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Solving 7th Grade Math Page 18 Exercise 2: Inverse Proportion, Connect the Knowledge with Life Book, provides detailed solutions for exercises 6.22, 6.23, 6.24, 6.25, 6.26 in the textbook on Inverse Proportion. Students can refer to easily solve exercises in the textbook, grasp solution methods, and detailed explanations.
Other excellent 7th Grade Math resources:
- Solving 7th Grade Math, Connecting Knowledge with Life Book
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Solving 7th Grade Math Page 18 Exercise 2, Connect the Knowledge with Life Book:
Inverse Proportion
1. Solve Exercise 6.22 Page 18 Math Textbook Grade 7
Problem: Given that x and y are two inversely proportional quantities. Replace each '?' in the table below with the appropriate number.
Write the formula describing the dependent relationship between the two quantities x and y.
Solution Guide:
If quantity y is inversely proportional to quantity x, then x.y = a.
Answer:
The proportionality constant is a = x.y = 2. (-6) = -12.
2. Solve Exercise 6.23 Page 18 Math Textbook Grade 7
Problem: According to the table below, are quantities x and y inversely proportional?
Solution Guide:
Answer:
a) Since 3.160 = 6.80 = 16.30 = 24.20, x and y are inversely proportional.
a) Since 3.160 = 6.80 = 16.30 = 24.20, x and y are inversely proportional.
b) Since 4.160 ≠ 25.26, quantity x is not inversely proportional to quantity y.
3. Solve Exercise 6.24 Page 18 Math Textbook Grade 7
Problem: Given that y is inversely proportional to x with a proportionality constant a, and x is inversely proportional to z with a proportionality constant b. Ask whether y is directly or inversely proportional to z, and what is the proportionality constant?
Solution Guide:
Answer:
4. Solve Exercise 6.25 Page 18 Math Textbook Grade 7
Problem: With the same amount of money to buy 17 books of A4 type I paper, how many books of A4 type II paper can be purchased, knowing that the price of type II paper is only 85% of the price of type I paper?
Solution Guide:
Answer:
Answer:
Let x be the number of type II A4 papers purchased (x > 0).
Assume the amount spent on 17 type I A4 papers is a.
Since the price of type II paper is only 85%, the cost is 0.85a.
- Since the amount spent on the paper is constant, the amount and the number of papers are two inversely proportional quantities.
- According to the properties of two inversely proportional quantities, we have:
So, the number of type II A4 papers that can be purchased is 20.
5. Solve Exercise 6.26 Page 18 Math Book Grade 7
Problem: Three plowing teams work on three fields of the same area. The first team completes the work in 4 days, the second team in 6 days, and the third team in 8 days.
Solution:
Since the amount of work is constant, the number of plows and the time to plow the field are two inversely proportional quantities.
Answer: Let x, y, and z be the number of plows in the first, second, and third teams, respectively (x, y, z > 0). According to the problem, we have: x - y = 2. Therefore: x = 1. 6 = 6; y = 1.4 = 4; z = 1.3 = 3.
Given: x, y, and z are the number of plows in the first, second, and third teams (x, y, z > 0).
Equation from the problem: x - y = 2
As the amount of work is constant: The number of plows and the time to plow the field are inversely proportional.
Result: x = 1. 6 = 6; y = 1.4 = 4; z = 1.3 = 3.
Result: Team 1 has 6 plows, Team 2 has 4 plows, and Team 3 has 3 plows.
Reference: Check out the solutions for Grade 7 math page 20 exercise 2 and review Grade 7 math page 14 exercise 2 to reinforce your knowledge.
- Grade 7 Math page 20 Exercise 2 Connect with Knowledge Book - Concentrated practice page 19
- Grade 7 Math page 14 Exercise 2 Connect with Knowledge Book - Exercise 22: Direct Proportional Quantity
