Renaming Numbers For Subtraction
Renaming numbers for subtraction (borrowing/regrouping) is a Grade 4 skill in Saxon Math Intermediate 4 (Chapter 2). A number's value stays the same when its place values are regrouped: 53 = 5 tens + 3 ones = 4 tens + 13 ones. For 72 - 19: rename 72 as 6 tens + 12 ones by borrowing one ten, then subtract. For 81 - 39: rename 81 as 7 tens + 11 ones. The critical error is reducing the tens digit without adding 10 to the ones digit.
Key Concepts
Property A number's total value remains the same even when its place values are regrouped. For instance, 5 tens and 3 ones is equal to 4 tens and 13 ones. $$53 = 50 + 3 = 40 + 13$$.
Examples The number 72 can be represented as 7 tens and 2 ones, or it can be renamed as 6 tens and 12 ones. The total value is still seventy two. Before solving $45 17$, you can rename 45 (4 tens, 5 ones) as 3 tens and 15 ones to make the subtraction possible.
Explanation Think about money! Having 5 ten dollar bills and 3 one dollar bills is the same as having 4 ten dollar bills and 13 one dollar bills. The total is still 53 dollars, but the bills are just arranged differently.
Common Questions
What does it mean to rename a number for subtraction?
Regrouping or borrowing: taking one ten from the tens place and converting it to 10 ones in the ones place. The total value is unchanged: 53 = 5 tens + 3 ones = 4 tens + 13 ones.
How do you rename 72 for subtracting 9?
7 tens + 2 ones becomes 6 tens + 12 ones (borrow 1 ten). Now 12 - 9 = 3 in the ones. Then 6 - 1 = 5 in the tens. 72 - 19 = 53.
How do you rename 81 to prepare for 81 - 39?
81 is 8 tens + 1 one. Borrow 1 ten: 7 tens + 11 ones. Now you can subtract: 11 - 9 = 2 ones, 7 - 3 = 4 tens. Answer: 42.
What is the most common regrouping error?
Reducing the tens digit by 1 but forgetting to add 10 to the ones digit. Borrowing is a trade — always add 10 to the ones place after reducing the tens.
Why does regrouping not change the number's value?
Trading one 10 for ten 1s leaves the total unchanged. Think of swapping a $10 bill for ten $1 bills — you still have $10.