Master the essential skill of regrouping, also known as 'borrowing'. Learn what to do when the top digit in a column is smaller than the bottom digit by borrowing from a higher place value.
If you regroup from the hundreds place to the tens place, what happens?
The hundreds digit decreases by \(1\), and you add \(10\) to the tens digit. For example, in \(435\), regrouping would make it \(3\) hundreds and \(13\) tens.
$$ 435 - 142 = ? $$
Regroup from the hundreds. The \(4\) becomes a \(3\), and the \(3\) becomes \(13\). Tens: \(13 - 4 = 9\). Hundreds: \(3 - 1 = 2\). Ones: \(5 - 2 = 3\). The answer is \(293\).
$$ 671 - 238 = ? $$
Regroup from the tens. The \(7\) becomes a \(6\), and the \(1\) becomes \(11\). Ones: \(11 - 8 = 3\). Tens: \(6 - 3 = 3\). Hundreds: \(6 - 2 = 4\). The answer is \(433\).
Let's solve \(345 - 16\). The ones place is \(5 - 6\). What's the first step?
You can't take \(6\) from \(5\), so you must regroup from the tens place. The \(4\) becomes a \(3\), and the \(5\) becomes a \(15\).
$$ 345 - 16 = ? $$
After regrouping, you solve \(15 - 6 = 9\) in the ones place, \(3 - 1 = 2\) in the tens place, and bring down the \(3\) in the hundreds place. The answer is \(329\).
$$ 814 - 567 = ? $$
This requires regrouping twice. First for the ones place, then for the tens place. The final answer is \(247\).
$$ 523 - 48 = ? $$
\(475\)
$$ 953 - 879 = ? $$
\(74\)
What do the dashes and new numbers written above the problem represent during regrouping?
They show the new value of each place after 'borrowing'. This helps you keep track of the changes as you work through the problem.
What is 'regrouping' in subtraction?
Regrouping (or borrowing) is trading \(1\) from a higher place value for \(10\) of the next lower place value. For example, trading \(1\) ten for \(10\) ones.
When do you need to regroup in subtraction?
You need to regroup when the digit on top in a column is smaller than the digit on the bottom. For example, in \(42 - 17\), you can't subtract \(7\) from \(2\) in the ones column.
In the problem \(52 - 17\), how do you regroup?
Take \(1\) ten from the \(5\) (leaving \(4\) tens). Add the \(10\) ones to the \(2\) (making it \(12\) ones). The problem becomes \(12 - 7\) in the ones place and \(4 - 1\) in the tens place.
$$ 52 - 17 = ? $$
After regrouping, you solve \(12 - 7 = 5\) and \(4 - 1 = 3\). The answer is \(35\).
