Analyze 1, first find out how many degrees the actual electricity consumption is saved than planned, and then divide it by the planned electricity consumption in May to get the percentage of the actual electricity consumption saved than planned.
How many degrees does the scheme 1 actually save electricity than the plan?
2500-2 125=375 (degrees)
What percentage of electricity is actually saved compared with the plan?
375÷2500=0. 15= 15%
Comprehensive formula: (2500-2 125)÷2500.
=375÷2500= 15%.
Analysis 2 takes the planned electricity consumption as the standard "1". First find out what percentage of the actual electricity consumption is planned, and then find out the difference between this percentage and "1", that is, the percentage actually saved is more than planned.
What percentage of the plan is Plan 2?
2 125÷2500=0.85=85%
What percentage of electricity is actually saved compared with the plan?
1-85%= 15%
Comprehensive formula:1-2125 ÷ 2500 =1-0.85 =15%.
A: The actual electricity consumption is less than planned 15%.
Explanatory solution 1 is a universal solution, easy to understand and master, and simple to operate, and it is a better method to solve this problem.
A factory produced 160 machine tools in May and 200 in June. Compared with May, what percentage did June increase?
(West District, Changsha City, Hunan Province)
The analysis of 1 first finds out how many units were added in June compared with May, and then divides by the number of units produced in May to get the percentage of increase in June compared with May.
Solution 1 How many more units were produced in June than in May?
200- 160=40 (Taiwan Province)
Compared with May, the output in June increased by a few percent.
40÷ 160=0.25=25%
Comprehensive formula: (200-160) ÷160 = 40 ÷160 = 25%.
In analysis 2, the number of production units in May is regarded as "1". First, calculate what percentage of the output unit in June is in May, and then subtract "1", that is, what percentage of the output in June is higher than that in May.
Solution 2 What percentage does June account for in May?
200÷ 160= 1.25= 125%
Compared with May, by what percentage did the number of production units increase in June?
125%- 1=25%
Comprehensive formula: 200 ÷160-1=1.25-1= 25%.
A: The output in June is 25% higher than that in May.
The explanation scheme 1 is simple and easy to operate, and it is also a commonly used scheme.
Example 7 1 hongxing machine tool factory planned to produce 200 machine tools last month, but actually produced 40 more than planned. What is the percentage of actual output? (Xicheng District, Beijing)
The analysis of 1 first finds out how many units are actually produced, and then divides by the number of units planned to be produced, and the percentage obtained is a few percent of the planned actual output.
Solution 1 How many machine tools are actually produced?
200+40=240 (unit)
What is the percentage of planned actual output?
240÷200= 1.2= 120%
Comprehensive formula: (200+40) ÷ 200 = 240 ÷ 200 =120%.
In analysis 2, the number of units planned for production is regarded as the standard "1". First, calculate the percentage of actual output exceeding the plan, and then add "1" to get the percentage of actual output exceeding the plan.
Solution 2: What percentage of actual output exceeds the plan?
40÷200=0.2=20%
What is the percentage of planned actual output?
1+20%= 120%
Comprehensive formula:1+40÷ 200 =1+0.2 =1.2 =120%.
Explanatory solution 1 is a common solution, with direct thinking, but complicated calculation. The second scheme is simple and easy to operate, which solves this problem well.
There are 50 students in class 5/kloc-0. A math exam, 1 students failed, and asked for a pass rate. (Nanning, Guangxi Zhuang Autonomous Region)
The analysis of 1 shall be based on "× 100% = pass rate", and the number of people will be tested first, and then the pass rate will be tested.
Solution/kloc-0 /×100% = 0.98×100% = 98%.
Analysis 2: Find out the percentage of people who failed in the class, that is, the failure rate, and then subtract the failure rate from the standard "1" to get the passing rate of this exam.
Solution 21-10 ÷ 50 =1-0.02 = 0.98 = 98%.
The passing rate of this math exam is 98%.
There are 24 girls in Class 3, Grade 6, accounting for 40% of the class. How many students are there in this class? (Jilin Province)
Analysis 1 Take the class size as the standard "1". According to "comparative quantity ÷ corresponding score = standard quantity", the number of girls is divided by 40% of the class number to get the class number.
Solution 124÷40% = 24×60 (person).
Analysis 2 converts 40% into 40∶ 100, then the class size can be divided into 100, including 40 girls. We can first find out how many people are in each part, and then find out how many people are in 100 part, that is, the class size.
Solution 2 24 ÷ 40×100 = 0.6×100 = 60 (person).
Analysis 3: According to the equation "Class size × 40% = number of girls".
Solution 3 let the class size be X.
x×40%=24
x = 24÷ 40 %
x=60
Analysis 4 takes the class size as the standard "1" and solves the problem by multiple ratio.
The solution is 424× (1 ÷ 40%) = 24× 5/2 = 60 (person).
Analysis 5 lists the proportion formula according to "the ratio of the number of girls to the number of classes is equal to its corresponding sharing ratio".
Solution 5 let the number of students in the class be X.
24∶x=40∶ 100
40x=24× 100
x=2400÷40
x=60
There are 60 students in this class.
Comment on solution 1 and solution 4, which are commonly used, concise and easy to understand. Other solutions change the quantitative relationship in the problem and change the thinking angle of solving the problem, which is the basic skill to solve the fractional application problem. Only by doing this can we use our knowledge flexibly and solve problems skillfully. Solution 3 is the best solution to this problem.
A steel mill produced 880,000 tons of steel last year, and plans to increase its output by 25% this year. How many ten thousand tons of steel do you plan to produce this year?
(Urumqi, Xinjiang Uygur Autonomous Region)
Analysis 1 First calculate that the planned output this year is higher than last year, and then add the steel output last year, that is, this year's steel output.
Solution 1 How much is the planned output increase this year compared with last year?
88× 25% = 22 (ten thousand tons)
How many ten thousand tons of steel do you plan to produce this year?
88+22= 1 10 (ten thousand tons)
Comprehensive formula: 88× 25%+88 = 22+88 =110 (ten thousand tons).
Analysis 2: First ask what percentage of the planned steel output this year is last year, and then ask the tens of thousands of tons of steel this year.
Solution 2 88× (1+25%) = 88× =110 (ten thousand tons).
According to the meaning of the question, last year's steel output can be understood as 100, and this year's planned steel output can be understood as (100+25). By using normalization method, we can get how many tens of thousands of tons per batch first, and then how many tens of thousands of tons from 125, that is, the planned steel output this year.
Solution 3 88÷ 100×( 100+25)
=88÷ 100× 125
= 0.88×125 =110 (ten thousand tons).
A: It is planned to produce 165438+ 10,000 tons of steel this year.
Comment solution 1 and solution 2 are commonly used solutions, which are easy to understand and master. Among them, scheme 2 is a better solution to this problem because of its concise thinking and simple operation.
A school-run factory produced 6900 sets of teaching AIDS in the first quarter of this year, up 15% year-on-year. How many sets of teaching AIDS were produced in the first quarter of last year?
(Hefei City, Anhui Province)
Analysis 1 Take the output of teaching AIDS in the first quarter of last year as the standard "1". First, find out what percentage of the output in the first quarter of this year is last year, and then calculate the output in the first quarter of last year according to "comparative quantity ÷ corresponding score = standard quantity".
The output in the first quarter of this year is a few percent of that of last year.
1+ 15%= 1 15%
What was the output in the first quarter of last year?
6900 ÷ 1 15% = 6000 (set)
Comprehensive formula: 6900 ÷ (1+ 15%)
=6900÷ 1 15%=6000 (sets).