What is Addition: Definition and 651 Discussions

Addition (usually signified by the plus symbol +) is one of the four basic operations of arithmetic, the other three being subtraction, multiplication and division. The addition of two whole numbers results in the total amount or sum of those values combined. The example in the adjacent image shows a combination of three apples and two apples, making a total of five apples. This observation is equivalent to the mathematical expression "3 + 2 = 5" (that is, "3 plus 2 is equal to 5").
Besides counting items, addition can also be defined and executed without referring to concrete objects, using abstractions called numbers instead, such as integers, real numbers and complex numbers. Addition belongs to arithmetic, a branch of mathematics. In algebra, another area of mathematics, addition can also be performed on abstract objects such as vectors, matrices, subspaces and subgroups.Addition has several important properties. It is commutative, meaning that order does not matter, and it is associative, meaning that when one adds more than two numbers, the order in which addition is performed does not matter (see Summation). Repeated addition of 1 is the same as counting; addition of 0 does not change a number. Addition also obeys predictable rules concerning related operations such as subtraction and multiplication.
Performing addition is one of the simplest numerical tasks. Addition of very small numbers is accessible to toddlers; the most basic task, 1 + 1, can be performed by infants as young as five months, and even some members of other animal species. In primary education, students are taught to add numbers in the decimal system, starting with single digits and progressively tackling more difficult problems. Mechanical aids range from the ancient abacus to the modern computer, where research on the most efficient implementations of addition continues to this day.

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  1. L

    Electrophilic addition, elimination and stuff like that

    Hi! I've made the following assignments and I'll appreciate it if anybody of you can help me with them and correct me if my answer is wrong. Thanks a lot! A) Provide reagents that could be used to effect the transformation of 'Stof A' to each of the following compounds (1-5)...
  2. T

    What is the result of adding f and g in set addition?

    Let f = {(-4.4),(-2,4),(1,3),(3,5),(4,6)} and g = {(-4,2),(-2,1),(0,2),(1,2),(2,2),(4,4)} Determine a)f + g
  3. C

    Simple vector addition question

    just a quick question, I've never dealt with vectors before, they say you are simply supposed to add them, the same way you would add any two numbers, ie: a + b = c yet whenever they add two vectors, they end up with a different sum.. ie: 1m + 2.5m = 7m this seems so simple, what am I...
  4. M

    Rules governing the creation of complex waveforms through addition of sine waves

    I'm interested in synthesizing complex waveforms using sine waves. I know that when two sine waves which differ slightly in frequency from one another are summed, amplitude modulation (AKA "beating") with a frequency equal to the difference in frequency between the two sine waves ensues. This...
  5. R

    Proof using the Axioms of Addition and Multiplication

    So does everybody know the Axioms of Addition and Multiplication? They are too long to type, but they are listed: A1, A2, A3, A4, A5, M1, M2, M3, M4, M5 and the distributive law, DL. anyways, I want to prove: 1. (-x)y = -(xy) and 2. (-x)(-y) = (xy) using ONLY the axioms of additon and...
  6. D

    Verifying A Cosines Addition Equation with Beats

    The problem asks me to show that the addition of two cosines with different wavelength and frequencies gives a solution with beats. Mathematically, I need to verify that A cos (k1x-w1t)+A cos (k2x-w2t) is equivalent to A cos (.5(k1+k2)x-.5(w1+w2)t) cos (.5(k1-k2)x-.5(w1-w2)t) I converted...
  7. C

    Multiplication preceeding addition

    Hi everybody, This may have been discussed before ( and by me) but I would like to see a proof of the following statement: " (ab)+(ac)=ab+ac" Ok let me explain a bit. When we want to set some axioms about the real numbers we say that we define two functions from RxR->R, addition(+) and...
  8. D

    Vector Addition and Angle Calculation Using Trigonometry

    Man, my online physics course sucks. Every time there is a lab or an assignment, it's on stuff I haven't done, lol. Anyway I have an angle of 155 degrees separating one 18 N vector going 85 degrees northwest, and another vector going about 60 degrees southwest. The other angle is 12 N. I...
  9. Q

    Addition Theorem for Spherical Harmonics

    Happy New Year all! i have a question regarding the addition theorem for spherical harmonics. In JD Jackson book pg 110 for e.g. the addition theorem is given as: P_{L}(cos(\gamma))=\frac{4\pi}{2L+1}\sum_{m=-L}^{L}Y^{*}_{Lm}(\theta',\phi')Y_{Lm}(\theta,\phi) where...
  10. N

    Question on Addition of Velocities

    When you calculate the relative velocity of two bodies moving towards each other at almost c, are you calculating the observed relative velocity, or the actually relative velocity. Because if it's the actual velocity then technically no body could ever move faster the 1/2c due to the fact that...
  11. H

    Derive most trigonometric identities from the addition formulas

    In the same way that it is possible to derive most trigonometric identities from the addition formulas, what is the way that the difference of sines and cosines formulas were derived, such as \sin{a}-\sin{b}=2\cos{\frac{a+b}{2}}\sin{\frac{a-b}{2}} thanks, I am trying to avoid as much...
  12. M

    How Do I Solve Linear Equations with Fractions and Word Problems in Algebra?

    5X-5/2Y=-55 4X+2Y=-12 USE ADDITION METHOD...HOW I DO THIS PROBLEM THE FRACTIONS THROW ME OFF ALSO A VENDOR SELLS HOT DOGS AND BAGS OF CHIPS.A CUSTOMER BUYS 2 HOT DOGS AND 2 BAGS OF CHIPS FOR $7.00.ANOTHER CUSTOMER BUYS 4 HOT DOGS AND 5 BAGS OF CHIPS FOR $15.00.FIND THE COST OF EACH ITEM...
  13. I

    Vector Addition of differing quantities

    My girlfriend had this problem on her first tutorial sheet at Univeristy. She is doing maths. I am doing physics and was interested in the answer. It asked what the result was when a displacement vector was added to a velocity vector. The vector addition can obviously be done on these two...
  14. R

    Cantor Expansion Addition algorithm?

    Could someone help me and write an algorithm to add 2 Cantor expansions. The algorithm to get a decimal number to cantor expansion is: procedure decimal-to-cantor(x: positive integer) n := 1 y := x fy is a temporary variable used so that this procedure won't destroy the original value of...
  15. S

    Treasure Hunt: Adding Vectors for Displacement

    You are on a treasure hunt and your map says "Walk due east for 52 paces, then walk 29.6° north of west for 44 paces, and finally walk due north for 25 paces." (a) What is the magnitude of the component of your displacement in the direction due north? b) What is the magnitude of the...
  16. K

    Perform mathematical calculations like addition

    My question seems to be so idiotic.please forgive me for that.On what basis we perform mathematical calculations like addition and subtraction?As for as decimal system is concerned we have only 10 uncontinuos digits.but we are doing so much magic(I don't know whether I am using the correct...
  17. P

    Relativistic addition question

    I understand that, given objects A and B moving away from a stationary point O and each other at relativistic speeds, you use the relativistic addition formula to find A's speed relative to B. How would you find A's speed relative to B if A and B are moving away from O at a 60 degree angle...
  18. A

    Calculating pH Change from HClO4 Addition

    when you add 10.0 mL of 1.0M HClO4 into 990.0mL water, the pH changes by 2. how would you find the change in pH?
  19. P

    Lagrangian remains invariant under addition

    what is the reason that the lagrangian remains invariant under addition of an arbtrary function of time?
  20. C

    Electrophilic addition of bromine

    Hi! I am stuck in revising the electrophilic addition of bromine across the alkene molecule... There are two sentences which really confuse me, I hope you can help me. When a bromine molecule approaches the pi electron cloud of the C=C bond...the bromide ion then attacks the pi complex...
  21. J

    Vector Addition: Components and Length of Vectors V(1) and V(2)

    Hi, The question is: The components of a vector V can be written as (V(x), V(y), V(z)). What are the components and length of a vector which is the sum of the two vectors, V(1) amd V(2). whose components are (8.0. -3.7,0.0) and (3.9,-8.1,-4.4)? Work For the components V(x)=...
  22. R

    Could someone explain why is division distributive over addition ?

    could someone explain why is division distributive over addition ? It's not intuitive to me. Thanks Roger
  23. N

    Vector Addition Q: Find Z Component of A X B

    Q. All four of the vectors below are added to vector E. Positive angles are measured counter-clockwise from the x axis. A = 2 m î + 3 m ĵ B = -7 m î -10 m ĵ C = 3 m at 62 ° D = 8 m at -226 ° a) What is C·D? C.D = |C| |D| cos theta I did this. 3* cos 62 + 8 cos -226 , but...
  24. M

    Adding I1,I2,I3,I4 to Get I5 - Tips & Tricks

    What is I5 I think its I3-I4+I2+I1 but not surehow to add em up any tips? thanks
  25. S

    Understanding Angular Momentum Addition: A Brief Overview

    Hi there. I was just confused with this addition of angular momentum! Any useful help or link about the mathematical consepts? Thanks in advance. Somy :smile:
  26. Y

    Baryons & addition of angular momentum

    I was wondering if someone could help me explain this problem. In a baryon, two quarks are in l=0 and one quark is in the l=1 state. Quarks are spin-1/2 particles. What values can the total angular momentum take? I know the answer is 1/2, 3/2, and 5/2, but I'm confused about how they...
  27. A

    Coffee temperature and time of milk addition

    Youri takes a coffee and adds some milk at room temperature to it. Saku takes a black coffee and adds the same amount of milk but 10 minutes later. Which coffee is the hotter and why? I think that Youri's coffee would be hotter since the temperature variation is proportional to the...
  28. M

    Velocity Addition: Solving the Mystery

    I'm trying to figure this problem out, and think it's not that hard, but am having trouble acquiring the answer. Here is the problem: You and a friend decide to "hitch" a ride in the mailcar of a train heading to Green Bay (due north). Halfway there, your friend asks you for a sandwich out...
  29. D

    Is Addition Really a Basic Skill?

    I reckon addition is a basic skill. But can it be proved? How?
  30. G

    How Do Components of Force Affect Barge Movement in Vector Addition?

    a horse pulls a barge along a canal using a rope 10m long. if the barge is 2m from the bank, the rope is taught and the tension in it is 500N. what are the components of this force at right angles to the canal? i worked this out to be 99.7N i used 500 x sin 11.5 (the angle between the rope...
  31. A

    Prove that Q under addition is not isomorphic to R+

    How do I prove that Q under addition is not isomorphic to R+ under multiplication?
  32. M

    Resultant velocity of a plane and a vector addition diagram

    --An airplane flies at 300 km/hr with a heading of 35* south of west, as a 78 km/hr wind blows in the direction of 55* south of east. The resultant velocity of the plane is... --A force of 85 N S50*E, a force of 50 N N45*E, and a force of 70 N N30*W act concurrently on an object. Draw a...
  33. C

    Solving Vector Addition Problems

    help me please! 1.a car drives straight off the edge of a cliff that is 55m high. the police at the scene of the accident note that the point of impact is 126m from the base of the cliff. how fast was the car traveling when it went over the cliff? I just need a hint of where to start...
  34. H

    Addition of Vectors: Finding the Angle

    One of my review questions is the following: "A box is pulled along the floor by a horizontal force of 35 N. Another force acts concurrently on the box with a force of 25 N at an angle of 40 degrees above the horizontal in the same direction as the first force. What is the sum of the two...
  35. S

    Using the Galilean transformation and classical velocity addition

    My problem is this: Let's say momentum is conserved in all frames... An observer on the ground observes two paticles with masses m1 and m2 and finds upon measurement that momentum is conserved. Use classical velocity addition to prove that momentum is conserved if the observer is on a train...
  36. U

    Solving Addition of Forces Involving Adults and Child

    Two adults and a child want to push a wheeled cart in the direction marked x in the figure (attached). The two adults push with horizontal forces F1 and F2 as shown in the figure (attached). A) Find the magnitude of the smallest force that the child should exert. You can ignore the effects of...
  37. C

    Understanding Vector Addition: 2 Forces with Same Magnitude F

    I need help getting in the right direction... Two forces have the same magnitude F. What is the angle between the two vectors if their sum has a magnitude of 2*F? sqrt(2)*F? zero?
  38. B

    How Do You Calculate Vector Distances on a Checkerboard?

    Hi again, I have what is seems to be a simple vector addition problem, but I am questioning a certain part of it. I would show a diagram but I can't at the moment as the computer I am on does not have a drawing program. It should be fairly easy to picture though. The base of the drawing is...
  39. B

    Addition of Vectors and displacement

    I think I have a trick question here. The section we are covering is addition of vectors by means of components. Here is my problem: You are on a treasure hunt and your map says, "Walk due east for 52 paces, then walk 26.6 degrees north of west for 42 paces, and finally walk due north for 25...
  40. M

    Solving Vector Addition Without Angle Measurements

    In class today we had a brief lesson on vector addition. I understand how to calculate the resultant when given a magnitude and angle measurent for each vector, but my teacher gave me no other examples. I have tons of homework problems that do not give me this information, but I am expected to...
  41. S

    Addition of three angular momentum

    How can I couple three angular momentum? I am confused about this, in fact I don't understand how can I do this... I need to build eigenstates of total angular momentum for three particles J=j_1+j_2+j_3, someone can help me? Thank's
  42. D

    Polygonal addition of forces is invalid->

    The traditional polygonal addition of force is invalid because it doesn't take the dependence of the forces on the positions where they act. We cannot simply drag the force-vectors across the space and expect them to remain the same. The forces must change respectively to the change of the...
  43. S

    Counting Theory and Addition Rule Confuses Me

    How many 16-bit strings contain exactly nine 1's? I said the total number is 2 to the 16th power, so to get half with 1's would be 2 to the 8th, or 256. How many 16-bit strings contain at least fourteen 1's? I have no idea. When determining a how to get 2 pair in a poker hand, why is...
  44. 1

    Exploring Math in Base -5: Addition & Multiplication Tables

    i am curious as to how this would look. i wonder how the addition tables would look in base -5? would the multiplication look the same? here is what i know so far: addition multiplication 0 1 2 3 4...
  45. Norman

    Is Griffiths' Statement About the Addition of Angular Momentum Always Correct?

    I am working through some old particle physics notes of mine and when reading Griffiths "Introduction to Elementary Particles" I stumbled across a very perplexing problem: Problem 4.9, pg 138: "When you are adding angular momentum... it is useful to check your results by counting the...
  46. K

    Einstein's Addition of Vectors

    Hey all, I guess Einstein has some counter-intuitive, at least naturally, vector addition formula whose result could be that two beams of light traveling towards each other is basically the same as one beam going towards a stationary object, right? Well..I hope you knwo waht I mean. That the...
  47. J

    What Is the Term for Decomposing Numbers into Additive Combinations?

    "Factoring" of addition? Is there a name for "factoring" addition? For example...let's say I'm working in a basis of all integers greater than 3. I can make 7 from 3+4; 8 from 4+4 or 3+5; 9 from 3+3+3 or 4+5 or 6+3... Is there a name for this? And if so...are there computer programs that...
  48. K

    Making Vector Addition programmeable

    Hello...I really want to make a program that can do vector addition and subtraction, given two or more vectors. The problem is, I'm not sure of the math that would be needed to do it. See, I want the person to be able to enter two or more vectors with a magnitude (length) and angle (with 0...
  49. O

    How Do Addition and Multiplication Differ in Boolean Logic?

    Hi, Can someone please show some example of Qualitative difference between Addition and Multiplication, when using Boolean Logic? (by Qualitative difference I mean that Quantity remains unchanged during addition or multiplication operations between n positive integers).
  50. N

    Stereochemistry of Bromine Addition to trans-Cinnamic Acid

    We determined our melting point to be 199 C. Which would correspond to (2R,2S) and (2S,3R) 2,3-dibromo-3-phenylpropanoic acid (mp 202-204 C) but we are trying to determine whether this is a syn or an anti addition. Any suggestions? Thanks Nautica
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