Audrey has more than a decade of experience teaching elementary. She has a bachelor's in journalism and a master's in education.
Borrowing Using Concrete Objects
Borrowing can be used for any place value. You will sometimes have to borrow from the tens place, the hundreds place, the thousands place, and even larger place values. For this lesson, we'll use the ones and tens places to subtract two-digit numbers. When we use concrete objects, this means we are using actual objects we can hold in our hands to compose and decompose the numbers we're working with. When we borrow, we are actually breaking the number in the place to the left.
For example, in the problem 61 - 27, since you can't subtract 7 from 1, you have to break a stick of ten or borrow a stick of ten from the tens place. Once you do that, you'll have 5 tens. Then, you'll move that stick of ten to the ones place so now you have 11 ones. Now you can subtract. 11 - 7 = 4. 5 - 2 = 3. So if you have 3 in the tens place and 4 in the ones place, the answer to 61 - 27 is 34. This is what it looks like to subtract with base ten blocks.
Using Pictures to Subtract
Once you are comfortable using base ten blocks to borrow when you are subtracting, you'll soon be able to do the same thing drawing pictures. If you have 43 rocks in your collection and sell 28 of them, you'll have to borrow to subtract. You can draw 4 tens and 3 ones with base ten blocks. Next, in order to subtract, borrow a stick of ten from the 4, which will leave you with 3 tens. Then add the stick of ten to the 3 ones, which gives you 13. You are now ready to subtract. 13 - 8 = 5. 3 - 2 =1. If you have 1 ten and 5 ones, your answer is 15.
Borrowing Using Abstract Numbers
By this point you understand how to borrow using concrete objects like base ten blocks and by drawing pictures. Now we'll look at subtracting only using numbers. In order to do this, you must understand the place the numbers are in and their values. If you have 75 jelly beans on Easter and give 36 away, in order to subtract you have to borrow a stick of ten from the 7. Doing this causes the 7 to become a 6 and and 5 to become 15. From there, 15 - 6 = 9 and 6 - 3 = 3. Now you have 3 tens and 9 ones so 75 - 36 = 39.
When you're borrowing, you have to get a stick of ten from the tens place and add it to the ones place. The same is true if you're subtracting a three-digit number, except you borrow a stick of ten from the hundreds place and then add it to the tens place. After you've borrowed, subtract the numbers in the ones place and then the tens place. If it's a three-digit number, continue subtracting in the hundreds place.
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