Solving 7th-grade Math page 14 exercise 2 in Connect Knowledge Book is a valuable resource for students, aiding in solving exercises 6.17, 6.18, 6.19, 6.20, 6.21 in the textbook's lesson on Proportional Quantities. Additionally, it serves as a tool for teachers in lesson planning with ease and speed.
Other recommended Math 7 study materials:
- Solving 7th-grade Math, Connect Knowledge Book
- Solve 7th-grade Math page 62, 63 exercise 1, Kite Book - Lesson 7: Proportional Quantities
- Solve 7th-grade Math page 14, 15 exercise 2, Creative Horizon Book - Lesson 2: Proportional Quantities
Solving 7th-grade Math page 14 exercise 2, Connect Knowledge Book:
Proportional Quantities
1. Solve Exercise 6.17 Page 14 Math Textbook Grade 7
Problem: Given x and y as two proportional quantities. Replace each '?' in the table below with a suitable number.
Write the formula describing the dependency relationship between the two quantities x and y.
Solution Guide:
The formula describing the dependency relationship between the two quantities x and y is: y = -3x.
2. Solve Exercise 6.18 Page 14 Math Textbook Grade 7
Problem: According to the value table below, are the two quantities x and y proportional?
Solution Guide:
Answer:
3. Solve Exercise 6.19 Page 14 Math Textbook Grade 7
Problem: Given y is proportional to x with a proportionality constant a, and x is proportional to z with a proportionality constant b. Ask whether y is proportional to z. If yes, what is the proportionality constant?
Solution Guide:
If the quantity y is proportional to the quantity x with a proportionality constant a, then y = ax.
Answer:
So, y is proportional to x with a proportionality constant a.
Equation: y = a.x (1)
x is proportional to z with a proportionality constant b.
Equation: x = b.z (2)
Substitute (2) into (1), we get:
Equation: y = a.b.z
So, y is proportional to z with a proportionality constant: a.b.
4. Solve Exercise 6.20 Page 14 Math Textbook Grade 7
Problem: Two rectangular water tanks have equal length and width, but the height of the first tank is 3/4 of the height of the second tank. It takes 4.5 hours to pump water into the first tank. How much time does it take to pump water into the second tank (using a pump with the same power)?
Solution Approach: The height of the tank and the time to pump water into the tank are two proportional quantities.
Answer:
Let x be the time to pump water into the second tank (x > 0).
Since the height of the tank and the time to pump water into the tank are proportional quantities, we have:
Result: It takes 6 hours to pump water into the second tank.
5. Solve Exercise 6.21 Page 14 Math Textbook Grade 7
Problem: To prepare for students' experiments, Ms. Huong divides 1.5 liters of chemical into three parts in proportion to 4: 5: 6 and stores them in three bottles. How much chemical does each bottle contain?
Solution Approach:
Let the amount of chemical in each bottle be x, y, z (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, z represent the number of liters of chemical in each bottle, respectively (x, y, z > 0).
Then, x + y + z = 1.5.
Hence, x = 0.1 * 4 = 0.4; y = 0.1 * 5 = 0.5; z = 0.1 * 6 = 0.6.
Therefore, the three bottles contain 0.4 liters, 0.5 liters, and 0.6 liters of chemical, respectively.
Here is the guide for solving 7th-grade Math page 14 exercise 2. Students can also refer to solving 7th-grade Math page 18, 19, and page 20, as well as reviewing solving 7th-grade Math page 10 exercise 2 to reinforce their knowledge.
- Solve 7th-grade Math page 18 exercise 2, Connect Knowledge Book - Lesson: 23 Proportional Inverse Quantities
- Solve 7th-grade Math page 20 exercise 2, Connect Knowledge Book - Practice focused on page 19
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