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1. Solve Exercise 6.33 Page 21 Math Book Grade 7
Problem: Determine all possible proportions that can be formed from the following four numbers: 0.2, 0.3, 0.8, 1.2.
Solution Guide:
+ Find the equation a.d = b.c from the given four numbers.
+ If a.d = b.c and a, b, c, d are all non-zero, then we have the following proportions:
Answer:
We have: 0.2 * 1.2 = 0.3 * 0.8.
From the above equation, we can form the following proportions:
2. Solve Exercise 6.34 Page 21 Math Book Grade 7
Solution Guide:
Answer:
3. Solve Exercise 6.35 Page 21 Math Book Grade 7
Solution Guide:
If a.d = b.c and a, b, c, d are all non-zero, then we have the following proportions:
Answer:
4. Solve Exercise 6.36 Page 21 Math Book Grade 7
Problem: Inch (pronounced as in-s) is the name of a length unit in the American measurement system. It is known that 1 inch = 2.54 cm.
a) Ask how tall a person who is 170 cm will be in inches (round the result to the nearest whole unit).
b) Is the height of a person measured in centimeters directly proportional to the height measured in inches? If yes, what is the proportionality factor?
Solution Guide:
a) Height of the person measured in inches = Height measured in centimeters : 2.54.
Answer:
a) A person who is 170 cm tall will have a height of: 170 : 2.54 = 66.93 (inch).
b) We observe that the height of a person measured in inches is equal to the height measured in centimeters divided by 2.54.
Therefore, the height of a person measured in centimeters is directly proportional to the height measured in inches. The proportionality factor is: 2.54
5. Solve Exercise 6.37 Page 21 Math Book Grade 7
Problem: The measures of three angles A, B, C of triangle ABC are in proportion to 5; 6; 7. Calculate the measures of the three angles of the triangle.
Solution Guide:
Let the measures of the three angles A, B, C of triangle ABC be x, y, z respectively (x, y, z > 0).
Represent the given conditions in formulaic form.
Apply the property of equal ratios to find x, y, z.
Answer:
Let x, y, and z be the measures of the three angles A, B, C of triangle ABC (unit: degrees; x, y, z > 0).
- According to the problem, we have: x + y + z = 180.
6. Solve Exercise 6.38 Page 21 Math Book Grade 7
Problem: Three teams of workers are assigned equal amounts of work. Team 1 completes the work in 4 days, Team 2 in 5 days, and Team 3 in 6 days. Calculate the number of workers for each team, knowing that Team 1 has 3 more workers than Team 2, and the productivity of the workers is the same throughout the process.
Solution Guide:
The number of workers for each team and the number of days to complete the work are inversely proportional quantities.
Answer:
Let x, y, and z be the number of workers in the first, second, and third teams respectively (x, y, z > 0).
- According to the problem, we have: x - y = 3 (Team 1 has 3 more workers than Team 2).
- Since the workload and productivity of the workers are the same, the number of workers for each team and the number of days to complete the work are inversely proportional quantities.
Hence, we deduce: x = 1.15 = 15; y = 1.12 = 12; z = 1.10 = 10.
Therefore, Team 1 has 15 workers, Team 2 has 12 workers, and Team 3 has 10 workers.
Here is the guide for solving 7th-grade Math page 21, Volume 2. Students can refer to solve 7th-grade Math page 24, Volume 2 and review 7th-grade Math page 20, Volume 2 to strengthen their understanding.
- Solve 7th-grade Math page 24, Volume 2 in the Connect Knowledge series - Exercise: 24 Algebraic expressions
- Solve 7th-grade Math page 20, Volume 2 in the Connect Knowledge series - Practice on page 19
