Understanding the Problem: 3 Divided by 1/2
To solve the division of 3 by 1/2 using repeated subtraction, we can visualize the process through shaded figures.
Step 1: Visualizing the Division
- Imagine a whole rectangle divided into 3 equal parts. Each part represents 1 unit.
- Now, we need to find out how many times we can subtract 1/2 from 3.
Step 2: Shaded Figures Representation
- Shade the entire rectangle, representing the initial value of 3.
- Next, visualize subtracting 1/2 repeatedly:
- 1st subtraction: Shade 1/2 of the rectangle (3 - 1/2 = 2.5)
- 2nd subtraction: Shade another 1/2 (2.5 - 1/2 = 2)
- 3rd subtraction: Shade another 1/2 (2 - 1/2 = 1.5)
- 4th subtraction: Shade another 1/2 (1.5 - 1/2 = 1)
- 5th subtraction: Shade another 1/2 (1 - 1/2 = 0.5)
- 6th subtraction: Shade another 1/2 (0.5 - 1/2 = 0)
Step 3: Counting the Subtractions
- We have successfully subtracted 1/2 a total of 6 times from 3.
Conclusion: Result of Division
- Therefore, 3 divided by 1/2 equals 6.
Final Thoughts
- This visual method effectively demonstrates division as repeated subtraction, making it easier to grasp the concept.
- Remember, dividing by a fraction can be interpreted as finding how many times the fraction fits into the whole!