About the calculation method of subtraction of rational numbers

Want a formula? Or whatever.

"The law of subtraction of rational numbers: subtracting a number is equal to adding the opposite of the number.

The addition of the same sign remains unchanged, and the addition of different signs changes or decreases. If you want to ask how to determine the symbol, the absolute value is large.

When performing the addition operation of rational numbers, it is generally adopted: it is the first addition (offset) of the opposite number of each other; the same number is added first; the same denominator is added first; Those who can make up integers are added first; The fractions of different denominators are added together, and then calculated; If several numbers can be added to get the whole defibrillation number, they can be added first.

Subtracting a number is equal to adding the opposite of that number. The subtraction of rational numbers can be converted to addition. It is summarized as "two changes and one unchanged", namely:

Subtraction becomes addition, and the subtraction becomes its opposite, and the subtraction does not change the orange. It can be expressed as: a-b=a+(ab).

Addition and subtraction of rational numbers:

1) Add two numbers with the same sign, take the same symbol as the additive, and add the absolute value.

2) The sum of the two numbers with different signs, if the absolute values are equal, the sum of the two numbers of the opposite numbers is 0; If the absolute values are not equal, take the sign of the addition with the greater absolute value, and subtract the smaller absolute value from the larger absolute value.

3) Add two numbers that are opposite to each other to get 0.

4) Add a number to 0 and still get this number.

5) Two numbers that are inverse numbers of each other can be added first.

6) Numbers with the same sign can be added first.

7) Numbers with the same denominator can be added first.

8) If several numbers can be added to get an integer, they can be added first.

Rational numbers are a class of numbers in mathematics that include integers, fractions, etc. When you need to calculate the difference of a rational number, you need to use the subtraction of a rational number. What is the arithmetic of subtraction of rational numbers?

In this article, we will delve into the arithmetic principles of rational number subtraction and explain how to do rational number subtraction operations.

The concept of subtraction of rational numbers.

Rational number subtraction is the subtraction of two rational numbers to get their difference. In rational number subtraction, we need to convert the fractions in two rational numbers to the same denominator, and then subtract them. If there are integer parts in the rational numbers, they also need to be merged into the final result.

For example, to solve the value of 3 4-1 3, we need to turn 3 4 into 6 12 and 1 3 into 4 12, so that we get 6 12-4 12 = 2 12, i.e. 1 6.

The arithmetic principle of the subtraction of rational numbers.

The arithmetic principle of subtraction of rational numbers is based on the rules of addition. We can convert the subtraction of rational numbers into addition, i.e., the inverse of the subtraction plus the subtraction. For example, 3-2 can be molded to convert to 3+(-2).

Therefore, the arithmetic principle of the subtraction of rational numbers can be expressed as: a-b is equal to a+(-b).

The operation steps of the subtraction of rational numbers.

The steps to perform the subtraction of rational numbers are as follows:

Convert the fractions of two rational numbers to the same denominator.

Subtract the integer part from the fraction part.

Add the difference between the integer part and the fraction part to get the final result.

For example, to solve the value of 4 5-1 2, we need to turn 4 5 into 8 10 and 1 2 into 5 10. Then, subtract each to get 3 10, which is simplified. If there are integer parts in the rational numbers, they also need to be merged into the final result.

For example, to solve the value of 5-2 3, we need to convert 5 to 15 3, and then subtract 15 3 from 2 3 to get 13 3, i.e. 4 remainder 1, so the final result is 4 1 3.

Application scenarios of rational number subtraction.

There are many applications of rational number subtraction in real life. For example, in financial management, if you need to calculate the difference between expenses and income, you need to use the rational number subtraction method. In physics, the difference between two vectors needs to be calculated, and the subtraction of rational numbers is also required.

In addition, the subtraction of rational numbers is also applied in Euclidean geometry, such as calculating the distance between two points.

Conclusion Rational number subtraction is a basic operation in mathematics, and its arithmetic principle is based on the operation rules of addition. The operation steps of rational number subtraction include converting the fractions of two rational numbers to the same denominator, subtracting the integer part and the fraction part separately, and simply adding the difference between the integer part and the fraction part to obtain the final result. There are many application scenarios in real life, which can help us effectively manage financial resources such as renting trousers, calculating physical quantities, measuring distances, etc.

Negative negative is positive, for example: negative number minus negative number: -3-(-5) = -3 + 5 = 5-3 = 2 positive number minus negative number: 5-(-3) = 5 + 3 = 8

Negative minus positive: -3-5 = -(3+5) = -8 (negative sign raised).

Negative reduction becomes positive addition.

Negative minus negative: -8 - (-3) = -8 + 3 = -5 positive minus negative: 8 - (-3) = 8 + 3 = 11

Negative minus positive: -8-3=-11

Negative minus negative: -5 - (-6) = 1

The minus the negative number of an integer is equivalent to the addition of a positive integer: -5-(-6)=1;5-（-6）=11

Negative minus positive: -6-5=-11

1.The law of subtraction of rational numbers.

Subtracting a number is equal to adding the opposite of the number. As you can see, subtraction is the inverse of addition. That is, the subtraction of rational numbers is actually converted to addition to calculate.

In the process of transformation, two symbols need to be changed at the same time: one is the operation symbol " " becomes "+" and the other is the symbol that changes the nature of the subtraction.

2.General steps of subtraction operations on rational numbers:

1) Change the minus sign to the plus sign; (2) use the opposite of the minus as an additive; (3) Use the law of rational number addition to find the result.

According to the upstairs, just to name a few examples:

10-(-5)+(6)=10+5-6=9Note: 35-36 can be seen as —(36-35)=-1, and in the same way, for ease of operation, the associative law of addition can be used: 10+25+3+[-36+9)]=38+(-45)=-(45-38)=-7

In full accordance with the addition and subtraction of the mixed operation, pay attention to the change of the symbol can be in: subtract a number is equal to add his opposite number, negative negative to positive, that is, 10-(-5) = 10 + 5 = 15 positive and negative look at the size: if the positive number |Negative number|, take the right; If it is positive, |Negative number|, take the negative.

i.e. 15 |-6|, take the right; or 5 |-6|, take the minus, i.e., 10-1=9

The subtraction operation of rational numbers mainly pays attention to symbols, and when you use it too much, you will naturally adapt to it.

Four operations, there is nothing to say.

15+（-22）=-(22-15)=-7

1. The law of addition of rational numbers.

1.Add two numbers of the same sign, take the same symbol, and add the absolute value to 2Add two numbers with unequal absolute values, take the sign of the addition with the larger absolute value, and subtract the smaller absolute value from the larger absolute value. Two numbers that are opposite to each other are added to give 0

3.Add a number to 0 and still get this number.

The law of subtraction of rational numbers.

Subtracting a number is equal to adding the opposite of the number.