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Solving Grade 7 math problem on page 68 of Cánh Diều textbook is a great Math resource, specifically for the lesson on Proportional Inverse Quantities. Students can refer to solve exercises 1, 2, 3... in the textbook easily, reinforce and master the knowledge effectively.
Refer to many good Grade 7 Math learning resources:
- View the full series of Solving Grade 7 Math Cánh Diều textbook
- Solving Grade 7 math problem on page 18 of textbook 2 Kết Nối Tri Thức - Exercise: 23 Proportional Inverse Quantities
- Solving Grade 7 math problem on page 20 of textbook 2 Chân Trời Sáng Tạo - Exercise 3: Proportional Inverse Quantities
Solving Grade 7 math problem on page 68 of Cánh Diều textbook
Exercise 8. Proportional Inverse Quantities
1. Solve Exercise 1 Page 68 Math Textbook Grade 7
Problem Statement: The values of two quantities x, y are given by the following table:
Do the two quantities x and y have an inverse proportion? Why?
Solution Guide:
Answer:
Two quantities x and y are inversely proportional to each other because 3.32 = 4.24 = 6.16 = 8.12 = 48.2 = 96.
2. Solve Exercise 2 Page 68 Math Textbook Grade 7
Problem Statement: Given that x, y are two quantities inversely proportional to each other and when x = 36 then y = 15.
a) Find the proportionality constant.
b) Write the formula to calculate y based on x
c) Calculate the value of y when x = 12; x =18; x = 60.
Solution Guide:
Since the workload remains constant and the productivity of each worker is the same, the number of workers and the time to complete the work are inversely proportional.
Answer:
Problem Statement: As planned, a group of 35 workers will build a building in 168 days. However, when they start working, some workers cannot participate, so the group is left with only 28 workers. How long will it take for the group to complete the building then? Assuming that each worker has the same productivity.
Solution Guide:
Since the workload remains constant and the productivity of each worker is the same, the number of workers and the time to complete the work are inversely proportional.
Using the property of two inversely proportional quantities: x1. y1 = x2. y2
Answer:
Let the time for the group of workers to complete the job be x (days) (x > 0).
Because the workload remains constant and the productivity of each worker is the same, the number of workers and the time to complete the work are inversely proportional.
Applying the property of two inversely proportional quantities, we have:
35 . 168 = 28 . x.
Hence, x = 35 . 168 : 28 = 210 (satisfies).
So, the group of workers will take 210 days to complete the building.
4. Solve Exercise 4 Page 68 Math Textbook Grade 7
Problem Statement: Miss Lan planned to buy 10 flowers with a predetermined amount of money. However, due to the holiday, the price of flowers increased by 25%. How many flowers can Miss Lan buy with that amount of money?
Guidance:
Since the amount spent on flowers remains constant, the quantity of flowers purchased and the price of flowers are inversely proportional.
Using the property of two inversely proportional quantities: x1. y1 = x2. y2.
Answer:
Guidelines: Convert the units of time into seconds.
Speed and time taken for a journey are two inversely proportional quantities.
Answer:
Explanation:
Converting 4 minutes 36 seconds 85 = 276.85 seconds.
4 minutes 38 seconds 78 = 278.78 seconds.
As the distance remains unchanged, speed and time are inversely proportional quantities.
Applying the property of two inversely proportional quantities, we have:
Therefore, the ratio between the average speed of Ánh Viên at the 2016 Summer Olympics and at the 2015 World Swimming Championships held in Kazan (Russia) is: 1.007.
6. Exercise 6 Page 68 Mathematics Textbook Grade 7
Problem: A type of high-speed train currently in Japan can travel at an average speed of 300 km/h, 1.43 times faster than the first generation of high-speed trains.
If that type of high-speed train runs a distance in 4 hours, how many hours will the first-generation high-speed train have to run that distance?
Guidelines:
Speed and time taken on the same distance are two inversely proportional quantities.
Answer:
Let t1, v1 respectively denote the time and speed of the first generation of high-speed trains.
t2, v2 respectively denote the time and speed of the current high-speed train.
Since the distance remains unchanged, speed and time are two inversely proportional quantities.
Applying the property of two inversely proportional quantities, we have:
So, if the current high-speed train runs a distance in 4 hours, the first-generation high-speed train will have to run that distance in 5.72 hours.
7. Exercise 7 Page 68 Mathematics Textbook Grade 7
Problem: A gear has 40 teeth, rotating 15 revolutions per minute, it meshes with a second gear. Assuming the second gear rotates 20 revolutions per minute. How many teeth does the second gear have?
Guidelines:
The number of teeth and the number of revolutions of the gear are two inversely proportional quantities.
Using the property of two inversely proportional quantities: x1. y1 = x2. y2 = x3. y3.
Answer:
Since the distance rotated by the 2 gears is the same, the number of teeth and the number of revolutions of the gear are two inversely proportional quantities.
Let the number of teeth of the second gear be x (x > 0).
According to the property of two inversely proportional quantities, we have:
40.15 = x . 20 so x = 40. 15 : 20 = 30 (satisfies).
So, the second gear has 30 teeth.
Thus, Solving Math Grade 7 page 68 Volume 1 of Kite Book is a useful resource for 7th-grade students, supporting effective Math solving and learning.
References:
- Math Solution 7 page 69, 70 Volume 1 Kite Book - Chapter 2 Review Exercises
- Math Solution 7 page 80 Volume 1 Kite Book - Exercise 1. Rectangular Prism. Cube
