In the teaching content of primary school mathematics, proportion is the proportion of the number of parts in a whole to the total, which is used to reflect the composition or structure of the whole. Two related quantities, one of which changes and the other changes with it. Two expressions with equal ratios are called proportions. There are four items in the proportion, namely two internal items and two external items.
After the proportion is written as a fraction, the denominator on the left and the numerator on the right are internal terms, and the numerator on the left and the denominator on the right are external terms. In a proportion, the product of two external terms is equal to the product of two internal terms, which is called the basic property of proportion. Two expressions with equal ratios are called proportions. It is one of the bases to judge whether two proportions can form a proportion. The four numbers that make up the proportion are called its terms, which are divided into internal terms and external terms.
The difference between seeking ratio and simplifying ratio
1, with different purposes. To find the ratio is to find the quotient of the former item divided by the latter item; Simplified ratio is to convert the ratio of two numbers into the simplest integer ratio, that is, the simplified ratio must meet two conditions: first, the front and rear terms of the ratio should be integers; Second, the two numbers of the former term and the latter term should be prime numbers.
2. The result is different. The result of the ratio is a number, which can be an integer, a decimal or a fraction. However, the final result of simplifying the proportion is still a proportion. Write in the form of ratio, and you can't get integer or decimal. There are two ways to write it, such as 6 to 4. You can write 6 to 4 and read 6 to 4.
3. Different reading methods. For example, the ratio of 6: 4 is 6: 4 = 6 ÷ 4 = =, which can also be written as 1.5 (the result is a number). The simplified ratio is 6: 4 = 6 ÷ 4 = = pronounced as three to two, or it can be written as 3: 2 (the result is a ratio).
Teaching objectives:
1, understand the meaning of ratio in specific situations, learn to read and write ratio, and master the names of each part of ratio and the method of finding ratio.
2. Experience the process of exploring the relationship between ratio, fraction and division, understand the internal relationship between mathematical knowledge, and grasp the essence of the meaning of ratio.
3. In autonomous learning, accumulate experience in mathematics activities, cultivate students' ability to analyze and summarize, and feel the fun of mathematics learning.