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Solving 7th-grade math problems on pages 62 and 63 in textbook 1 Cánh Diều is a good study material for the lesson Proportional quantities. Students can refer to grasp the knowledge, study Math 7 well, improve their scores to the best.
Refer to many good Math 7 study materials:
- See the full set Solve Math 7 Cánh Diều textbook
- Solve 7th grade math problems on page 14 textbook 2 Connect Knowledge - Exercise: 22 Proportional quantities
- Solve 7th grade math problems on pages 14, 15 textbook 2 Creative Horizon - Exercise 2: Proportional quantities
Solve 7th-grade math problems on pages 62 and 63 in textbook 1 Cánh Diều
Exercise 7. Proportional Quantities
1. Solve Exercise 1 Page 62 Math Textbook Grade 7
Problem: The corresponding values of mass m (g) and volume V (cm3) are given by the following table:
a) Find the appropriate number for ?.
b) Are the quantities m and V directly proportional? Why?
c) Determine the proportionality coefficient of m with respect to V. Write the formula to calculate m according to V
Solution Guide:
Answer:
a)
2. Solve Exercise 2 Page 63 Math Textbook Grade 7
Problem: Given that x, y are two quantities proportional to each other:
a) Determine the proportionality coefficient of y with respect to x. Write the formula to calculate y according to x.
b) Determine the proportionality coefficient of x with respect to y. Write the formula to calculate x according to y.
c) Find the appropriate number for ?.
Solution Guide:
Answer:
c)
3. Solve Exercise 3 Page 63 Math Textbook Grade 7
Problem: On average, every 5 liters of seawater contains 175 grams of salt. How many grams of salt does an average of 12 liters of seawater contain?
Solution Guide:
The amount of seawater and the amount of salt it contains are directly proportional.
Answer:
Let the mass of salt in 12 liters of seawater be x (g) (x > 0).
Because the amount of seawater and the amount of salt it contains are directly proportional, according to the property of directly proportional quantities, we have:
So the mass of salt in 12 liters of seawater is 420 g.
4. Solve Exercise 4 Page 63 Math Textbook Grade 7
Problem: Every 12 minutes, a machine produces 27 products. How many minutes does it take for the machine to produce 45 products?
Solution Guide: Time to produce and number of products produced are directly proportional.
Answer:
Let the time to make 45 products be x (minutes) (x > 0)
Because the time to make and the number of products made are directly proportional, according to the property of directly proportional quantities, we have:
So the time to make 45 products is 20 minutes.
5. Solve Exercise 5 Page 63 Math Textbook Grade 7
Problem: To make cough medicine, people soak cherries with honey and sugar at the ratio: Every 0.5 kg of cherries requires 250 g of sugar and 0.5 liters of honey. With that ratio, if you want to soak 2.5 kg of cherries, how many kilograms of sugar and how many liters of honey do you need?
Solution Guide:
The mass of cherries and sugar is directly proportional.
The mass of cherries and the volume of honey are directly proportional.
Answer:
Convert 250 g = 0.25 kg.
Let the mass of sugar and the volume of honey needed to soak 2.5 kg of cherries be x (kg), y (liters) (x, y > 0).
Because the weight of lemons and sugar is directly proportional; the weight of lemons and the volume of honey is also directly proportional. Therefore, according to the nature of these two directly proportional quantities, we have:
So, 1.25 kilograms of sugar and 2.5 liters of honey are needed.
6. Solve Exercise 6 Page 63 Math Textbook Grade 7
Problem: According to the official announcement from the manufacturer, Ms. Hạnh's car consumes fuel as follows:
Consuming 9.9 liters per 100 kilometers on mixed roads.
Consuming 13.9 liters per 100 kilometers in urban areas;
Consuming 7.5 liters per 100 kilometers on highways.
a) According to the given data, if the fuel tank of that car contains 65 liters of gasoline, how many kilometers (rounded to the nearest unit) can Ms. Hạnh travel on urban roads? Mixed roads? Highways?
b) To travel a distance of 400 km on urban roads, how many liters of gasoline does Ms. Hạnh's car need at least?
c) To travel a distance of 300 km on mixed roads and 300 km on highways, how many liters of gasoline does Ms. Hạnh's car need at least?
Solution Guide:
The number of liters of gasoline and the distance traveled are two directly proportional quantities.
Answer:
a) When Ms. Hạnh travels on urban roads, she can travel:
65 : 13.9 . 100 ≈ 468 (km)
When Ms. Hạnh travels on mixed roads, she can travel:
65 : 9.9 . 100 ≈ 657 (km)
When Ms. Hạnh travels on highways, she can travel:
65 : 7.5 . 100 ≈ 867 (km)
b) To travel a distance of 400 km on urban roads, Ms. Hạnh's car needs at least:
400 : 100 . 13.9 = 55.6 (liters)
c) To travel a distance of 300 km on mixed roads and 300 km on highways, Ms. Hạnh's car needs at least:
300 : 100. 9.9 + 300 : 100 . 7.5 = 52.2 (liters).
Above is the solution for Grade 7 math problems on pages 62 and 63 of the Cánh Diều textbook, students can refer to solve exercises 1, 2, 3... regarding Directly Proportional Quantities easily and accurately.
Reference:
- Solving Math 7 page 68 Volume 1 of the Cánh Diều textbook - Exercise 8. Inverse Proportional Quantities
- Solving Math 7 pages 69, 70 Volume 1 of the Cánh Diều textbook - Chapter 2 review exercises
