Regrouping In One Step
Grade 4 students learn one-step regrouping to subtract across zeros in Saxon Math Intermediate 4. Instead of borrowing twice from 405, students view the hundreds and tens digits together as 40 tens, borrow one ten to get 39 tens and 15 ones, then subtract normally. For 803 − 257, treat 80 as 80 tens, borrow one to get 79 tens, giving 13 ones. This Chapter 5 shortcut prevents the common error of only changing the hundreds digit and forgetting the tens, making multi-digit subtraction with zeros faster and more accurate.
Key Concepts
Property You can regroup across zero in a single step. Instead of borrowing twice, view the higher place values as a single number. For example, in $405$, see the '40' in the hundreds and tens place as '40 tens'.
Examples Example: Solve $405 126$. View 40 tens, borrow 1, leaving 39 tens and 15 ones. $$ \begin{align } &\phantom{ }39 {15} \\ &\cancel{40}5 \\ &126 \\ \hline &279 \end{align } $$ Example: Solve $900 442$. View 90 tens, borrow 1, leaving 89 tens and 10 ones. $$ \begin{align } &\phantom{ }89 {10} \\ &\cancel{90}0 \\ &442 \\ \hline &458 \end{align } $$ Example: Solve $602 345$. View 60 tens, borrow 1, leaving 59 tens and 12 ones. $$ \begin{align } &\phantom{ }59 {12} \\ &\cancel{60}2 \\ &345 \\ \hline &257 \end{align } $$.
Explanation Why take two steps when you can take one? Just group the digits together! Think of 405 not as 4 0 5, but as 'forty tens' and 5 ones. Borrowing one ten leaves you with 39 tens, making subtraction super quick and slick!
Common Questions
What is one-step regrouping in subtraction?
One-step regrouping lets you borrow across zeros in a single step. In 405, instead of trying to borrow from zero in the tens place, you view the first two digits (40) as 40 tens. Borrow one ten to get 39 tens and 15 ones, then subtract normally.
How do you solve 803 minus 257 using one-step regrouping?
View the 80 in 803 as 80 tens. Borrow one ten: you now have 79 tens and 13 ones. Subtract each column: 13 − 7 = 6, 9 − 5 = 4, 7 − 2 = 5. The answer is 546.
Why is one-step regrouping faster than borrowing twice?
Borrowing twice requires two separate steps and leaves room for errors at each stage. One-step regrouping treats multiple place values as a single group, reducing steps and keeping calculations simpler.
What is the most common mistake in one-step regrouping?
The most common mistake is changing the hundreds digit but forgetting to change the tens digit. When borrowing from 80 tens, the result is 79 tens — not 70. Always decrease the whole group number by exactly one.
What grade level teaches one-step regrouping?
One-step regrouping is taught in Grade 4 in Saxon Math Intermediate 4, Chapter 5 (Lessons 41–50), as a strategy for efficient multi-digit subtraction with zeros.