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Detailed solutions for exercises 1 to 8 in the Proportions - Equal Ratio Sequences section of Solve Math Grade 7 page 10 Workbook 2 Creative Horizon Book. This resource is valuable not only for students but also for teachers preparing lesson plans following the new curriculum.Other recommended Math resources:
- Solve Math Grade 7 Creative Horizon Book
- Solve Math Grade 7 page 58 Workbook 1 Kite Book - Exercise 6. Equal Ratio Sequences
Solve exercises on page 10 of Workbook 2 Creative Horizon Book, Proportions - Equal Ratio Sequences
Proportions - Equal Ratio Sequences
1. Solve Exercise 1 Page 10 Math Grade 7 Textbook
Problem: Find equal ratios among the given ratios and then establish the proportional relationships.Solution Guide: Calculate the ratios and then compare them. Form proportional relationships from the equal ratios.Calculate the ratios and compare them.Form proportional relationships from the equal ratios.Answer:We have:2. Solve Exercise 2 Page 10 Math Grade 7 Textbook
Problem: Generate all possible proportional ratios from the following equations:
a) 3 . (-20) = (-4) . 15 b) 0.8 . 8.4 = 1.4 . 4.8.
Answer:
+ If a.d = b.c and a, b, c, d are all non-zero, then we have the following proportional relationships:
Answer:
3. Solve Exercise 3 Page 10 Math Grade 7 Textbook
Problem: Find two numbers x, y such that:
Answer:
4. Solve Exercise 4 Page 10 Math Grade 7 Textbook
Problem: a) Find two numbers a, b such that 2a = 5b and 3a + 4b = 46.
b) Find three numbers a, b, c such that a : b : c = 2 : 4 : 5 and a + b - c = 3.
b) Find three numbers a, b, c such that a : b : c = 2 : 4 : 5 and a + b - c = 3.
Answer:
+ Establish ratios from the given equations.
+ Apply the property of equal ratio sequences to find a, b, c.
Answer:
5. Solve Exercise 5 Page 10 Math Grade 7 Textbook
Problem: Calculate the area of a rectangle with a perimeter of 28 cm and the lengths of its two sides are in the ratio of 3:4.
Solution Guide:
+ Gọi độ dài 2 cạnh hình chữ nhật lần lượt là x, y (x, y > 0).
+ Biểu diễn các dữ kiện đề bài cho theo x, y.
+ Áp dụng tính chất của dãy tỉ số bằng nhau, tìm x, y.
+ Tính diện tích hình chữ nhật.
Answer:
6. Solve Exercise 6 Page 10 Math Grade 7 Textbook
Problem: In a garment factory, within one hour, teams A, B, C collectively produce a total of 60 products. The number of products produced by teams A, B, C is in the ratio of 3:4:5. Determine how many products each team produces per hour.
Solution Guide:
Answer:
Therefore, the number of products produced per hour by teams A, B, C are 15 products, 20 products, and 25 products, respectively.
7. Solve Exercise 7 Page 10 Math Grade 7 Textbook
Problem: A company has three branches: A, B, C. The financial results for the past month at branches A and B are profitable, while branch C is at a loss. Given that the profits and losses of branches A, B, C are in the ratio of 3:4:2. Find the profits and losses of each branch for the past month, knowing that the company made a profit of 500 million VND in that month.
Solution Guide:
+ Let the profits and losses of branches A, B, C be x, y, z (million VND) respectively (x, y, z > 0).
+ Represent the given conditions in terms of x, y, z.
+ Apply the property of equal ratio sequences to find x, y, z.
Answer:
So, in that month, branch A made a profit of 300 million VND, branch B made a profit of 400 million VND, and branch C incurred a loss of 200 million VND.
8. Solve Exercise 8 Page 10 Math Grade 7 Textbook
Solution Guide:
Answer:
Here is the solution guide for Math Grade 7 page 10 Workbook 2. Students can also refer to Math Grade 7 page 14, 15 Workbook 2 and review Math Grade 7 page 109, 110 Workbook 1 to reinforce their knowledge.
- Solve Math Grade 7 page 14, 15 Workbook 2 Creative Horizon Book - Exercise 2: Directly Proportional Quantities
- Solve Math Grade 7 page 20 Workbook 2 Creative Horizon Book - Exercise 3: Inversely Proportional Quantities
