Regrouping in subtraction fractions, often called "borrowing," involves rewriting a mixed number to increase the fractional part so that you can subtract a larger fraction from a smaller one.
Here's a breakdown of the process:
When Do You Need to Regroup?
You need to regroup when subtracting fractions when the fraction you are subtracting from (the minuend) is smaller than the fraction you are subtracting (the subtrahend). For example, if you're trying to solve 5 1/4 - 2 3/4, you'll need to regroup because 1/4 is smaller than 3/4.
The Regrouping Process:
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Identify the Need: Make sure the fractional part of the first mixed number (minuend) is smaller than the fractional part of the second mixed number (subtrahend). If it is, you need to regroup.
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Borrow from the Whole Number: Decrease the whole number part of the first mixed number by 1.
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Convert the Borrowed 1 to a Fraction: Convert the borrowed 1 into a fraction with the same denominator as the existing fraction. For example, if your denominator is 4, then 1 becomes 4/4.
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Add the Fractions: Add the new fraction (representing the borrowed 1) to the existing fraction in the first mixed number.
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Rewrite the Mixed Number: You now have a new, equivalent mixed number where the fractional part is large enough to subtract from.
Example:
Let's say you want to solve 5 1/4 - 2 3/4:
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Identify the Need: 1/4 < 3/4, so we need to regroup.
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Borrow from the Whole Number: Reduce the 5 to a 4.
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Convert the Borrowed 1 to a Fraction: 1 becomes 4/4 (because the denominator is 4).
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Add the Fractions: 1/4 + 4/4 = 5/4
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Rewrite the Mixed Number: 5 1/4 becomes 4 5/4.
Now you can subtract: 4 5/4 - 2 3/4 = 2 2/4, which simplifies to 2 1/2.
Example from Reference:
As mentioned in the reference text, 252 and 4/6 is regrouped to 251 + 1 and 4/6. Then, the '1' is converted to 6/6, so it becomes 251 and (4/6 + 6/6) = 251 and 10/6. This allows you to subtract a larger fraction (e.g., 5/6, 7/6, etc.) from 10/6.
Key Takeaways:
- Regrouping is essential for subtracting fractions when the first fraction is smaller than the second.
- You "borrow" 1 from the whole number, convert it to a fraction with the same denominator, and add it to the existing fraction.
