Multiplier and multiplicand are both mathematical terms, which refer to the numbers in the multiplication of four operations.
The multiplicand is generally placed in front of the formula, and the multiplier is generally placed behind the layout.
Like 4x5.
The multiplier refers to 4.
Multiplier means 5.
When primary school students learn multiplication, they are young, have poor acceptance ability and have no knowledge base of multiplication exchange law. The meaning of multiplication is formed on the basis of seeking the sum of addends. Distinguishing multiplicand and multiplier correctly and explaining their writing positions are helpful to understand and master the meaning of multiplication and understand the origin of the formula. After learning the law of multiplication and exchange, as long as it is the operation of finding the sum of the same addend when solving practical problems, the product of two factors can be correctly found, which is reasonable and correct. There is no need to distinguish which factor is the multiplicand and which factor is the multiplier, let alone emphasize the status of the two when you graduate from primary school. As for the names of the parts of the multiplication formula, the product is still called the product; Multiplier and multiplier are collectively referred to as factors of product, so there is no need to consider their position order.
Introduction to multiplication
Multiplication is a shortcut to add up the same numbers. The result of its operation is called product, and "X" is the symbol of multiplication. From the philosophical point of view, multiplication is the result of qualitative change caused by additive quantity. The multiplication of integers (including negative numbers), rational numbers (fractions) and real numbers is a systematic summary of this basic definition.
Multiplication can also be seen as calculating the objects arranged in a rectangle (integer) or finding the area of a rectangle with a given side length. The area of the rectangle does not depend on which side is measured first, which shows the exchange property. The product of two measured values is a new type of measurement, for example, multiplying the length of two sides of a rectangle to get its area, which is the theme of size analysis.
Integer multiplication meets the following requirements: exchange law, association law, distribution law and elimination law.
With the development of mathematics, the object of operation has developed from integer to more general group.
Intra-group multiplication is no longer needed to satisfy the commutative law. The most famous noncommutative example is the quaternion group discovered by Hamilton. But the law of association is still satisfied.
1. Multiplicative commutative law: ab=ba. Note: letters are multiplied by letters, and the multiplication sign need not be written, or can it be written? .
2. Multiplicative associative law: AB (c) = A (BC);
3. Multiplication distribution law: (a+b)c=ac+bc.
The traditional definition of multiplication requires strict distinction between multiplier and multiplicand, which has always been a difficult problem in primary school mathematics education. Especially when solving application problems, it is required that the multipliers and multiplicands of the listed formulas cannot be reversed, and only each copy can be regarded as the multiplicand and the number of copies as the multiplier.
If the multiplier and the multiplicand are reversed, even if the result is right, it cannot be said that the problem is right. However, after students learn multiplication and division, especially after learning the multiplication and division relationship, both the multiplier and the multiplicand are called factors, and the position before and after is no longer a problem. At this time, students will have questions. Obviously, the multiplier and the multiplicand can be reversed and the result is the same. Why can't the formula be reversed? Questioning this question may make students doubt mathematics and lose confidence in learning mathematics. The difference between multiplicand and multiplier in multiplication formula has been criticized by many parents and experts. There is a view that it is against the law of education to distinguish the multiplicand from the multiplier, which is not in line with the students' understanding level and real life. In March 2000, the "Nine-year Compulsory Education Primary School Mathematics Syllabus (Revised Trial)" was published, and the distinction between multiplier and multiplicand was abolished, which was called multiplier (also called factor) and was welcomed by teachers and students. The standard experimental draft of mathematics curriculum published in July, 2006, 5438+0 followed the definition of multiplication in the revised outline. This can reduce many unnecessary burdens on teachers and students, and also help students to reduce many mistakes and unnecessary psychological pressure when learning multiplication, especially when solving multiplication-related problems. It is a happy review for students, teachers and parents.