Why should we stipulate multiplication and division first and addition then subtraction Everyone knows that in the mixed four-rule operation that includes both addition and subtraction and multiplication and division, the operation must be carried out according to the rule of "multiplication and division first, then addition and subtraction". So why follow such rules? First of all, unlike operations that only add and subtract or only multiply and divide, in the mixed four-rule operation, the result of the operation is related to the order of the operation, for example: 3+2×4=? The answer to the operation according to the rule of multiplication and division before addition and subtraction is 11; if you don't follow this rule, but instead proceed from left to right, add first, and then multiply, the result becomes 20. Therefore, the order of operations must be specified so that the results can be consistent, otherwise it will be chaotic. But this explanation alone is not satisfactory. People can't help but ask: Why is it not stipulated that addition and subtraction should be first followed by multiplication and division? Naturally, rules are artificial, and it is okay to stipulate that addition and subtraction first followed by multiplication and division. But a good rule should be relatively natural, reasonable and convenient. Let's first look at what multiplication is? Multiplication was originally a simple operation of adding the same number. For example, 3×4 is three consecutive additions of 4s, that is, 3×4=4+4+4. If we want to calculate 3+4+4+4, because the addition operation has associative law, we can calculate 3 consecutive additions of 4 first, so that 3+4+4+4=3+(4+4)=3+3×4=3+12=15. Obviously, in the above 3+3×4, we must calculate 3×4 first. For example, 4+2+3+2+2+3+5+3+3, using the commutative law and associative law of addition, 4+2+3+2+2+3+5+3+3=4+2+2+2+3+3 + 3 +3+5=4+2×3+ 3 +3+5=4+2×3+3×4+5=4+6+12+5=27. At this time, multiplication should also be calculated first. In this way, from the perspective of multiplication being a simple operation of continuous addition, it is relatively reasonable to multiply first and then add. Division is to multiply the inverse of a number, and subtraction is to add the negative number of a number. Therefore, it is more reasonable to stipulate that multiplication and division are first followed by addition and subtraction. On the other hand, in people's daily life and practical applications, there are far more cases where multiplication and division are needed first and subtraction then than where addition and subtraction are needed first and then multiplication and division. For example: The rent is 1500 yuan per month and has to be paid for half a year. The property management fee is 300 yuan per month and needs to be paid for one quarter. The electricity bill is 4.5 cents per kilowatt-hour, and the total amount is 1560 kilowatt-hours. To calculate the total amount of fees paid, naturally it is necessary to first calculate the rent, property management fees and electricity bills that need to be paid separately, and then calculate the total payment. To list the formulas in this way, we still need to multiply and divide first, then add and subtract: 1500×6+300×3+0.45×1560=9000 +702=10602 (yuan). Such problems can be found everywhere in people's daily lives. The stipulation of multiplication and division before addition and subtraction also reflects the objective situation and practical needs. In fact, if the expression also has a square root operation in addition to addition, subtraction, multiplication and division, then just as the multiplication is the same number and the addition should precede the addition operation, the square is the continuous multiplication of the same number, and it should also be calculated before the multiplication. Therefore, number operations are divided into three levels: addition and subtraction are the first level operations; multiplication and division are the second level operations; and multiplication and root are the third level operations. For high-level operations, operations should be carried out in the order of multiplication first, multiplication and division second, and finally addition and subtraction.
Why should we stipulate multiplication and division first and addition then subtraction
This paper discusses why the mixed four-rule operation stipulates that multiplication and division first followed by addition and subtraction. First, it points out that inconsistent operation order will lead to confusion in the results, and then explains its rationality from the perspective of multiplication being a simple operation of continuous addition. Combined with daily expense calculation examples, it finally extends to the hierarchical rules of number operations.
