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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
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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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: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.
**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.
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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