"Mixed Operations of Addition and Subtraction of Rational Numbers" PPT courseware

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"Mixed Operations of Addition and Subtraction of Rational Numbers" PPT courseware

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(1) What is the addition rule for rational numbers?

Addition rules for rational numbers:

(1) Add two numbers with the same sign, take the same sign, and add the absolute values;

(2) Add two numbers with different signs whose absolute values ​​are not equal, take the sign of the addend with the larger absolute value, and subtract the smaller absolute value from the larger absolute value;

(3) The addition of two numbers that are opposite to each other gives zero;

(4) Adding a number to zero still yields the number;

(2) What is the subtraction rule for rational numbers?

Subtraction rules for rational numbers:

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

That is a -b = a + (-b)

Addition and subtraction are unified into addition

In algebra, all addition and subtraction operations can be unified into addition operations. In a sum, the usual plus sign can be omitted, as can the parentheses for each number.

For example, 4.5+(-3.2)+1.1+(-1.4) can be written without brackets:

4.5 - 3.2 + 1.1 - 1.4 (can still be regarded as a sum)

Read as "the sum of plus 4.5, minus 3.2, plus 1.1, and minus 1.4"

Can also be read as "4.5 minus 3.2 plus 1.1 minus 1.4"

bracket removal rule

There is a "+" sign in front of the brackets. If you remove the brackets and the "+" sign in front of them, the items in the brackets will remain unchanged;

There is a "-" sign in front of the bracket. If the bracket and the "-" sign in front of it are removed, each item in the bracket becomes its opposite number.

Look at the following example again:

(-8) - (-10) + (-6) - (+4)

=(-8) + (+10)+(-6) + (-4) (unify subtraction operations into addition operations)

=-8+10-6-4 (omit parentheses and plus sign)

Read as: the sum of negative 8, positive 10, negative 6, and negative 4.

Or: minus 8 plus 10 minus 6 minus 4.

This is the algebraic sum omitting the plus sign.

think

1. The formula 2-3-8+7 can be regarded as the algebraic sum of which rational numbers?

2. Can all expressions containing mixed operations of addition and subtraction of rational numbers be converted into algebraic sums of rational numbers?

3. Which operational laws are satisfied by the addition operation of rational numbers?

4. How to calculate -3＋5-9＋3＋10＋2-1 is relatively simple?

-3+5-9+3+10+2-1

=(-3+3)+[(-1-9)+10]+5+2

=0＋0＋5+2

=7

Since the calculation formula can be understood as the sum of seven numbers such as -3, 5, -9, 3, 10, 2, -1, the law of addition and commutativity is applied. These seven numbers can be combined and exchanged for calculations at will, so that The calculation is simple.

1. Basic steps of mixed operations of addition and subtraction

⑴ Convert subtraction in mixed operations to addition and write it in the form of a plus sign in front;

⑵Omit the plus sign and parentheses;

⑶Appropriately use the commutative law of addition and the associative law to simplify calculations;

⑷In each step of operation, the symbol must be determined first, and then the numerical value must be calculated.

2. Commonly used methods for mixed operations of addition and subtraction

⑴According to the order of operations, calculate one by one from left to right;

⑵ Unify the mixed operations of addition and subtraction into addition, write them in the form of sums, and then use the laws of arithmetic to perform calculations.

3. Summary of skills in mixed operations of addition and subtraction

(1) Use the laws of arithmetic to add positive and negative numbers respectively.

(2) Fractions with the same denominator or multiples are combined and added.

(3) If there are both fractions and decimals in the formula, unify the decimals into decimals or unify the fractions into decimals.

(4) Two numbers that are opposite to each other can be added first.

(5) The integer part of a mixed fraction, the decimal part can be separated and added.

4. Points to note:

⑴After you become proficient in arithmetic, you can omit the step of changing from subtraction to addition and directly write it in a form that omits the plus sign;

⑵ When exchanging the front and rear positions of a number, it should be exchanged together with the symbol in front of it;

⑶ When performing mixed operations, the method of determining the order of operations learned in elementary school still applies. If there are parentheses, the ones in the parentheses should be calculated first.

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"Mixed Operations of Addition and Subtraction of Rational Numbers" Rational numbers and their operations PPT courseware:

"Mixed Operations of Addition and Subtraction of Rational Numbers" Rational numbers and their operations PPT courseware Add + or - sign in front of the numbers 2, 3, 4, 5, 6, 7, 8, 9 so that their sum is 10. How many numbers can you find? How to add? 2 3 4 5 6 7 8 9 Fill in the blanks in Example 1: (-8) +__..

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Update Time: 2024-09-28

This template belongs to Mathematics courseware Hebei Education Edition Seventh Grade Mathematics Volume 1 industry PPT template

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