Who can teach the addition and subtraction of rational numbers, the addition and subtraction of rati

Rational numbers are numbers that can be expressed as fractions, in fact, addition and subtraction are similar to what I have learned before, and there are only a few cases.

Think of it this way:

Decide on the symbol first.

Addition: positive number + positive number = positive number.

Negative number + negative number = negative number.

The absolute value of a positive number is greater than the absolute value of a negative number, then:

Positive number + negative number = positive number.

The absolute value of a positive number is less than the absolute value of a negative number, then:

Positive number + negative number = negative number.

Subtraction: Positive (large) - positive (small) = positive.

Positive (small) - positive (large) = negative.

Positive number + negative number = positive number.

Negative - Positive = Negative.

Negative (large absolute value) - Negative number (small absolute value) = negative number.

Negative (small absolute value) - Negative number (large absolute value) = positive number.

Note: The absolute value is to replace the sign in front of this number with a positive sign.

Example: The absolute value of -1 is 1

The absolute value of 123 is 123

Once the symbol is determined, the large absolute value is subtracted from the small absolute value (before and after), and the symbol is added.

You can be very proficient as long as you practice more, and I believe you will be able to do it =I hope my answer can help you ==

Hello landlord: Mine. I'm going to be in the second year of junior high school, can I teach you? As the saying goes: learn from the past. I'll just brush up on my homework! Before you add me, be sure to say who you are.

Content from user: soybean sprouts.

Addition and subtraction of rational numbers.

Key points of knowledge: 1. The law of addition of rational numbers:

Add two numbers of the same sign, take the same symbol, and add the absolute values.

If the two numbers with unequal absolute values are added, the additive sign with the larger absolute value is taken, and the smaller absolute value is subtracted from the larger absolute value.

Add a number to 0 and still get this number.

1. The operation steps of rational number addition:

The law is the basis of the operation, according to the operation rule of the addition of rational numbers, the operation steps of addition can be obtained:

Determine the symbol of the sum;

The absolute value of the sum, i.e., the sum or difference that determines the absolute value of two additive numbers.

2. The arithmetic law of the addition of rational numbers:

The two additions are added together, the position of the added number is exchanged, and the sum is unchanged. (Commutative law of addition) Add three numbers, add the first two numbers first, or add the last two numbers first, and the sum does not change.

Additive associative law).

3. Calculation skills of rational number addition:

When there are both fractions and decimals, they should be reduced to a uniform form first.

Fractions can be divided into two parts: integers and fractions.

When adding multiple additions, if there are two numbers that are opposite to each other, you can combine them to get zero first.

If there are numbers that can be rounded, that is, when adding to get an integer, you can combine and add them first.

If there are fractions with the same denominator or scores with easy access scores, they should be combined first.

Numbers with the same sign can be combined first.

4. The law of subtraction of rational numbers:

Subtracting a number is equal to adding the opposite of that number. 5. The operation steps of the subtraction of rational numbers:

Change the minus sign to the plus sign (change the operator symbol).

Change the subtraction to its opposite (change the property symbol).

Seek 11Of the following calculations, the correct one is ()14If |a|=2，|b|=1, then the value of a b is ()20 so that Equation|－5－x|=|－5|＋|x|The x that holds is ().

Conceptual analysis of "Addition and Subtraction of Rational Numbers".

1) Rational number addition rule:

That is, add two numbers with the same sign, take the same symbol, and add the absolute value. If the two numbers with unequal absolute values are added, the additive sign with the larger absolute value is taken, and the smaller absolute value is subtracted from the larger absolute value. Two numbers that are opposite to each other are added to give 0.

Add a number to 0 and still get this number.

2) The law of subtraction of rational numbers:

That is, subtracting a number is equal to adding the opposite of that number. The subtraction of rational numbers can be converted to addition.

Idea analysis] as long as you keep the various algorithms in mind.

And you can use it skillfully.

Do more exercises.

Problem Solving Process] 1.When the addition and subtraction of rational numbers is carried out, the subtraction can be converted into addition according to the subtraction law of rational numbers, which unifies the addition and subtraction of rational numbers into a single addition operation. At this point, it becomes the sum of several positive and negative numbers.

2.When converting mixed operations into addition operations, write algebraic sum, pay attention to the two different readings of algebra and form.

3.The form of the sum omitted from parentheses can be seen as an addition operation of rational numbers. Therefore, the addition law can be used to simplify the calculation, and attention should be paid to the rationality of the operation.

Positive + Positive = Positive Positive (Large) + Negative (Small) = Positive Positive (Small) + Negative (Large) = Negative Negative + Negative = Negative.

Gone! bye!

Rational numbers contain positive numbers, negative numbers, and zeros. For example, -7 is a negative rational number, and -6 is a negative rational number.

Subtract the same sign to get the negative, and the different sign to subtract the negative.

is minus 6, so it is positive, i.e. -7-(-6)=-7+6=-1. If it is represented on the number line, the computer really means that it is not easy to draw.

Addition of rational numbers:

Add the same sign, take the same symbol, and add the absolute value.

Add or subtract the two numbers with unequal absolute values, take the sign 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.

Add a number to 0 and still get this number.

Rational number subtraction:

The law of subtraction of rational numbers: subtracting a number is equal to adding the opposite of the number. Among them: two variations: subtraction becomes addition, and subtraction becomes its opposite. One constant: the subtracted number does not change.

1. On the addition of rational numbers.

1. Rule: Add two numbers with the same sign, take the same symbol, and add the absolute value.

2. When the two numbers of different numbers are added, the sum is zero when the absolute value is equal, and when the absolute value is not equal, take the sign of the addition with the larger absolute value, and subtract the smaller absolute value with the larger absolute value.

3. If a number is added to zero, this number is still obtained.

2. The arithmetic law of the addition of rational numbers.

1. Associative law: two numbers are added together, and the position of the added number is exchanged, and its sum is unchanged.

2. Commutative law: add three numbers, add the first two numbers first, or add the last two numbers first, and the sum remains unchanged.

1 The following statement is true (

ba The sum of two rational numbers must be greater than each of them.

b When two non-zero rational numbers are added, the simple beam and the stoppable nuclear transport capacity are equal to zero.

c The sum of two rational numbers is negative, and both rational numbers are negative.

d Add two negative numbers to add the absolute values.

2 Add two numbers, and if the sum is 0, then the two numbers (ca are both positive.

b Also negative.

c are inverses of each other.

d One is 0 and one is negative.

a．a＜0b．b＋c＜0

c．a＋c＜0

d c4 a number is added , and the sum is 0

6, then this number is (c

a．－b．－

c 3d 5 The following conclusion is correct (

In aa rational number subtraction, the subtracted number is not necessarily greater than the subtracted number.

b Subtract a number to add that number.

c Subtract one number from zero, and still get this number.

d Subtract two opposite numbers to give 0

1. True/False questions (1 point for each question, 4 points in total).

1 The opposite of a number must be smaller than the original. （

2.If two rational numbers are not equal, then the absolute values of these two rational numbers are also not equal. （

4.If a+b=0, then a,b are inverse numbers to each other. (

2. Multiple choice questions (1 point for each question, 6 points in total).

1 The opposite number is the number of itself which is ( ) a 1 b. -1 c. 0 d.does not exist.

2 In the following statement, the correct one is ( ).

a.There is no such thing as the smallest natural number bThere is no such thing as the smallest positive rational number.

c.There is the largest positive rational number dThere is a minimum negative rational number.

3 If the sum of two numbers is positive, then these two numbers ( ).

a.are all positive numbers bOne positive and one negative care all negative dAt least one is a positive number.

4. The distance between the two points of the number 8 and 2 represented on the number line is (

a、6 b、10 c、-10 d-6

5. The absolute value of a rational number is equal to itself, and this number is (

a, positive b, non-negative c, zero d, negative.

3. Fill-in-the-blank questions (1 point per blank, 32 points in total).

1.The opposite number is 2 and the number whose absolute value is equal to 2 is

3.The largest negative integer is the smallest positive integer is

4.There are integers with an absolute value less than 5; There are negative integers with absolute values less than 6.

5.The three elements of the number line are

6.If a rise of 6 meters is recorded as 6 meters, then 8 meters is denoted .

7.The two numbers represented on the number line are always greater than the number of .

8.The opposite of 0 is 4, and the opposite of 0 is , and 4) is .

9.The smallest number with absolute value is , and the absolute value of 3 is .

10 The number represented by a point of 1 unit length on the number axis at a distance from a point representing 2.

In rational numbers, the largest negative integer is , the smallest positive integer is , the smallest non-negative integer is , and the smallest non-negative number is .

11 Insert the following numbers in the corresponding curly brackets:

6,,7,0,,200%,30,000,

Positive integer sets, negative integer sets, fraction sets, natural numbers sets, negative sets, positive sets.

4. Calculation questions.

In fact, there is no subtraction, that is, change the minus sign into an plus sign, and then change the subsequent minus sign (positive numbers to negative, negative numbers to positive).

For example, the first question.

It is the sum of one positive and one negative.

Let's first look at which number has the absolute value (in fact, it is a question of who is the bigger number after the symbol.) If the absolute value of 8 is greater than +5, then the -8 symbol is used, i.e. the minus sign "-".

Then the two absolute values are subtracted (8-5) = 3 to get the addition of the two negative numbers in the second question of -3.

The symbol is the minus.

The absolute values are added (6+5) = 11 to get -11

The third question is also one positive and one negative, the same as the first question.

Subtract the absolute value (3-3) = 0, and the answer is 0

Question 4: 1 positive and 1 minus: 4 and 1 3 is greater than 3 and 1 2

Then take the "-" sign of -4 and 1 2.

Subtract the absolute value (4 and 1 3-3 and 1 2) = 5 6 to get -5 6 The fifth question is positive and negative 3 4 is greater than.

So take the positive sign of 3 and 4.

Subtract again (3, get +

The absolute value of the same sign is added and the difference is subtracted

-3-11

Try to turn a negative number into a positive number: add a negative number to subtract a positive number.

Everything else is just as ...... as positive arithmetic

(1) Solution: =-(==+

2)-1 4+5 6+2 3-1 2 (same solution as above) (3) solution = 12 + 18-70-15 (this will do!) (4) Solution = same.

Because negative and negative are positive, and positive and negative are negative (we have just finished learning).

An odd number of negative signs is negative, and an even number of negative signs is positive.

May I?