- Decomposing a ten (borrowing) is required when the units digit of the minuend is smaller than the units digit of the subtrahend.
- In \(26 - 4\), \(6 \ge 4\), so no regrouping is needed.
- In \(34 - 8\), \(4 < 8\), so regrouping (decomposing a ten) is required.
- In \(47 - 3\), \(7 \ge 3\), so no regrouping is needed.
- Only the expression \(\boxed{34 - 8}\) requires decomposing a ten.
Explanation
- Understanding Decomposing a Ten
Decomposing a ten (often referred to as borrowing or regrouping) in subtraction is necessary when the digit in the units place of the number being subtracted (the subtrahend) is greater than the digit in the units place of the number we are subtracting from (the minuend). In such cases, we must break apart one of the tens from the minuend to add it to the units, allowing us to perform the subtraction correctly. We examine the three expressions: \(26 - 4\), \(34 - 8\), and \(47 - 3\).
- Analyzing 26 - 4
First, consider the expression \(26 - 4\). The minuend is 26, which is \(2\) tens and \(6\) units. The subtrahend is 4. Since the units digit of the minuend (\(6\)) is greater than or equal to the units digit of the subtrahend (\(4\)), we can subtract directly: \(6 - 4 = 2\). Thus, the difference is \(22\). This expression does not require decomposing a ten.
- Analyzing 34 - 8
Next, consider the expression \(34 - 8\). The minuend is 34, which is \(3\) tens and \(4\) units. The subtrahend is 8. Since the units digit of the minuend (\(4\)) is less than the units digit of the subtrahend (\(8\)), we cannot subtract 8 from 4 directly. We must decompose one ten from the 3 tens, leaving 2 tens and converting 1 ten into 10 units. Now, we have \(10 + 4 = 14\) units. Subtraction becomes \(14 - 8 = 6\), and we keep the remaining 2 tens. The difference is 26. Therefore, this expression requires decomposing a ten.
- Analyzing 47 - 3 and Final Conclusion
Finally, consider the expression \(47 - 3\). The minuend is 47, which is \(4\) tens and \(7\) units. The subtrahend is 3. Since the units digit of the minuend (\(7\)) is greater than or equal to the units digit of the subtrahend (\(3\)), we can subtract directly: \(7 - 3 = 4\). The difference is 44. This expression does not require decomposing a ten. The only expression that requires regrouping is \(34 - 8\). The final result is \(\boxed{34 - 8}\).
Examples
Imagine you are at a candy store with 34 pieces of candy, and you want to give 8 pieces to a friend. Since 4 is less than 8, you cannot simply take 8 away from the 4 single pieces you are holding; you must open one of your 3 bags of 10 to get more single pieces. By opening that bag, you gain 10 more pieces, making it easier to share the candy. This process of opening a 'ten' to handle smaller units is exactly what we do when we decompose a ten in subtraction.