The application problem of multiplication and division of numbers is a key point in the teaching of mathematics textbooks in primary and high schools, and it is also a difficult point for students to learn. Because such questions are abstract, students are often prone to misinterpretation due to analysis errors. Applying this formula to let students answer such questions can greatly improve the accuracy of students' solving such problems, and the effect is very remarkable. This formula is: use multiplication to know "1" and use division to find "1".
Use formula
Let's use the previous example as the basic condition to illustrate.
(1. 1) The number of girls in my class is the number of boys. There are 25 boys and how many girls? Analysis: This question is based on the number of boys "1", and the number of boys is known. The multiplication formula of "1" is known as: 25× = 20 (person).
(1.2) The number of girls in my class is the number of boys. There are 20 girls and how many boys? Analysis: In this problem, the number of boys is still regarded as the unit "1", and the amount sought is also the number of boys, that is, the amount sought is the unit "1". According to "1", the divisor formula is: 20 ÷ = 25 (person).
(2. 1) There are 30 peach trees in the orchard, and the number of peach trees is less than that of pear trees. How many pear trees are there? Analysis: This question takes the number of pear trees as the unit "1". Finding the number of pear trees means finding the unit "1". The number of peach trees is equal to the number of pear trees (1-). So the divisor formula of "1" is: 30 ÷ (1-) = 50 (tree).
(2.2) There are 30 pear trees in the orchard, and the number of peach trees is less than that of pear trees. How many peach trees are there? Analysis: This question is still based on the number of pear trees "1", and 30 pear trees are known. And the number of peach trees is equivalent to the number of pear trees (1-). According to knowledge, the multiplication formula of "1" is: 30× (1-) = 18 (tree).
General steps
Find out the number of units "1" in the problem; Judging whether the quantity of unit "1" is a known quantity or a quantity to be found; According to "1" multiplication, find the formula of "1" division and calculate it; Test and write the answers.