什么是算术？定义、基本操作、示例

算术很可能在当时具有最长的历史。它是一种计算方法，自古以来就被用于常规计算，例如测量、标记和其他日常计算，以获得精确的结果。这个名字来源于希腊语“arithmos”，意思是“数字”。

Arithmetic is the fundamental area of mathematics that studies numbers and the characteristics of conventional operations such as addition, subtraction, multiplication, and division.

除了标准的加法、减法、乘法和除法运算之外，算术还包括复杂的计算，例如百分比、对数、取幂和平方根等。算术是处理数字及其常规运算的数学领域。

算术的基本运算

算术有四个基本操作，用于根据语句执行计算：

1. 添加
2. 减法
3. 乘法
4. 分配

加法 (+)

The simple definition for addition will be that it is an operation to combine two or more values or numbers into a single value. The process of adding n numbers of value is called summation.

• 0 被称为加法的单位元素，因为当将 0 加到任何值上时，它会给出相同的结果。例如，如果我们将 0 添加到 7，结果将与 7 相同。

0 + 7= 7

• 并且，逆元素包括相反值的相加。添加逆元素的结果将是一个为 0 的单位元素。例如，如果我们将 4 与它的相反值 -4 相加，那么结果将是：

4 + (-4) = 0

减法 (-)

Subtraction is the arithmetic operation that computes the difference between two values (i.e. minuend minus the subtrahend). 

• 在被减数大于减数的情况下，差为正。它是加法的逆运算。

4 – 2 = 2

• 同时，如果减数大于被减数，则它们之间的差异将为负数。

2 – 4 = -2

乘法 (×)

The two values involved in the operation of multiplication are known as multiplicand and multiplier. It combines two values that is multiplicand and multiplier to give a single product.

• 假定为 p 和 q 的两个值的乘积以 pq 或 p × q 形式表示。

5 × 6 = 30

除法 (÷)

The division is the operation that computes the quotient of two numbers. It is the inverse of multiplication. 

• 其中涉及的两个值称为除数的除数，如果商大于 1，如果除数大于除数，则结果将为正数。

12 ÷ 3 = 4

什么是简单算术？

Arithmetic most likely has the longest history at the time. It is a calculating approach that has been used since ancient times for routine calculations such as measurements, labelling, and other day-to-day computations to achieve precise results. The name derives from the Greek word “arithmos,” which meaning “numbers.”

Arithmetic is the fundamental area of mathematics that studies numbers and the characteristics of conventional operations such as addition, subtraction, multiplication, and division.

Aside from the standard operations of addition, subtraction, multiplication, and division, arithmetic also includes sophisticated computations such as percentage, logarithm, exponentiation, and square roots, among others. Arithmetic is a field of mathematics that deals with numbers and their conventional operations.

简单算术示例问题

问题1：两个数之和是30，它们的差是20。找出这些数。

解决方案：

Let the numbers be a and b. Now, as per the situation,

a + b = 30                                                                                                                                                                                     ………(1)

and a – b = 20                                                                                                                                                                              ………(2)

We can write, a = 30 – b, from equation (1),

no put the value of a in equation (2), we get,

30 – b – b = 20

30 – 2b = 20

2b = 30 – 20 = 10

b = 10/2 = 5

b = 5

And 

a = 30 – b

   = 30 – 5

a = 25

Therefore, the two numbers are 25 and 5.

问题 2：解决 45 + 2(36 ÷ 3) - 9

解决方案：

45 + 2(36 ÷ 3) – 9

⇒ 45 + 2(12) – 9

⇒ 45 + 24 – 9

⇒ 69 – 9 = 60

问题 3：在给定的方程 3a – 18 = 3 中找到 a 的值。

解决方案：

According to the equation,

3a – 18 = 3 

       3a = 18 + 3

       3a = 21

        a = 7

Therefore, the value of a is 7.

问题 4：求解 a 的值：

3a – 2(15 ÷ 3) – 5 × 2 = 22

解决方案：

3a – 2(15 ÷ 3) – 5 x 2 = 22

3a – 2(5) – 10 = 22

  3a – 10 – 10 = 22

         3a – 20 = 22

                3a = 22 + 20

                3a = 42

                 a = 14

Therefore the value of a is 14.