Teaching process:
1. Students, let's recall first. How much do you know by comparison? Hmm. The meaning of ratio, the name of ratio part, the relationship between ratio and fraction, division, etc.
2. Do you remember the basic nature of the score? Oh, the numerator and denominator of a fraction are multiplied or divided by a non-zero number at the same time, and the value of the fraction remains the same.
3. So what are the rules in the comparison? Who can say, well, you think it should be that the first term and the last term of the ratio are multiplied or divided by the same number (except 0) at the same time, and the ratio remains unchanged. Is everyone's guess right? This needs us to prove through research.
Next, please study in groups to verify whether the previous guess is correct.
5. The cooperation requirement is (1) independent completion: write a comparison and verify it in your favorite way. (2) Group discussion and study. Each student should show his research results and say that the clean-up work should be completed by (3) choosing a classmate to speak on behalf of the group.
6. Which group will report? For your team. Your verification is based on the relationship between ratio and score. The former term of the ratio is equivalent to the numerator, and the latter term is equivalent to the denominator. For example, the numerator and denominator of 1.2 are multiplied or divided by 3 at the same time, and the fractional value is still three quarters. Therefore, the first and second terms of the ratio are multiplied or divided by 3 at the same time, and the ratio remains unchanged.
7. For your group, verify your group according to the relationship between ratio and division. Divider and divisor are multiplied or divided by a number (except 0) at the same time, and the quotient remains unchanged. The former term of the ratio is equivalent to the dividend, the latter term is equivalent to the divisor, and the ratio is equivalent to the quotient, so the former term and the latter term are divided by a number (except zero) at the same time, and the ratio remains unchanged.
8. For your team. You verified it according to the proportion. 16:20=( 16 divided by 4):(20 divided by 4) = 0.8.
9. We make full use of the old knowledge to verify that the former item and the latter item are multiplied or divided by the same number (except zero) at the same time, and the ratio is unchanged. This is the basic nature of the ratio. Writing on the blackboard (the basic nature of ratio)
10. Guess, what's the use of the basic nature of Bi?
1 1. You tell me. Oh, you can simplify the ratio and get the simplest integer ratio. What is the simplest integer ratio? Yes, the inter-prime integer ratio of the former term and the latter term is called the simplest integer ratio.
12. Look at the following ratios, which are the simplest integer ratios, and briefly explain the reasons. 3:4 18: 12 19: 10; 0.75:2。
13. The judgment is accurate and the reasons are sufficient. So let's simplify these two ratios. 18: 12= 0.75:2。
14. Who can tell me how you did it? For you, you divide 18 and 12 by the greatest common divisor of the former and the latter. 6. Simplify this to 3: 2. You tell me. You can divide the first and second items by 3 at the same time, and then divide them by 2 at the same time, which can be simplified to 3: 2, but it is easier to divide them directly.
15. You tell me. Hmm. Convert 0.75:2 into integer ratio first, and then simplify it.
16. You still want to say. Oh, you summed up how to simplify the ratio. Integer divides the former term and the latter term by their least common multiple; If there are decimals, they should be converted into integers before simplification. If there is a fraction, multiply it by the least common multiple of the denominator at the same time, and then simplify it.
17. Do you have any questions?
18. You ask, is simplifying the proportion the same as seeking the proportion? Who will answer? Well, the final result of simplifying the ratio is a ratio, and the final result of finding the ratio is a number.
19. Through their own efforts, the students verified the basic properties of ratios and summarized the methods of converting various ratios into the simplest integer ratios. Then let's try to practice and turn the following ratio into the simplest integer ratio.
20. This class is coming to an end. What are you going to say?
My trial is over. Thank you, judges.