A-114 Chapter 6 . Division 6.5 Fraction Division From The Ho In-1-Group Perspective Ow-Many-Units- Class Activity 6P Division Problems How-Many-Uni Its-In-1-Group
The Correct Answer and Explanation is :
In the context of fraction division, the “How-Many-Units-In-1-Group” perspective involves determining how many times a divisor (the number you’re dividing by) fits into the dividend (the number you’re dividing).
Understanding Fraction Division:
Dividing fractions can be approached by multiplying the dividend by the reciprocal of the divisor.
Example:
Consider the division problem: 3 ÷ 1/2.
- Identify the Dividend and Divisor:
- Dividend: 3
- Divisor: 1/2
- Find the Reciprocal of the Divisor:
- The reciprocal of 1/2 is 2/1.
- Multiply the Dividend by the Reciprocal:
- 3 × 2/1 = 6
Therefore, 3 ÷ 1/2 equals 6.
Applying the “How-Many-Units-In-1-Group” Perspective:
This perspective asks how many units of the divisor fit into the dividend.
- In this case, how many 1/2 units fit into 3?
- Since 1/2 fits into 3 exactly 6 times, the result is 6.
General Rule:
To divide by a fraction, multiply by its reciprocal.
Example:
For 5 ÷ 2/3:
- Identify the Dividend and Divisor:
- Dividend: 5
- Divisor: 2/3
- Find the Reciprocal of the Divisor:
- The reciprocal of 2/3 is 3/2.
- Multiply the Dividend by the Reciprocal:
- 5 × 3/2 = 15/2
- 15/2 can be written as 7.5 or 7 1/2.
Therefore, 5 ÷ 2/3 equals 7.5 or 7 1/2.
Conclusion:
The “How-Many-Units-In-1-Group” perspective simplifies fraction division by focusing on how many times the divisor fits into the dividend. By multiplying the dividend by the reciprocal of the divisor, you can efficiently solve fraction division problems.