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This document discusses the four operations of integers: addition, subtraction, multiplication, and division. It describes four cases of integers operations: 1) starting with positive numbers and adding to make a positive result, 2) starting with positive numbers and subtracting to make a positive result, 3) starting with negative numbers and adding or subtracting to make a more negative result, and 4) starting with negative numbers and subtracting to make a positive result. Examples are provided for each case.
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2.2 add integers ws day1
The document provides examples and rules for adding integers. It explains that to add numbers with the same sign, you add the numbers and keep the sign, while to add numbers with opposite signs you subtract the numbers and keep the sign of the number with the larger absolute value. It then gives practice problems for students to apply these rules for adding integers.
Estimating sums and differences (lesson 6.5)
This document provides guidance on estimating sums and differences of fractions by rounding fractions to benchmarks of 0, 1/2, or 1. It explains that benchmarks are easy reference numbers to use when estimating. Examples are provided that show how to change each fraction in a sum or difference to the nearest benchmark, then calculate the sum or difference. For mixed numbers, the fraction part should be rounded up to 1 if it is greater than 1/2, or rounded down to 0 if it is less than 1/2 before calculating. This allows for quick estimation of fraction calculations.
Adding and subtracting integers
Adding integers involves combining numbers with the same sign by adding their absolute values and keeping the sign, or ignoring different signs, subtracting the smaller number from the larger and keeping the original sign. Subtracting integers can be done by changing the subtraction sign to addition, changing the subtracted number's sign, and using integer addition rules. Examples show -2 + (-9) = -11, -30 + (-8) = -38, and 9 - (-3) = 12.
Chapter1.4
The document provides examples and explanations for adding, subtracting, and evaluating expressions with integers on a number line and using absolute value. It includes step-by-step work with integers like finding the sum of -7 + -7, evaluating expressions like 13 + r for r = -15, and an example word problem about the number of dogs in a shelter.
Adding and subtracting decimals
To add and subtract decimals:
1) Line up the decimals by writing zeros in empty decimal places as needed.
2) Add or subtract the numbers as usual, carrying or borrowing across the decimal.
3) The decimal point belongs in the answer in the same column as in the original numbers.
Decimals Add and Subtract
1. This document provides a lesson on adding and subtracting decimals. It emphasizes lining up the decimals and notes that adding and subtracting decimals follows the same process as whole numbers.
2. Examples are provided that demonstrate adding decimals by lining them up under each other with the decimals in the same column before adding. Adding zeros as placeholders is explained to help line up the decimals.
3. Subtracting decimals is demonstrated with examples of lining up the numbers with the larger number on top and subtracting left to right, borrowing as needed from the left.
Adding & Subtracting Integers in Everyday Life
Integers can represent positive and negative values and are useful for modeling real-world situations involving amounts that can be above or below a given level.
Some examples of using integers to model real situations include:
1) Using positive integers to represent amounts of money deposited in a bank account and negative integers to represent withdrawals, allowing addition and subtraction of integers to track the account balance.
2) Using positive integers for distances gained in sports like football and negative integers for distances lost, allowing integer operations to calculate total gains or losses.
3) Representing floors of a building as integers where positive numbers are above ground level and negative are below, so integer addition and subtraction can track elevator movement between floors.
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This document provides information on numerical concepts in physics such as:
1) Determining the number of significant figures in measurements and calculations.
2) Converting numbers between normal and scientific notation.
3) Using unit analysis to convert between different units of measurement like centimeters to meters.
It defines key terms like significant figures and scientific notation. It also provides examples of operations using significant figures and scientific notation, as well as guidelines for unit conversions between the metric system and other units.
Recommended
2.2 add integers ws day1
The document provides examples and rules for adding integers. It explains that to add numbers with the same sign, you add the numbers and keep the sign, while to add numbers with opposite signs you subtract the numbers and keep the sign of the number with the larger absolute value. It then gives practice problems for students to apply these rules for adding integers.
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This document provides guidance on estimating sums and differences of fractions by rounding fractions to benchmarks of 0, 1/2, or 1. It explains that benchmarks are easy reference numbers to use when estimating. Examples are provided that show how to change each fraction in a sum or difference to the nearest benchmark, then calculate the sum or difference. For mixed numbers, the fraction part should be rounded up to 1 if it is greater than 1/2, or rounded down to 0 if it is less than 1/2 before calculating. This allows for quick estimation of fraction calculations.
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Adding integers involves combining numbers with the same sign by adding their absolute values and keeping the sign, or ignoring different signs, subtracting the smaller number from the larger and keeping the original sign. Subtracting integers can be done by changing the subtraction sign to addition, changing the subtracted number's sign, and using integer addition rules. Examples show -2 + (-9) = -11, -30 + (-8) = -38, and 9 - (-3) = 12.
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The document provides examples and explanations for adding, subtracting, and evaluating expressions with integers on a number line and using absolute value. It includes step-by-step work with integers like finding the sum of -7 + -7, evaluating expressions like 13 + r for r = -15, and an example word problem about the number of dogs in a shelter.
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1) Line up the decimals by writing zeros in empty decimal places as needed.
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1. This document provides a lesson on adding and subtracting decimals. It emphasizes lining up the decimals and notes that adding and subtracting decimals follows the same process as whole numbers.
2. Examples are provided that demonstrate adding decimals by lining them up under each other with the decimals in the same column before adding. Adding zeros as placeholders is explained to help line up the decimals.
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Integers can represent positive and negative values and are useful for modeling real-world situations involving amounts that can be above or below a given level.
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1) Using positive integers to represent amounts of money deposited in a bank account and negative integers to represent withdrawals, allowing addition and subtraction of integers to track the account balance.
2) Using positive integers for distances gained in sports like football and negative integers for distances lost, allowing integer operations to calculate total gains or losses.
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2) Converting numbers between normal and scientific notation.
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Syllabus
Chapter-1
Introduction to objective, scope and outcome the subject
Chapter 2
Introduction: Scope and Specialization of Civil Engineering, Role of civil Engineer in Society, Impact of infrastructural development on economy of country.
Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
Linear Measurements: Instruments used. Linear Measurement by Tape, Ranging out Survey Lines and overcoming Obstructions; Measurements on sloping ground; Tape corrections, conventional symbols. Angular Measurements: Instruments used; Introduction to Compass Surveying, Bearings and Longitude & Latitude of a Line, Introduction to total station.
Levelling: Instrument used Object of levelling, Methods of levelling in brief, and Contour maps.
Chapter 4
Buildings: Selection of site for Buildings, Layout of Building Plan, Types of buildings, Plinth area, carpet area, floor space index, Introduction to building byelaws, concept of sun light & ventilation. Components of Buildings & their functions, Basic concept of R.C.C., Introduction to types of foundation
Chapter 5
Transportation: Introduction to Transportation Engineering; Traffic and Road Safety: Types and Characteristics of Various Modes of Transportation; Various Road Traffic Signs, Causes of Accidents and Road Safety Measures.
Chapter 6
Environmental Engineering: Environmental Pollution, Environmental Acts and Regulations, Functional Concepts of Ecology, Basics of Species, Biodiversity, Ecosystem, Hydrological Cycle; Chemical Cycles: Carbon, Nitrogen & Phosphorus; Energy Flow in Ecosystems.
Water Pollution: Water Quality standards, Introduction to Treatment & Disposal of Waste Water. Reuse and Saving of Water, Rain Water Harvesting. Solid Waste Management: Classification of Solid Waste, Collection, Transportation and Disposal of Solid. Recycling of Solid Waste: Energy Recovery, Sanitary Landfill, On-Site Sanitation. Air & Noise Pollution: Primary and Secondary air pollutants, Harmful effects of Air Pollution, Control of Air Pollution. . Noise Pollution Harmful Effects of noise pollution, control of noise pollution, Global warming & Climate Change, Ozone depletion, Greenhouse effect
Text Books:
1. Palancharmy, Basic Civil Engineering, McGraw Hill publishers.
2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House.
4. BCP, Surveying volume 1
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