Buzz
Solving Grade 7 Math Workbook Page 20 Connect Knowledge Book provides detailed solutions for exercises 6.27, 6.26, 6.29, 6.30, 6.31, 6.32 in the Focused Practice section of the textbook. Students can refer to these solutions for easier homework solving, improving their math skills day by day.
Other helpful Grade 7 Math materials:
- Solving Grade 7 Math Workbook Connect Knowledge Book with Real-life Applications
- Solving Grade 7 Math Workbook Page 69, 70 Volume 1 Kite Book - Chapter 2 Review Exercises
- Solving Grade 7 Math Workbook Page 23 Volume 2 Horizon of Creativity Book - End-of-chapter exercises for Chapter 6
Solving Grade 7 Math Workbook Page 20 Connect Knowledge Book with Real-life Applications
Concentrated Practice
1. Solve Exercise 6.27 Page 20 Mathematics Textbook Grade 7
Problem: The values of two quantities x and y are given by the following table:
Are the two quantities x and y directly proportional or inversely proportional? Write the formula relating x and y.
Solution Guide:
Answer:
Therefore, quantity x is directly proportional to quantity y.
+ The formula relating x and y is: y = 5x.
2. Solve Exercise 6.28 Page 20 Mathematics Textbook Grade 7
Problem: Given three quantities x, y, z. Find the relationship between x and z, knowing that:
a) x and y are directly proportional, y and z are directly proportional;
b) x and y are directly proportional, y and z are inversely proportional;
c) If x and y are inversely proportional, y and z are inversely proportional.
Solution Guide:
Answer:
a) If x and y are directly proportional, y and z are directly proportional, then x and z are directly proportional.
b) If x and y are directly proportional, y and z are inversely proportional, then x and z are inversely proportional.
c) If x and y are inversely proportional, y and z are inversely proportional, then x and z are directly proportional.
3. Solve Exercise 6.29 Page 20 Mathematics Textbook Grade 7
Problem: To obtain a type of bronze, pure copper and zinc are mixed in a ratio of 6:4. Calculate the masses of pure copper and zinc needed to produce 150 kg of bronze.
Solution Guide:
Since the mass of copper and zinc is directly proportional to the mixing ratio, we have: x : y = 6 : 4. Hence,
Therefore: x = 15.6 = 90; y = 15.4 = 60.
So, the mass of copper is 90kg and the mass of zinc is 60kg.
4. Giải Bài 6.30 Trang 20 SGK Toán Lớp 7
Đề bài: Với thời gian để một thợ lành nghề làm được 12 sản phẩm thì người thợ học việc chỉ làm được 8 sản phẩm. Hỏi người thợ học việc phải mất bao nhiêu thời gian để hoàn thành khối lượng công việc mà người thợ lành nghề làm trong 48 giờ?
Guide:
The number of items and the time it takes to complete the work are inversely proportional quantities.
Solution:
Let x represent the time the apprentice takes to complete the workload that the skilled worker can do in 48 hours.
Since the number of items and the time to complete the work are inversely proportional, we have: 8.x = 12.48.
So, the apprentice will take 72 hours to complete the workload that the skilled worker can do in 48 hours.
Problem:
Students in Grade 7 have collected some books to donate to the library. The number of students in classes 7A, 7B, 7C, and 7D is 38, 39, 40, and 40 respectively. Knowing that the number of donated books is proportional to the number of students in the class, and class 7D donates 4 more books than class 7A. How many books did each class donate?
Solution Guide:
The number of donated books and the number of students in each class are directly proportional quantities.
Answer:
- According to the problem, we have: t - x = 4.
Since the number of donated books is directly proportional to the number of students in the class, we have:
Therefore:
x = 2.38 = 76
y = 2.39 = 78
z = 2.40 = 80
t = 2.40 = 80
So, class 7A has donated 76 books, class 7B has donated 78 books, class 7C has donated 80 books, and class 7D has donated 80 books.
6. Solve Exercise 6.32 Page 20 Mathematics Textbook Grade 7
Problem: The middle school library purchases three reference books for Grade 6, Grade 7, and Grade 8, totaling 121 books. The price of each reference book for Grade 6, Grade 7, and Grade 8 is 40 thousand dong, 45 thousand dong, and 50 thousand dong, respectively. How many reference books did the library buy for each grade, knowing that the amount spent on each type of book is the same?
Solution Guide:
The number of reference books purchased for each grade is inversely proportional to the price of each type.
Answer:
- According to the problem, we have: x + y + z = 121.
Since the amount spent on each type of book is the same, the number of books purchased for each type is inversely proportional to the price of each type of math book.
