How is the principle of addition used, and what is addition ?

In connection with the reality of life, the use of object teaching.

The act of merging two numbers (or numbers) into a single number is called addition. The addition isFour arithmeticOne of the symbols that express addition is the plus sign "+", and when the addition is carried out, the items are connected with a plus sign.

Addition is one of the easiest numerical tasks. The most basic addition: 1 + 1, can be calculated by a five-month-old baby, or even by other animal species. In primary education, students are taught in the decimal system.

The system carries out superposition calculations of numbers, starting with a single digit and gradually solving more difficult number calculations.

The meaning of the other four operations:

The meaning of subtraction: It is known that the sum of two additions and one of them is called subtraction. In subtraction, the sum of two known additions is called the subtracted number, one of the additions is called the subtraction, and the other addition is called the difference.

The meaning of multiplication: multiplying a number by an integer is a simple operation to find the sum of several identical additions, or to find how many multiples of this number are.

The meaning of division: the operation of knowing the product of two factors and one of them is called division. In division, the product of two known factors is called the dividend.

One of the factors is called the divisor, and the other is called the quotient.

Principle of addition. The principle of addition is the principle of classification and counting, which is often used in permutations and combinations, specifically refers to: doing a thing, completing it has n types of methods, the first type of methods have M1 methods, and the second type of town shelter hall has M2 methods ,......The nth type of method has mn hidden method, so there are m1+m2+...... to complete this thingmn methods.

For example, from Wuhan to Shanghai, there are 3 ways to take a train, a plane, and a ship to choose from, and a train, plane, and ship have K1, K2, and K3 departures respectively, so there are K1+K2+K3 ways to reach from Wuhan to Shanghai.

Addition principle: The principle of addition is often used in permutations and combinations. For example, if he wants to accomplish n things, there are m1 methods for the first category and m2 methods for the second category.

And so on, to get the nth kind, there are mn methods. Then there is a total of m1+m, 2+m3+ to mn.

For example, from Beijing to Shanghai, you can choose between trains, planes, and ships. Trains, planes, and ships, each of which has a 1A2A3 departure. Then there are a total of A1 + A2 + A3 methods to reach Shanghai.

For example: <>

How many ways are there to get from A to C?

The answer is: there are 3 ways to go directly from A to C in the first class, and there are 2x3=6 ways to go from A to C through B in the second category, so there are 3+6=9 different ways to go from A to C.

Addition principle: to do a buried chain bend and shoot Sun thing, there are n types of ways to complete it, there are M1 different methods in the first type of method of greeting shirts, and there are M2 different methods in the second type of method ,......There are m(n) different methods in the nth type of approach, so there are m1+m2+...... to accomplish this thingm(n) different methods.

For example, there are 3 ways to get from Beijing to Shanghai directly, 1: train K1 2: plane K2 3: ship K3, then the method from Beijing to Shanghai is n=k1+k2+k3

Addition and Multiplication Principle Concept:

There are often such situations in life: when doing a thing, there are several different types of methods, and when doing it specifically, as long as one of the methods in one of these categories can be completed, and these types of methods do not affect each other.

There is also such a situation: when Yan quietly does a thing, it takes several steps to complete, and when completing each step, there are several different ways to know how many ways to complete this thing, you have to use the principle of multiplication to solve it.

When applying the principle of addition and multiplication, it is necessary to pay attention to the following points.

1. The principle of addition is to divide the methods of completing one thing into several categories, and any one of the methods in each category can complete the task, so the number of different methods to complete the task is equal to the sum of the number of various methods.

2. The principle of multiplication is to complete a thing in several steps, and these steps are indispensable, so the number of different methods to complete the task is equal to the product of the number of methods in each step.

3. In many topics, the principle of addition and the principle of multiplication do not appear separately, which requires us to be able to skillfully use these two principles, comprehensively analyze, and correctly classify and step by step.

The principle of addition and the principle of multiplication are the two most commonly used and most basic principles in counting research The so-called counting is to count, counting the specific number of some objects Of course, when the situation is simple, you can count one by one If the number is large, it is not feasible to count one by one, using the addition principle and the multiplication principle, it can help us count

Principle of addition. There are n ways to complete a job, there are m1 ways to complete it in the first way, and there are m2 ways to complete it in the second way,..., there are mn ways to complete the nth way, then, there are a total of ways to complete this work.

m1+m2+…+mn

For example, there are three modes of transportation from city A to city B: train, car, and plane There are 2 departures per day by train; There are 3 daily departures by car; There is only one flight per day by plane, so there are 2+3+1=6 ways to get from city A to city B

Principles of multiplication. There are n steps to complete a job: there are m1 methods to complete the first step, and m2 methods to complete the second step,...There are mn ways to complete the nth step, so there are common ways to complete this work.

m1·m2·…·mn

For example, if you have to pass through City C in the middle of City A to City B, there are 3 routes from City A to City C (set as A, B, C), and from City C to City B there are 2 routes (set to M, T), then, there are 3 2=6 routes from City A to City B, and they are:

am，at，bm，bt，cm，ct．

The principles of addition and multiplication are the principles of permutation and combination.

1. Addition principle: to complete one thing, there are n types of methods, the first type of methods have M1 different methods, the second type of methods have M2 different methods, the third type of methods have M3 different methods, and the fourth type of methods have M4 different methods,......There are different methods of mn (n is the subscript) in the nth type of method, and there are n=m1+m2+m3+m4+...... to accomplish thismn (n is the subscript) different methods. In today's textbooks, it's called the "Principle of Differential Counting".

2. Multiplication principle: to complete a thing, it needs to be divided into n steps, the first step method has M1 different methods, the second step method has M2 different methods, the third step method has M3 different methods, and the fourth step method has M4 different methods,......There are different methods of mn (n is the subscript) in the nth step method, so there are n=m1+m2+m3+m4+...... to complete this thingmn (n is the subscript) different methods. Today's textbooks call it the "Step-by-Step Counting Principle".

There are n ways to do a thing and complete it, the first way has m1 methods, and the second type has m2 methods,......There are m(n) methods in the nth category, so there are m1+m2+...... to accomplish thismn methods.

For example, there are 3 modes of transportation from Wuhan to Shanghai: train, plane and ship, and train, plane and ship have K1, K2 and K3 flights respectively, so there are n=k1+k2+k3 ways to reach from Wuhan to Shanghai.

No matter how big the number is added, its most basic principle is the addition principle within 20, and the quick calculation formula for carry addition within 20 is: a few plus nine into ten minus.

First, a few plus eight into ten minus.

Second, a few plus seven into ten minus.

Three, a few plus six into ten minus four. Since addition has a commutative law, we only need to remember these few sentences, in addition within 100, first observe the two digits, find out the larger number between them, and calculate according to the formula to quickly calculate the answer.

Example 126+39

We observed that the two numbers are 6 and 9, 6 + 9 is greater than 10, it needs to be carried forward, and the larger one is 9, so the ten digits that apply "a few plus nine into ten minus one" to get the answer are 2 + 3 + 1 = 6, and the single digit is to give 6 minus 1 equals 5, so the answer is 65

Addition is the addition of several numbers, which can also be said to be a method of adding another number to get the final number.

The operation of combining two numbers or quantities of the same kind together is called addition