with 1.44 MB of storage space. 
Advantages: (a) Portable, (b) Inexpensive, (c) Reusable.
Disadvantages: (a) Small storage capacity, (b) Delicate, (c) Slow to access and retrieve data, (d) Often data is lost because of weak structure of the disk.
Hard Disks: It is used to store large volume of data. It contains more than one disk arranged on a single spindle. Now-a-days hard disks of huge data storage capacity equivalent to 1 Trillion GB are being used.
Advantages: (a) Large storage capacity (b) Can store and retrieve data in seconds, (c) More reliable and permanent storage.
Disadvantages: (a) It needs to be fixed inside CPU; (b) It is slower than RAM/ROM
Compact Disk (CD): It is a low-cost optical media or optical storage device. A blank, standard CD has a diameter of 120 mm, and can hold up to 700 MB of digital data equivalent of approximately 80 minutes of audio. There are three types of CDs: (1) CD-ROM (Compact Disk - Read Only Memory, (2) CD-R (Compact Disk - Recordable), (3) CD-RW (Compact Disk - Rewritable). The 120 mm disc has a storage capacity of 74 minutes of audio or 650 MB data. CD-R/RWs are available with capacities of 80 minutes of audio or 700 MB.
DVD (Digital Versatile Disk): DVD is a digital optical disc storage format that looks same as Compact Disk and is used to store high capacity data like high quality videos and movies. It is also used to store operating system. It is invented and developed by 4 companies named Philips, Sony, Toshiba and Panasonic in 1995. DVD is able store about 15 times as much information (data) and also 20 times faster than CD. A DVD is a Super Destiny Disk (SD).
DVD storage capacity
Disc type
Data capacity
DVD-quality video (hrs)
Single-layer, single-sided
Single-layer, double-sided
Dual-layer; single-sided
Dual-layer, double-sided

Pen Drive (PD): Pen Drive also referred as USB flash drive is a portable device which allows user to transfer data (text, images, videos etc) to and from computer quickly. Users can easily read and write the data on the Pen Drive by plugging it into the USB port on the computer. The first USB flash drive appeared on the market in late 2000, providing a storage capacity of 8 MB.  The world's new largest flash drive is the 2TB Kingston Data Traveler Ultimate GT.
OMR (Optical Mark Reader): Optical Mark Recognition (also called Optical Mark Reader and OMR) is the process of capturing human-marked data from document forms such as surveys and tests. Optical Mark Readers are input devices which are used to read questionnaires, multiple choice examination papers in the form of lines or shaded areas.
OCR (Optical Character Reader): OCR (Optical Character Recognition) recognizes all the characters from the paper document, collects and stores them into editable document. This device not only scans the marks but also scans each character. The difference between OMR and OCR is that OMR can read the marks filled in circles but it can't recognize the characters.
MICR (Magnetic Ink Character Reader): MICR devices are used to read recognize the characters which are printed with special ink called as Magnetic Ink Characters. It is mainly used in Banks to find the Duplicate cheques or DD and in Post Offices to find duplicate IPO. 
Scanner: Scanner is an input device. It is similar to a photo copier which creates an electronic form of a printed image into a computer. There are three types of scanners: (1) Hand-held Scanner (2) Flat-bed Scanner (3) Drum Scanner
Barcode Reader: It is one of the most widely used input devices now-a-days. A barcode (also bar code) is an optical, machine-readable, representation of data; the data usually describes something about the object that carries the barcode. Traditional barcodes systematically represent data by varying the widths and spacing of parallel lines printed on the product’s label.
Biometric Sensors: It is an input device used for identifying Human features such as DNA identification, Face shape recognition, Voice & Fingerprint identification.
Output Unit or Output Devices: The devices which are used to take the output given by the computer are called as Output Devices. Example: Monitors, Printers, Plotters, Speakers.
Monitor: It is the most commonly used output device in computers. It is used to display the information or data on the screens. A character / image is formed by grouping tiny dots called as pixel (picture elements). There are various kinds of monitors like: Cathode Ray Tube (CRT), Liquid Crystal Display (LCD), Thin Film Transistor (TFT).
Impact Printers: It is an output device used for creating paper copies from the computer. Impact printer refers to a class of printers that work by banging a head or needle against an ink ribbon to make a mark on the paper. This includes dot-matrix printers, daisy-wheel printers, and line printers.
Non-Impact Printers: In these printers there is no mechanical contact between the print head and the paper. These printers print without banging a ribbon onto paper. Non-impact printers do not use a striking device to produce characters on the paper; and since these printers do not hammer against the paper they are much quieter than impact printers. Laser, LED, inkjet, solid ink, thermal wax transfer and dye sublimation printers are examples of non-impact printers.

Class 11 Informatics Practices (IP) - Hardware Concepts  Guess Questions

1.       What is a computer?
2.       What do you understand by I-P-O Cycle?
3.       What are the functional parts of a computer?
4.       What are the components of a CPU?
5.       What is the function of ALU?
6.       What role does the input unit play in computer?
7.       What is the difference between Internal and External Memories?
8.       What do you mean by the terms Hardware, Software, Firmware?
9.       What is the difference between RAM and ROM?
10.    Give examples of Non-Impact printers.
11.    How are the computers classified (type of computers)?
12.    What is scanner? Is scanner output or input device?
13.    What is OMR? What is the difference between OMR and OCR?
14.    Make a sketch of the basic structure of a computer.