Lesson 3: Subtract Whole Numbers

New Concept

This lesson explores subtraction, the method for finding the difference between two whole numbers. You'll learn to express subtraction using proper notation, perform multi-digit calculations, and translate real-world scenarios into mathematical problems.

What’s next

Next, you'll dive into worked examples showing how to subtract multi-digit numbers, followed by interactive practice cards and challenge problems.

Property

When we subtract, we take one number away from another to find the difference. The notation we use to subtract 3 from 7 is $7 - 3$. We read $7 - 3$ as seven minus three and the result is the difference of seven and three.

Examples

• The expression $9 - 2$ is read as 'nine minus two', and the result is called 'the difference of nine and two'.
• The expression $35 - 15$ is read as 'thirty-five minus fifteen', which represents 'the difference of thirty-five and fifteen'.
• The expression $200 - 75$ is read as 'two hundred minus seventy-five', and the result is 'the difference of two hundred and seventy-five'.

Explanation

Subtraction is the process of finding what is left when you take a number away from another. The minus sign, $-$, is our key symbol for this action. The answer we get is called the 'difference'.

Property

A model can help us visualize the process of subtraction just as it did with addition. We can use base-10 blocks, where a block represents 1 and a rod represents 10.

To model subtraction, such as $7 - 3$:

1. Start by modeling the first number, 7, with 7 blocks.
2. Take away the second number, 3, by removing 3 blocks.
3. Count the remaining blocks to find the difference. In this case, 4 blocks remain, showing $7 - 3 = 4$.

Examples

• To model $7 - 3$, you would start with 7 one-blocks, remove 3 of them, and count the 4 that are left. Thus, $7 - 3 = 4$.
• To model $15 - 7$, start with 1 ten-rod and 5 one-blocks. Exchange the ten-rod for 10 ones, giving you 15 one-blocks. Removing 7 leaves 8 blocks. So, $15 - 7 = 8$.
• To model $52 - 28$, begin with 5 ten-rods and 2 one-blocks. Exchange 1 ten-rod for 10 ones. From 4 rods and 12 ones, remove 2 rods and 8 ones. This leaves 2 rods and 4 ones, or 24.

Property

Addition and subtraction are inverse operations. This means addition undoes subtraction, and subtraction undoes addition. We can check a subtraction problem by adding.

How to Find the Difference of Whole Numbers:

1. Write the numbers so each place value lines up vertically.
2. Subtract the digits in each place value, working from right to left. If the top digit is smaller than the bottom digit, borrow from the next place to the left.
3. Continue subtracting each place value, borrowing if needed.
4. Check by adding the result to the number you subtracted. The sum should be the number you started with.

Examples

• To solve $97 - 52$, subtract the ones ($7 - 2 = 5$) and then the tens ($9 - 5 = 4$). The result is 45.
• To solve $52 - 38$, borrow from the tens place. This gives $12 - 8 = 4$ in the ones place and $4 - 3 = 1$ in the tens place. The result is 14.
• To solve $305 - 87$, you need to borrow across the zero. The result is 218.

Property

To translate a word phrase into math notation for subtraction, look for keywords. The order of the numbers is important.

Examples

• The phrase 'the difference of 15 and 6' translates to the expression $15 - 6$, which equals 9.
• The phrase 'subtract 18 from 35' means you take 18 away from 35. This translates to $35 - 18$, which equals 17.
• The phrase '9 less than 20' means you start with 20 and take away 9. This translates to $20 - 9$, which equals 11.

Explanation

Certain words are signals for subtraction. While 'minus' and 'difference' keep the number order the same, phrases like 'less than' and 'subtracted from' flip the order. Pay close attention to these to set up the problem correctly.