I. Overview
In mathematics, division is a basic arithmetic operation. For division with divisor close to integer 10, we usually use "quintuple method" to try quotient. This method can help us calculate the division result quickly and accurately. The core idea of the "five-term method" trial quotient is to regard the divisor as a close integer ten, and then judge whether the quotient is appropriate by comparing the quotient with the divisor.
Second, the specific steps
1. Observe the divisor and determine its nearest integer 10. For example, if the divisor is 37, then the nearest integer is 40. Take this integer as a new divisor and divide it by the dividend to get a preliminary quotient. For example, if the dividend is 98 and the new divisor is 40, then the initial quotient is 2 (because 98 ÷ 40 = 2... 18).
2. Compare the size of the initial quotient and the original divisor. If the initial quotient is less than the original divisor, it means that our estimation is small. We should add 1 to the initial quotient and recalculate. If the initial quotient is greater than or equal to the original divisor, it means that our estimation is appropriate or too large, and the initial quotient should remain unchanged or decrease by 1. Repeat steps 2 and 3 until a suitable quotient is obtained.
Discussion on division
1, the definition and nature of division: division is a binary operation, expressed as a÷b=c, where a is the dividend, b is the divisor and c is the quotient. When dividend a can be divisible by dividend b, quotient c is an integer; Otherwise, quotient c is a decimal or fraction. Division has the following properties: commutative law: a ÷ b = b ÷ a; Law of association: (a÷b)÷c=a÷(b×c).
2. Arithmetic of division: When carrying out division, the following rules need to be followed: first, turn the dividend and divisor into integers; Starting from the highest bit of the dividend, compare it with the divisor, and if the dividend is greater than or equal to the divisor, perform subtraction operation, and write the result into the corresponding position of the quotient; Repeat the above steps until the dividend is less than the divisor.
3. Application of division: Division is widely used in daily life, such as calculating price, area and volume. In addition, division is often used in scientific research, engineering design and other fields. Division is an important basic operation in mathematics. Mastering the concept and operation method of division is of great significance to students' mathematics study and daily life.