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Solving algebraic expressions in 8th-grade pages 44, 45, 46, 47, 48 of Kite book volume 1 - Exercise 3: Multiplication, and division of algebraic fractions are practical exercises on the rules of multiplying two algebraic fractions and dividing algebraic fractions. Invite students to refer to the answers to grasp the lesson content.
Solving 8th-grade Math Kite volume 1 pages 44, 45, 46, 47, 48
Exercise 3: Multiplication, and division of algebraic fractions
Solving Math Problems in 8th Grade Kite Volume 1 Page 47
1. Solve problem 1 - Kite 8th Grade Volume 1 Page 47
Problem Statement:
Perform the arithmetic operation:
Solution Method:
Apply the rule of multiplying two algebraic fractions for calculation.
Answer:
Solving 8th-grade Math Kite volume 1 page 48
2. Solve problem 2 - Kite 8th Grade Volume 1 Page 48
Problem Statement:
Perform the arithmetic operation:
Solution Method:
Apply the rule of dividing two algebraic fractions to perform the arithmetic operation.
Answer:
3. Solve problem 3 - Kite 8th Grade Volume 1 Page 48
Problem Statement:
Calculate reasonably:
Solution Method:
Apply the properties of algebraic fraction multiplication to calculate in a reasonable manner.
Answer:
Utilize algebraic operations, including multiplication and fraction division, to compute algebraic expressions with results independent of variables.
Answer:
Solving Challenge 5 - Kite Class 8 Volume 1 page 48
Task Description:
A planned industrial plant needs to produce 120 tons of goods within a specified number of days. Thanks to technological improvements, the plant has completed the plan one day ahead and produced an additional 5 tons of goods. Let x represent the planned number of days.
a) The number of tons of goods the plant produces per day as planned;
b) The actual number of tons of goods the plant produces per day;
c) The ratio of the actual number of tons of goods produced per day to the planned production per day.
Solution Approach:
The number of tons produced in a day is the total tons produced divided by the total number of days worked.
Answer:
The total tons of goods the plant produces according to the plan is: 120 (tons)
The actual total tons of goods the plant produces is: 120 + 5 = 125 (tons)
The planned total number of days worked is: x (days)
The actual total number of days worked is: x - 1 (day)
a) The number of tons of goods the plant produces per day as planned is: 120/x (tons)
b) The actual number of tons of goods the plant produces per day is: 125/(x-1) (tons)
c) The ratio of the actual number of tons of goods produced per day to the planned production per day is:
Solving Challenge 6 - Kite Class 8 Volume 1 page 48
Task Description:
A cargo car travels from point A to point B in x hours. After delivering the goods at point B, the car returns to point A, but the time it takes to travel back to A is only x-1 hours. Knowing that the distance AB is 160 km, express it as a fraction in terms of x:
a) The speed of the car when traveling from A to B;
b) The speed of the car when traveling from B to A;
c) The ratio of the speed of the car when traveling from A to B to the speed of the car when traveling from B to A.
Solution Approach:
The speed of the car is the distance divided by the time.
Answer:
The distance AB is 160 km.
The time the car travels from A to B is x hours.
The time the car travels from B to A is x - 1 hours.
a) The speed of the car when traveling from A to B is: 160/x (km/h)
b) The speed of the car when traveling from B to A is: 160/(x-1) (km/h)
c) The ratio of the speed of the car when traveling from A to B to the speed of the car when traveling from B to A is:
Here is the guidance for solving math problems in Grade 8, pages 44-48 of Kite Volume 1: Multiplication, division, and algebraic fractions. To prepare for the next lesson, you can preview the instructions for solving math problems in Grade 8, page 49 of Kite Volume 1 - Exercise at the end of Chapter II. Additionally, the section Solving math problems in Grade 8, pages 38-43 of Kite Volume 1 - Exercise 2: Algebraic addition and subtraction will help reinforce your knowledge; you can review the answers here. Best of luck with your math studies.
Explore more Grade 8 math resources:
- Solving math problems in Grade 8 with Kite
