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All exercises 1, 2, 3... from Chapter II Review Exercises are guided in the document Solving math problems Grade 7 pages 69, 70 Cánh Diều textbook. With detailed solutions, students can visualize how to solve math problems and effectively improve their scores.
Referring to multiple good math study materials for Grade 7
- Complete set of Solving math problems Grade 7 Cánh Diều textbook
- Solving math problems Grade 7 page 39 Volume 1 Kết Nối Tri Thức textbook - Exercises at end of Chapter 2
- Solving math problems Grade 7 page 45 Volume 1 Chân Trời Sáng Tạo textbook - Exercises at end of Chapter 2
Solving math problems Grade 7 pages 69, 70 Cánh Diều textbook
Chapter II Review Exercises
1. Solve Exercise 1 Page 69 Math Grade 7 SGK
Problem: Find the irrational numbers among the following numbers:
Solution Guide:
An irrational number is a number expressed in the form of an infinite non-repeating decimal.
Answer:
We have:
2. Solve Exercise 2 Page 69 Math Grade 7 SGK
Problem: Compare:
Solution Guide:
Answer:
3. Solve Exercise 3 Page 69 Math Grade 7 SGK
4. Solve Exercise 4 Page 69 Math Grade 7 SGK
Problem: Calculate.
Solution Guide:
Answer:
5. Solve Exercise 5 Page 69 Math Grade 7 SGK
Problem: Find the non-negative number x, given:
Solution Guide:
Answer:
6. Solve Exercise 6 Page 69 Math Grade 7 SGK
Problem: Find the number x in the following proportions:
Solution Guide:
Answer:
7. Solve Exercise 7 Page 69 Math Grade 7 SGK
Solution Guide:
Apply the property of equal ratio sequence to prove.
Answer:
8. Solve Exercise 8 Page 69 Math Grade 7 SGK
9. Solve Exercise 9 Page 69 Math Grade 7 SGK
Problem: Class 7A has 45 students. In the midterm of Semester I, the number of students at the Excellent, Good, and Average levels are in the ratio of 3:4:2. Calculate the number of students at each level, knowing that there are no students at the Fail level in the class.
Solution Guide:
Answer:
10. Solve Exercise 10 Page 70 Math Grade 7 SGK
Problem: Sister Phuong planned to buy 2 kg of apples with a predetermined amount of money. When she went to the supermarket at the right time, she received a 25% discount on the price of apples. How many kilograms of apples did Sister Phuong buy with that amount of money?
Solution Guide:
Since the amount spent on apples remains constant, the quantity of apples purchased and the price of apples are inversely proportional.
Utilizing the property of two inversely proportional quantities: x1. y1 = x2. y2.
Answer:
Let's assume the original price of apples is a, then the price of apples after the discount is a - 0.25a = 0.75a.
Since the amount spent on apples remains constant, the quantity of apples and the price of apples are two inversely proportional quantities.
Applying the property of two inversely proportional quantities, we have:
So, Phuong bought 8/3 kilograms of apples.
11. Solution for Exercise 11 Page 70 Math Textbook Grade 7
Problem: Every 15 minutes, Sister Lan runs 2.5 kilometers. How many kilometers does she run in 1 hour? Given that Sister Lan's running speed is constant.
Solution:
With constant speed, distance and time are two directly proportional quantities.
Answer:
So, in 1 hour, Sister Lan runs 10 kilometers.
12. Solution for Exercise 12 Page 70 Math Textbook Grade 7
Problem: A worker can produce 20 units in 30 minutes. How many units can they produce in 75 minutes? Given that the worker's productivity remains constant.
Solution:
Since the work productivity remains constant, time and the number of products produced are directly proportional.
Answer:
So, in 75 minutes, the person produces 50 units.
13. Solution for Exercise 13 Page 70 Math Textbook Grade 7
Problem: Exchanging 1,158,000 Vietnamese dong yields 50 US dollars.
How many Vietnamese dong are needed to obtain 750 US dollars?
Solution:
The amount of US dollars and Vietnamese dong exchanged for each other are directly proportional.
Answer:
So, the amount of Vietnamese dong needed to exchange for 750 US dollars is 17,370,000 dong.
14. Solution for Exercise 14 Page 70 Math Textbook Grade 7
Problem: Last month, every 6 hours, the production line produced 1,000 units. But this month, due to improvement, the productivity of the production line is 1.2 times that of last month. How much time does the production line need to produce 1,000 units this month?
Guide:
With the same workload, productivity and completion time are two inversely proportional quantities.
Utilizing the property of two inversely proportional quantities: x1. y1 = x2. y2.
Answer:
So, it takes 5 hours for the production line to complete 1,000 units.
15. Solution for Exercise 15 Page 70 Math Textbook Grade 7
Problem: White bronze is an alloy of copper and nickel. An alloy of white bronze has copper and nickel in a ratio of 9 to 11. Find the amount of copper and nickel needed to create 25 kg of this alloy.
16. Solution for Exercise 16 Page 70 Math Textbook Grade 7
Problem: Three rectangles have the same area. It is known that the widths of the three rectangles are proportional to the numbers 1, 2, and 3. Calculate the length of each rectangle, given that the total length of the three rectangles is 110 cm.
Therefore,
So, the lengths of the three rectangles are respectively 60 cm, 30 cm, 20 cm.
17. Solution for Exercise 17 Page 70 Math Textbook Grade 7
Problem: Figure 9a depicts the shape of a milk carton and the amount of milk it contains. Figure 9b depicts the shape of a milk carton and the amount of milk it contains when the carton is placed upside down. Calculate the ratio of the volume of milk in the carton to the volume of the entire carton.
Guide:
Calculate the ratio of the volume of the milk-containing part to the volume of the non-milk-containing part.
With constant base area, the volume and height of the box are two directly proportional quantities.
Answer:
Considering Figure 9b, the part of the carton without milk has the shape of a rectangular box with the same base as the milk-containing part and a height of 12 - 7 = 5 (cm).
Considering Figure 9a, the milk-containing part has the shape of a rectangular box with the same base as the carton and a height of 6 cm.
Because the base area remains constant, the volume and height of the box are directly proportional, so the volume of the part without milk to the part with milk is the ratio of the height of the part without milk to the height of the part with milk, which is 5/6. This means the volume of the part with milk is 6 parts, the part without milk is 5 parts, and the total volume of the carton is: 5 + 6 = 11 parts.
So, the ratio of the volume of milk in the carton to the volume of the entire carton is 6/11.
Above is the documentation for solving math problems in Grade 7, pages 69 and 70, Volume 1 of the Kite book. Students can refer to it to improve their math skills and scores.
References:
- Solving Math 7 on page 80 Volume 1 of the Kite book - Exercise 1. Rectangular box. Cube
- Solving Math 7 on pages 85, 86 Volume 1 of the Kite book - Exercise 2. Triangular prism. Quadrilateral prism
