Subtracting With Regrouping
Subtracting with regrouping is a Grade 4 skill in Saxon Math Intermediate 4 Chapter 3 that teaches borrowing across place values. When a top digit is smaller than the bottom digit in a column, students exchange 1 ten for 10 ones (or 1 hundred for 10 tens) to make the subtraction possible. For example, solving 536 minus 278 requires regrouping twice: in the ones place (creating 16 minus 8) and in the tens place (creating 12 minus 7), yielding 258. Special care is needed when borrowing across a zero, which requires borrowing from a higher place first.
Key Concepts
Property When you can't subtract in one column because the top digit is smaller, you must regroup or 'borrow'. You exchange 1 from the next higher place value for 10 of the current place value, like trading 1 ten for 10 ones.
Find $452 179$. Borrow from the tens place for the ones, then from the hundreds place for the tens. $$ \begin{align } &\phantom{ }\,452 \\ & \,179 \\ \hline &\phantom{ }\,4\,{}^{4}\!5\,{}^{12}\!2 \\ & \,1\,7\,9 \\ \hline &\phantom{ }\,{}^{3}\!4\,{}^{14}\!5\,{}^{12}\!2 \\ & \,1\,7\,9 \\ \hline &\phantom{ }\,2\,7\,3 \end{align } $$ Find $543 286$. First, borrow from the 4 to make 13 ones. Then, borrow from the 5 to make 13 tens. $$ \begin{array}{rrrr} & {}^4\!5 & {}^{13}\!4 & {}^{13}\!3 \\ & 2 & 8 & 6 \\ \hline & 2 & 5 & 7 \\ \end{array} $$.
Common Questions
What is regrouping in subtraction?
Regrouping means exchanging a unit from a higher place value to enable subtraction. For example, trading 1 ten for 10 ones so the ones digit becomes large enough to subtract from.
How do I subtract 278 from 536 with regrouping?
Ones: 6 minus 8 requires borrowing; 16 minus 8 equals 8. Tens: the borrowed-from 3 becomes 2; 2 minus 7 requires borrowing; 12 minus 7 equals 5. Hundreds: 4 minus 2 equals 2. Answer: 258.
How do I borrow across a zero?
If the tens digit is 0, you must first borrow from the hundreds place to give the tens place a value, then borrow from tens to give the ones place.
What is the most common mistake when regrouping?
Forgetting to reduce the digit you borrowed from. After borrowing 1 ten, that tens digit must decrease by 1.
How is regrouping like making change?
Just like breaking a 10-dollar bill into ten 1-dollar bills, borrowing 1 ten gives you 10 extra ones to work with in subtraction.