Additive commutative law and the law of association can be used to analyze this problem, and the numbers that can add whole ten, whole hundred and whole thousand can be added first to make the calculation simple.
Solution formula =(298+502)+(304+ 196)
=800+500
= 1300.
As the symbol moves
In addition, addition, subtraction, multiplication and division, the position of numbers can be exchanged according to the needs of operation and the characteristics of the topic, which makes the calculation simple. Special reminder: exchange the positions of numbers, and note that the operation symbols also change positions.
Example 2. Calculation: 464-545+836-455=
Through the analysis and observation of examples, we will find that if we want to calculate from left to right according to the convention, 464 MINUS 545 is not enough at all. In primary school, students can't do it, so to do this problem, we must first observe the characteristics of numbers and make simple calculations.
Solution formula =464+836-545-455
= 1300-(545+455)
=300.
Thinking: Can 4.75÷0.25-4.75 move with the symbol? When can I move with a sign? What should I pay attention to when moving with signs?
3. Break down the numbers and round them off
According to the law of operation and the characteristics of numbers, the numbers in formulas are often divided and reorganized flexibly to form integer ten, integer hundred and integer thousand respectively.
Example 3. Calculation: 998+ 14 13+9989=
The analysis shows that 998 plus 2 can be added to 1000, and 9989 plus 1 1 can be added to 10000, so we divide 14 13 into14000.
Solution formula = (998+2)11400+(11+9989)
= 1000+ 1400+ 10000
= 12400.
Example 4. Calculation: 73. 15×9.9=
The analysis regards 9.9 as the difference of 10 minus 0. 1, and then multiplication and division can simplify the operation.
The solution formula is = 73.15× (10-0.1)
=73. 15× 10-73. 15×0. 1
=73 1.5-7.3 15
=724. 185.
Find the benchmark number
Many figures add up. If these numbers are close to a certain number, you can determine this number as a reference number, compare other numbers with this number, add the redundant part to the multiple of the reference number, and subtract the insufficient part, which can make the calculation simple.
Example 5. Calculation: 8.1+8.2+8.3+7.9+7.8+7.7 =
The six addends in the analysis example are all around 8, so 8 can be used as the reference number. First of all, you can find the sum of six eights, and add the less added part of the number greater than 8, and the more added part of the number less than 8 can be subtracted.
The solution formula is = 8× 6+0.1+0.2+0.3-0.1-0.2-0.3.
=48+0
=48.
5. Equivalence change
Micro-shift equivalent transformation is an important thinking method in primary school mathematics. When adding, we often use such an identity deformation: when one addend increases, another addend decreases the same number, and their sum remains the same. In subtraction, the minuend and the minuend increase or decrease by the same number at the same time, and the difference remains the same.
Example 6. Calculation: 1234-798=
The analysis takes 798 as 800, after subtracting 800, add the extra subtracted 2 to the difference.
Solution formula = 1234-800+2
=436.
6. The method of removing the bracket
In the mixed operation of addition and subtraction, the parentheses are preceded by "plus sign or multiplication sign", so after removing the parentheses, the operation symbols in the parentheses remain unchanged; If there is a "minus sign or division sign" in front of the bracket, the operation sign in the bracket will change when the bracket is deleted.
Example 7. Calculation: (4.8× 7.5× 8.1) ÷ (2.4× 2.5× 2.7) =1
Firstly, the brackets are removed according to the principle of removing brackets, and then the calculation is simplified according to the principle that each number can move with its previous symbol in the same level of operation.
The solution formula = 4.8× 7.5× 8.1÷ 2.4 ÷ 2.5 ÷ 2.7.
=(4.8÷2.4)×(7.5÷2.5)×(8. 1÷2.7)
=2×3×3
= 18.
7. Reduce at the same tail first
In subtraction calculation, if the mantissa of the minuend and the minuend is the same, subtracting the minuend with the same mantissa first can make the calculation simple.
Example 8. Calculation: 2356- 159-256=
In the analytical formula, the mantissa of the second subtree 256 is the same as the mantissa of the minuend 2356, and the positions of the two numbers can be interchanged, so that 2356 can be subtracted first.
Solution formula =2356-256- 159
=2 100- 159
= 194 1.
8. Extract common factors
The response error rate of the distribution law of dialing multiplication is high, which generally includes three types.
(1) direct extraction
Example 9. Calculation: 3.65×23+3.65×77=
This problem is relatively simple to analyze. The common factor of 3.65 can be obtained directly by using the inverse application of multiplication and division.
Solution formula =3.65×(23+77)
=3.65× 100
=365.
(2) Omit the topic × 1.
Example 10. Calculation: 6.3× 10 1-6.3=
By analyzing and completing the formula, 6.3×101-6.3×1,students can easily see that the two multiplication formulas have the same factor of 6.3.
The solution formula = 6.3× (101-1)
=6.3× 100
=630.
(3) Law of product invariance (mainly the change of decimal point)
Example 1 1. Calculation: 6.3×2.57+25.7×0.37=
According to "the product of multiplication is unchanged, one factor enlarges the other factor and reduces the same multiple, and the product is unchanged", 25.7×0.37 can be converted into 2.57× 3.7, and the two parts have the same factor of 2.57, thus creating conditions for using the law of multiplication and distribution.
The solution formula is =6.3×2.57+2.57×3.7.
=2.57×(6.3+3.7)
=25.7.