两个数字的和是 40,它们的差是 10。找出这些数字。
算术是数学的一个分支,它处理古代的数字、数制及其运算。该术语最初源自希腊语“arithmos”,简单的意思是数字。最好得到一个确定的单一值。传统的算术运算方法是加法、差法、乘法和除法的组成部分。几个世纪以来,这些行动都是为了人类社会和经济发展而进行的。
算术史
- 17世纪的印度数学家布拉马笈多是“算术之父”。
- 卡尔·弗里德里希·高斯在 1801 年提供了数论的基本原理。
Arithmetic is the elementary branch of mathematics that specifically deals with the study of numbers and properties of traditional operations like addition, subtraction, multiplication, and division.
除了传统的加减乘除运算外,还包括百分比、对数、取幂、平方根等高级计算方法。
算术中的基本运算类型
下面讨论算术的四种基本运算-
加法 (+)
加法或也称为求和是将两个或多个值或数字组合成单个值的操作。将 n 个值相加的过程称为求和。
0 被认为是加法的单位元素,因为将 0 加到任何值都会得到相同的结果。例如,如果我们将 0 添加到 5,结果将与 5 相同。
0 + 3 = 3
并且,将相同数的相反值相加称为逆元。逆元相加的结果是一个为 0 的单位元。例如,如果我们将 2 与它的反值 -5 相加,那么结果将是
5 + (-5) = 0
减法 (-)
算术运算确定两个值之间的差值(即被减数减去减数)是减法。在被减数大于减数的情况下,差值是正数。它是加法的逆运算。
9 – 3 = 6
同时,如果减数大于被减数,则它们之间的差异将为负数。
3 – 9 = -6
乘法 (×)
乘法是将被乘数和乘数这两个值结合起来得到一个乘积的运算。乘法运算中涉及的两个值称为被乘数和乘数。
假设 x 和 y 的两个值的乘积以 xy 或 x×y 形式表示。
除法 (÷)
除法是计算两个数字的商的操作。它是乘法的逆。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。
10/5 = 2
两个数字的和是 40,它们的差是 10。找出数字
回答:
Let the two numbers be x and y.
According to the question,
x + y = 40……(i)
x – y = 10……..(ii)
Now, to know the value of one of the variables we need to solve one of the equations given above and substitute the value in the other equation.
Now, from equation (i) we can obtain the value of x by isolating it.
=>x = 40 – y
Then, substituting the value of x in equation (ii)
=>40 – y – y = 10
=>40 – 2y = 10
=>y = 30/2
=>y = 15
Substituting the value of y = 15 in x = 40 – y
=>x = 40 – 15 = 25
Hence, the two variables are x = 25 and y = 15.
类似问题
问题1:两个数之和为8,差为4。求变量。
回答:
Let the two numbers be x and y.
According to the question,
x + y = 8…….(i)
x – y = 4……(ii)
Now, to know the value of one of the variables we need to solve one of the equations given above and substitute the value in the other equation.
Now, from equation (i) we can obtain the value of x by isolating it.
=>x = 8 – y
Then, substituting the value of x in equation (ii)
=>8 – y – y = 4
=>8 – 2y = 4
=>-2y = -4
=>y = -4/-2 = 2
Substituting the value of y = 2 in x = 8 – y
=>x = 8 – 2 = 6
Hence, the two variables are x = 6 and y = 2.
问题 2:如果两个数之和是 95,其中一个比另一个多 15,那么这些数是多少?
回答:
Let the two numbers be x and x + 15
Now, according to the question,
=>x + x + 15 = 95
=>2x = 95 – 15
=>2x = 80
x = 80/2 = 40
If the first number is x = 40. Then, the value of the second number is given by
=>x + 15 = 40 + 15 = 55
Therefore, the two numbers are 40 and 55.
问题 3:两个数之和为 25,差为 13。求数。
回答:
Let the two numbers be x and y.
According to the question,
x + y = 25……(i)
x – y = 13……(ii)
Now, to know the value of one of the variables we need to solve one of the equations given above and substitute the value in the other equation.
Now, from equation (i) we can obtain the value of x by isolating it.
=>x = 25 – y
Then, substituting the value of x in equation (ii)
=>25 – y – y = 13
=>25 – 2y = 13
=>2y = 25 – 13
=>2y = 12
=>y = 38/2 = 6
Substituting the value of y = 6 in x = 25 – y
=>x = 25 – 6 = 19
Hence, the two variables are x = 19 and y = 6.
问题 4:如果两个非零数的和是 8,它们的差是 7。求数的值。
回答:
Let the two numbers be x and y.
According to the question,
x + y = 25……(i)
x – y = 7……(ii)
Now, to know the value of one of the variables we need to solve one of the equations given above and substitute the value in the other equation.
Now, from equation (i) we can obtain the value of x by isolating it.
=>x = 25 – y
Then, substituting the value of x in equation (ii)
=>25 – y – y = 7
=>25 – 2y = 7
=>2y = 25 – 7
=>2y = 18
=>y = 18/2 = 9
Substituting the value of y = 9 in x = 25 – y
=>x = 25 – 9 = 16
Hence, the two variables are x = 16 and y = 9.