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. M

    Addition and Subtraction of Vectors

    A plane, traveling with a velocity relative to the air of 320km/h [28 S of W], passes over Winnipeg. The wind velocity is 72km/h [s]. Determine the displacement of the plane from Winnipeg 2.0 h later. Cosine Law -> c^2 = b^2 + a^2 - 2*b*a*Cos<C Sine Law- (Sin<A)/a = (Sin<B)/b = (Sin<C)/c...
  2. D

    Vector Addition of Electric Forces in a Plane

    The problem I'm trying to solve involves the effect that two charges has on a third and I need to find the magnitude of the resulting force. In this particular problem it's the effect of A and B on C. The work I've done so far is attached so please take a look. I've been trying to add...
  3. E

    Finding Probabilities of Spin 1/2 System Measurement

    [SOLVED] Addition of Spin 1/2 Homework Statement A system is composed of two spin 1/2. The system's hamiltonian is H=w_1 S_1z + w_2 S_2z. The initial state of the system is, at t=0, | \psi (0) > = \frac{1}{\sqrt(2)}[|+ -> + |-+>] . a) At time t, we measure S^2 = (S1+S2)^2 What...
  4. L

    Geometric vs Componentwise Vector Addition

    Homework Statement Which of following sets of conditions (A - F), if true, would show that the expressions 1 and 2 above define the same vector C_vec as expressions 3 and 4? 1. The two pairs of expressions give the same length and direction for C_vec. 2. The two pairs of...
  5. H

    Vector addition in electric field

    Homework Statement Two positive charges = = 2.0 are located at = 0, = 0.30 and = 0, = -0.30 , respectively. Third point charge = 4.0 is located at = 0.40 , = 0.What is the net force ((a)magnitude and (b)direction) on charge exerted by the other two charges? Homework Equations Columbs...
  6. L

    Has a Benficial Addition Mutation been observed?

    To jump from a single celled organism to a multicellular one, we need beneficial addition mutations in DNA sequences. My question is this: has this phenomena ever been observed? By beneficial I mean a mutation in the genotype that serves to cause some phenotype that can be used by an organism...
  7. H

    Why does multiplication precede addition?

    We all know BEDMAS from grade school: brackets, exponents, division, multiplication, addition, subtraction. My question is, why does multiplication precede addition, and likewise their inverse operations?
  8. M

    Solving pH of Solution After NaOH Addition

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  9. K

    Derivation of Phase Angle Addition Formula

    For two phasors a and b, with magnitudes of A,B respectively and phase angles of \phi_{a) and \phi_{b}, the angle of the sum of the phasors (call it p) has a magnitude of: P^{2} = A^{2} + B^{2} , and a phase angle of: \phi_{p} = -tan^{-1}(\frac{B}{A}) The magnitude identity makes...
  10. M

    How Accurate Are My Vector Addition Results?

    a. 2cm N + cm W b. 5m S+ 8cm N c. 30m/s W+ 50m/s S d. 5cm N + 7cm W +9cm S My answers: a.7.2 b.9.43 c.58 d.? I want to know if a,b, and c are right; I don't know d.
  11. I

    What Forces Are Needed to Maintain Equilibrium on a Frictionless Surface?

    Homework Statement A 5.0 Kg block at rest on a frictionless surface is acted on by forces F1= 5.5N and F2= 3.5N, as illustrated in the figure. A) What additional force (in unit vector notation) is required to keep the block at rest? B) What additional force (in unit vector notation) is...
  12. C

    How Does the Potential of a Coalesced Drop Compare to Its Original Drops?

    Homework Statement 27 drops of salt water with same radius, are each charged to a potential of V volts. They are made to coalesce into a single drop. How is the potential of a new drop compared to the potential of the original drops. Homework Equations V ( potential ) = k* q/r...
  13. M

    Example of a Non-Subspace in R^2 Closed Under Addition and Inverses?

    I don't understand this, can someone help?: What is an example of a subset of R^2 which is closed under vector addition and taking additive inverses which is not a subspace of R^2? R, in this question, is the real numbers. Thanks!
  14. R

    Checking if Rationals are Closed Under Addition and Scalar Multiplication

    Homework Statement Check to see if the (vector space) set of rational numbers is closed under addition and scalar multiplication Homework Equations The book says this holds for addition but fails for scalar multiplication. The Attempt at a Solution Im a little confused. You can...
  15. S

    Non-Standard Addition & Multiplication in R^2: Zero Vector

    rather than use the standard definitons of addition and scalar multiplication in R^2, suppose these two operations are defined as follows. (x1,y1)+(x2,y2)=(x1,0) c(x,y)=(cx,y) what would the zero vector be? can it be (0,-y1)? why or why not? I think it should fail this axiom u+0=u.
  16. D

    How Do You Solve for Variables in Vector Addition Equations?

    Homework Statement Given: \vec{A}=(6.0\hat{i} - 8.0\hat{j}) \vec{B}=(-8.0\hat{i} + 3.0\hat{j}) \vec{C}=(26.0\hat{i} + 19.0\hat{j}) If aA+bB+C=0, what are the magnitudes of a and b? Homework Equations The Attempt at a Solution a(6.0\hat{i} - 8.0\hat{j}) + b(-8.0\hat{i} +...
  17. A

    Vector Addition for Displacement: Finding Magnitude and Direction

    Homework Statement I am not sure where I am having trouble here. A car id driven 125km west and then 95km southwest. What is the mag and direction of displacement?Homework Equations Triangle method says that if I draw the vectors from tip to tail, the displacement vector is the vector that...
  18. ~christina~

    Understanding Vector Addition Using Unit Vectors and Magnitude and Direction

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  19. K

    Calculating 2A + 3(B+C): Vector Addition

    vector A= (2,-1,1) vec. B = ( 3, 0, 5) vec. C = (1,4,-2) what is 2A + 3(B+C) this is what i did: 2A = 2(2,-1,1) = (4,-2, 2) (B+C) = (4,4,3) x 3 = (12,12, 9) 2A + 3(B+C) = (16,10,11) is this the correct way to think and do this problem?
  20. B

    Vector Addition and Magnitude: Finding the Magnitude of a Vector Resultant

    If B is added to C = 2.5 i + 3.5 j, the result is a vector in the positive direction of the y axis, with a magnitude equal to that of C. What is the magnitude of B? I have tried 0, which seems to make sense to me, but it is wrong. and I don't know if it means b+c=2.5i+3.5j or if b=? and...
  21. S

    The addition of three simple harmonic motion

    [SOLVED] the addition of three simple harmonic motion Homework Statement A particle is simultaneously subjected to three simple harmonic motions, all of the same frequency and in the x direction. If the amplitudes are 0.25, 0.20 and 0.15 mm, respectively, and the phase difference between...
  22. T

    How Do You Calculate the Final Displacement Angle of a Roller Coaster?

    Homework Statement A roller coaster moves 200 ft horizontally and then rises 135 ft at an angle of 30* above the horizontal. It then travels 135 ft at an angel of 40* downward. What is its displacement from its starting point? Homework Equations Standard trig, I guess. The Attempt...
  23. P

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  24. E

    Einstein velocity addition rule

    Car 1 is traveling at 3/4c. Car 2 in behind Car 1 is traveling at 1/2c. Car2 fires a bullet that travels at 1/3 c. OK. In order to determine whether the bullet reaches Car 1 or not we need to use Einsteins velocity addition rule and determine whether the relative velocity of the bullet...
  25. P

    Angle Addition Formula for three angles?

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  26. S

    Decreasing grain size with element addition

    Hello, I have found that in some processing cases that additional elements are added to metals which result in increased potential for smaller grain size. Does anyone know why this is so? Am I signiificantly misunderstanding the issue? Thanks, -scott
  27. Holocene

    Addition of velocities: What actually happens?

    Say a spacecraft is traveling just a few miles per hour under the speed of light. Now say a person on board this spacecraft starts running towards the front of the ship. If the craft is already moving just under light speed, and the person inside is running at a speed of say 8MPH, isn't the...
  28. M

    Subspace Addition: Understanding the Union of A and B

    I just wanted to know if subspace A + subspace B is the same as the "union of A and B".
  29. M

    Does Mixing 2-Propanone and 2-Ethylhexanol Create C11 H24 O2?

    If I add the chemicals C3 H6 O (2-propanone) and C8 H18 O (2-ethylhexanol) will I wind up with the chemical formula C11 H24 O2 ? thanks
  30. M

    Vector addition and displacement

    Homework Statement During a rodeo, a clown runs 8.0 m north, turns 55 degrees north of east, and runs 3.5 m. Then, after waiting for the bull to come near, the clown turns due east and runs 5.0 m to exit the arena. What is the clown's total displacement? The Attempt at a Solution I drew a...
  31. M

    What does the 'sum' in vector addition refer to?

    I have a question on 'vector addition'. I know that resultant is the sum of two or more vectors. But this sum doesn't mean the sum of magnitudes of two or more vectors, right? So what does that 'sum' refer to? Combined effect? Hope you can answer my question, thanks.
  32. E

    Vector addition (?) with acceleration and velocities given in vectors

    Homework Statement Particle is at (9, 4) on coordinate plane. Initial velocity: 5.5 x - 7 y Acceleration: 1 x + 8.5 y Time: 1.5s 1: What is the x-component of velocity after that 1.5s? 2: Y-component? 3: Magnitude from origin of graph? Homework Equations sqrt(x^2 + y^2) for magnitude...
  33. E

    Vector addition - Finding V2 when V1 and V1+V2 are given

    Homework Statement Particle has two displacements. 1 - 11m, 89 degrees 2 - ? 1+2 - 8.6m, 129 degrees So: 1 = (11, 89°) 2 = ? 1+2 = (8.6, 129°) Homework Equations X-component = M x cos(Θ) Y-component = M x sin(Θ) Total magnitude = sqrt((total x-component)² + (total y-component)²) Total...
  34. T

    Addition of alkali before extraction

    This is just a general question that I hope someone can answer. Why do we add alkali before extraction rather than afterwards? This is in the experiment I recently did, which was the preparation of p-Toluidine? This was my main thought... that it helps to saturate the solution so that when...
  35. J

    Can an Equation Account for Heat Exchange Between Two Liquids in a Solution?

    Homework Statement hi, i have a lab for thermal physics in which the cooling of coffee is monitored. The variable change is the amount of milk that is added once the coffee is brewed. My question is whether there is an equation that relates heat exchange between 2 liquids in a solution? (an...
  36. Loren Booda

    ?, exponentiation, multiplication, addition, ?

    What simple operations, if any, precede or succeed the series ". . . exponentiation, multiplication, addition. . ."?
  37. B

    Special Relativity - addition of velocities

    Homework Statement A K-meson at rest decays into two pi-mesons, and each pi meson has a speed of 0.85c. If a K-meson traveling at a speed of 0.9c decays, what is the greatest speed the one of the pi-mesons can have? Homework Equations u\prime = \frac{u-v}{1-\frac{v}{c^2}u} The...
  38. U

    Proving Addition & Multiplication in Zn Are Well-Defined

    Homework Statement So I have to prove that addition and multiplication in Zn are well defined. Homework Equations The Attempt at a Solution I have no idea where to start.
  39. M

    Trigometric addition of complex numbers

    Hello I got some funny idears don't know if they are true, but I will share them with you. Homework Statement I would like to prove these formula (1)sin(z_1 + z_2) = sin(z_1) \cdot cos(z_2) + sin(z_2) \cdot cos(z_1) (2)cos(z_1 + z_2) = sin(z_1) \cdot sin(z_2) - cos(z_2) \cdot...
  40. R

    Can \cos(\theta-\lambda) Be Used to Show Sin C in Addition Formula/Sine Rule?

    http://img117.imageshack.us/img117/1482/graph015tt6.png I know an alternative way of showing Sin C is cos 'theta'. Thanks
  41. R

    How to Calculate Tension for Fundamental Frequency at 60hz

    Fundamental frequencies Using the formula Would it be correct to say that to determine the necessary tension for the fundamental frequency at 60hz, substitute into the equation f, m, and L, then solve for T?
  42. Useful nucleus

    Addition theorem for gegenbauer poly

    Please , can you help in finding the addition theorem of gegenbauer polynomials on the web? many thanks
  43. R

    Does cos + sin always equal 0?

    does cos + sin = 0?
  44. B

    Velocity Addition in MG and Light Scenarios

    Consider a scenario which involves a stationary machine gun (MG) and a moving target T. MG emits successive bullets at constant time intervals t(e) which hit the moving target at constant time intervals t(r). The bullets move with velocity U and the target with velocity V. The first bullet...
  45. B

    Relativistic addition of velocities without lorentz transformations

    I have studied N.David Mermin "Relativistic addition of velocities directly from the constancy of the velocity of light," Am.J.Phys. 51 1130 1983 and others with the same subject quoted by the Author. He describes a derivation of the addition law that dispenses not only with the LT but also...
  46. R

    Addition of Vectors by means of Components

    Homework Statement A football player runs the pattern given in the drawing by the three displacement vectors A, B, and C. The magnitudes of these vectors are A = 5 m, B = 14.0 m, and C = 23.0 m. Using the component method, find the magnitude and direction of the resultant vector A + B + C...
  47. A

    Angular Velocity after addition of mass?

    Homework Statement A merry-go-round is a common piece of playground equipment. A 4 m diameter merry-go-round with a mass of 220 kg is spinning at 16 rpm. John runs tangent to the merry-go-round at 5.0 m/s, in the same direction that it is turning, and jumps onto the outer edge. John's mass is...
  48. D

    Addition Theorem Proof - Foundations of Analysis by Edmund Landau

    Hi! I'm currently reading Edmund Landau's book Foundation of Analysis. I kinda got stuck right at the beggining where the author tries to develop the natural numbers theory from axioms. Theorem 4 states the following: (where x' denotes the successor of x) The following proof is quite hard...
  49. K

    Addition formulae - Trig help requested

    addition formulae - Trig help requested! I have a problem with this with regard to Sin 120 or Cos 120. Eg sin 165 sin (120 +45) sin120.cos45-cos120.sin45 How do I deal with sin 120 or cos 120? I know that cos 45 is 1/square root 2 and so is sin 45. But in the above problem, the...
  50. R

    Arccos(x+y)=? addition theorems for inverse trigonometric functions?

    Hi. Are there any addition theorems for inverse trigonometric functions? Like arccos(x+y)=? or something... I was wondering about this when I tried to find the derivative of f(x)=arccos(x) by setting f'(x)=\frac{\arccos(x+\Delta x)-\arccos(x)}{\Delta x}
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