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After completing the lesson on Inverse Proportions, students should work on exercises 1 through 9 to reinforce their understanding at home. If unsure of the solution method or afraid of making mistakes, students can refer to the document Solving 7th Grade Math Page 20 Volume 2 of Creative Horizon Textbook below.
Other recommended study materials for Grade 7 Mathematics include: - Solving 7th Grade Math Creative Horizon Textbook - Solving 7th Grade Math Page 18 Volume 2 of Knowledge Connection Textbook - Exercise solutions for Grade 7 Math Page 68 Volume 1 of Kite Textbook - Lesson 8: Inverse Proportions
Solutions to exercises on page 20 of Textbook Volume 2, Creative Horizon
Inverse Proportions
Solve Exercise 1 Page 20 Grade 7 Mathematics Textbook
Problem Statement: Given two quantities a and b are inversely proportional to each other and it is known that when a = 3 and b = -10.
a) Find the proportionality constant.
b) Express a in terms of b
c) Calculate the value of a when b = 2, b = 14
Solution:
Answer:
a) Since a is inversely proportional to b with the proportionality constant k, therefore
For a = 3, b = -10, we have: k = 3 * (-10) = -30.
2. Solve Exercise 2 Page 20 Grade 7 Mathematics Textbook
Problem Statement: Given two quantities x and y are inversely proportional to each other.
a) Find the proportionality constant.
b) Find the unknown values in the table above.
Solution:
Two quantities x and y are inversely proportional to each other with the proportionality constant a = x*y.
Answer:
b)
3. Solve Exercise 3 Page 20 Grade 7 Mathematics Textbook
Problem Statement: There are 20 workers with equal productivity who finish building a ship in 60 days. If only 12 workers remain, how many days will it take for them to finish the ship?
Solution:
Since the amount of work remains constant and the productivity is the same, the number of workers is inversely proportional to the number of days to complete the task.
Using the property of inverse proportions: x1 * y1 = x2 * y2.
Answer:
Let the number of days for 12 workers to complete the ship be x (days) (x > 0).
Since the amount of work remains constant and the productivity of each worker is the same, the number of workers and the number of days to complete the ship are inversely proportional.
Applying the property of inverse proportions, we have:
So, 12 workers will complete the ship in 100 days.
4. Solve Exercise 4 Page 20 Grade 7 Mathematics Textbook
Problem Statement: The Quyet Tien production team uses x harvesters (with equal productivity) to harvest a field in y hours. Are the two quantities x and y inversely proportional?
Solution:
Answer:
Since the amount of work remains constant (the same field) and the productivity of each harvester is equal, the number of harvesters and the time to harvest the field are inversely proportional.
So, the two quantities x and y are inversely proportional.
5. Solve Exercise 5 Page 20 Grade 7 Mathematics Textbook
Problem Statement: Given a (m) as the circumference of a wheel, b is the number of rotations of the wheel on the road segment from A to B. Are a and b inversely proportional?
Solution:
Solution:
Answer:
The distance traveled from A to B is equal to the circumference of the wheel multiplied by the number of rotations.
Since the distance from A to B remains constant, the circumference of the wheel and the number of rotations are inversely proportional.
So, a and b are inversely proportional.
6. Solve Exercise 6 Page 20 Grade 7 Mathematics Textbook
Problem Statement: Based on the corresponding values in the table for two quantities in each case below, determine whether the following two quantities are inversely proportional or not?
Solution:
Answer:
a) We observe: 1.60 = 2.30 = 3.20 = 4.15 = 5.12 so a and b are inversely proportional.
b) Since 2.12 = 24; 3.9 = 27 then 2.12 is not proportional to 3.27.
Therefore, m and n are not inversely proportional.
7. Solve Exercise 7 Page 20 Grade 7 Mathematics Textbook
Problem Statement: A farm has 2 harvesters (with equal productivity) that finished harvesting a field in 4 hours. If there are 4 harvesters, how long will it take to finish harvesting the same field?
Solution:
The number of harvesters and the hours of harvesting are inversely proportional.
Using the property of inverse proportions: x1 * y1 = x2 * y2.
Answer:
For the same field and the same productivity of each harvester, the number of harvesters and the hours of harvesting are inversely proportional.
8. Solve Exercise 8 Page 20 Grade 7 Mathematics Textbook
Problem Statement: Lan wants to cut a rectangle with an area of 24 cm2. Let n (cm) and d (cm) be the lengths of the two sides of the rectangle. Prove that n and d are inversely proportional and find n in terms of d.
Solution:
Answer:
Since Lan wants to cut a rectangle with an area of 24 cm2 (constant), n*d = 24. Therefore, n and d are inversely proportional.
9. Solve Exercise 9 Page 20 Grade 7 Mathematics Textbook
Problem Statement: A train moves uniformly on a distance of 200 km with a speed v (km/h) in time t (h). Prove that v, t are inversely proportional and find t in terms of v.
Solution:
Answer:
We have: Since the train moves uniformly on a distance of 200 km (constant), Therefore, v, t are inversely proportional.
Here is the guide to solving math problems for Grade 7, page 20, exercise 2. Students, please refer to Grade 7 math solutions on page 23, exercise 2, and review Grade 7 math exercises on pages 14 and 15, exercise 2 to ensure understanding.
- Grade 7 Math Solutions on page 23, exercise 2, Chân Trời Sáng Tạo - Final exercise of chapter 6
- Grade 7 Math Solutions on page 28, exercise 2, Chân Trời Sáng Tạo - Exercise 1: Numerical expression, algebraic expression
