regrouping in the subtraction problem 231 – 67. Draw (simplified) pictures to aid your explanation.
regrouping in the subtraction problem 231 – 67. Draw (simplified) pictures to aid your explanation.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:To explain regrouping in the subtraction problem 231 - 67, you can use simplified pictures to aid your explanation.
**Step-by-Step Explanation:**
1. **Number Breakdown:**
- **231**: This number consists of 2 hundreds, 3 tens, and 1 one.
- **67**: This number consists of 6 tens and 7 ones.
2. **Subtraction Process:**
- Start subtracting from the rightmost digit (ones place).
- **Ones Place:** You cannot subtract 7 from 1. Thus, you need to regroup (borrow) from the tens place.
3. **Regrouping:**
- Take 1 ten from the tens place of 231, leaving 2 tens. Convert this into 10 ones and add it to the 1 one. This gives you 11 ones.
- Now subtract 7 ones from 11 ones, resulting in 4 ones.
4. **Tens Place:**
- After regrouping, you have 2 tens in the number 231.
- Subtract 6 tens from 2 tens. To do this, you need to borrow 1 hundred from the hundreds place, converting it into 10 tens, and add it to the remaining 2 tens. This gives you 12 tens altogether.
- Now subtract 6 from 12, resulting in 6 tens.
5. **Hundreds Place:**
- After borrowing, you have 1 hundred left.
- There is no need for additional subtraction in the hundreds place for this problem.
6. **Final Result:**
- The subtraction gives you 164.
**Visual Aid:**
To visualize this, you can draw blocks or use place value charts:
- **Hundreds:** Represented with large squares.
- **Tens:** Represented with vertical lines or rods.
- **Ones:** Represented with small dots or circles.
By arranging them as described, you provide a clear visual representation of regrouping that aids in understanding the subtraction process.

Transcribed Image Text:**Using Bundled Toothpicks for Educational Purposes**
**Question:**
Describe how to use bundled toothpicks (or bundles of other objects) to explain.
**Explanation:**
Bundled toothpicks can be an effective visual and tactile teaching tool in various educational contexts. Here’s how they can be used:
1. **Mathematics**:
- **Counting and Grouping**: Use bundles of ten toothpicks to teach counting by tens and reinforce the concept of grouping.
- **Place Value**: Demonstrate place value by grouping into units, tens, and hundreds.
- **Addition and Subtraction**: Manipulate bundles to easily visualize and solve problems.
2. **Science**:
- **Structures and Models**: Construct simple models to explain molecular structures or design simple engineering projects.
- **Forces and Stability**: Use them to explore balance, tension, and compression in structures.
3. **Art and Creativity**:
- **Sculpture**: Create 3D art projects, promoting creativity and spatial awareness.
Using bundled objects is a hands-on approach that can enhance comprehension and engagement across various subjects.
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