Subtract Whole Numbers

Use subtraction notation

Suppose there are seven bananas in a bowl. Elana uses three of them to make a smoothie. How many bananas are left in the bowl? To answer the question, we subtract three from seven. When we subtract, we take one number away from another to find the difference. The notation we use to subtract $3$ from $7$ is

We read $7 - 3$ as seven minus three, and the result is the difference of seven and three.

Example. Translate from math notation to words: (a) $8 - 1$ (b) $26 - 14$.

(a) We read this as eight minus one. The result is the difference of eight and one. (b) We read this as twenty-six minus fourteen. The result is the difference of twenty-six and fourteen.

Model subtraction of whole numbers

A model can help us visualize the process of subtraction, much as it did with addition. Again we use base-10 blocks: a block represents $1$ and a rod represents $10$. Let’s model the expression we just considered, $7 - 3$. We start with $7$ ones blocks, circle $3$ of them to show we are taking them away, and count what remains:

There are $4$ ones blocks left. We have shown that $7 - 3 = 4$.

What about a subtraction like $13 - 8$? Model $13$ with $1$ tens rod and $3$ ones blocks. There are not $8$ ones to take away — so exchange the tens rod for $10$ ones. Now there are $13$ ones, and we can take $8$ of them away, leaving $5$: so $13 - 8 = 5$.

The same idea works with larger numbers. To model $43 - 26$, start with $4$ tens and $3$ ones. To take away $26$ — that is, $2$ tens and $6$ ones — we cannot take $6$ ones from $3$ ones, so we exchange $1$ ten for $10$ ones, giving $3$ tens and $13$ ones. Taking away $2$ tens and $6$ ones leaves $1$ ten and $7$ ones: $43 - 26 = 17$.

Subtract whole numbers

Addition and subtraction are inverse operations — addition undoes subtraction, and subtraction undoes addition. We know $7 - 3 = 4$ because $4 + 3 = 7$. Knowing the addition facts helps with subtraction, and it also lets us check a subtraction by adding:

To subtract numbers with more than one digit, write the numbers vertically in columns, just as with addition — align the digits by place value, then subtract each column starting with the ones and working left.

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. Work from right to left, starting with the ones place. If the digit on top is less than the digit below, borrow as needed.
3. Continue subtracting each place value from right to left, borrowing if needed.
4. Check by adding.

When we modeled $43 - 26$, we exchanged $1$ ten for $10$ ones. Doing this without the model is called borrowing: we borrow $1$ from the tens place and add $10$ to the ones place.

Example. Subtract $43 - 26$. Line up the place values. We cannot subtract $6$ from $3$, so borrow $1$ ten: the $4$ tens become $3$ tens and the $3$ ones become $13$ ones. Subtract the ones, $13 - 6 = 7$, then the tens, $3 - 2 = 1$. The difference is $17$. Check: $17 + 26 = 43$. ✓

Example. Subtract $207 - 64$. Subtract the ones: $7 - 4 = 3$. For the tens, we cannot subtract $6$ from $0$, so borrow $1$ hundred, making $10$ tens: $10 - 6 = 4$. In the hundreds, $1 - 0 = 1$. The difference is $143$. Check: $143 + 64 = 207$. ✓

Example. Subtract $910 - 586$. We cannot subtract $6$ from $0$, so borrow $1$ ten to get $10$ ones: $10 - 6 = 4$. Now the tens place holds $0$, and we cannot subtract $8$ from $0$ — borrow $1$ hundred to get $10$ tens: $10 - 8 = 2$. Finally the hundreds: $8 - 5 = 3$. The difference is $324$. Check: $324 + 586 = 910$. ✓

Borrowing can happen in every column. In $2{,}162 - 479$, each of the ones, tens, and hundreds requires a borrow: $12 - 9 = 3$, $15 - 7 = 8$, $10 - 4 = 6$, and the thousands give $1 - 0 = 1$, so $2{,}162 - 479 = 1{,}683$. Check: $1{,}683 + 479 = 2{,}162$. ✓

Translate word phrases to math notation

As with addition, word phrases can tell us to operate on two numbers using subtraction. Look for key words that indicate subtraction:

Watch the order carefully. With difference, the numbers stay in the same order as the phrase: the difference of $13$ and $8$ translates to $13 - 8$, which is $5$. But subtract from and less than reverse the order: subtract $24$ from $43$ means take $24$ away from $43$, so it translates to $43 - 24$, which is $19$.

Subtract whole numbers in applications

To solve applications with subtraction, we use the same plan as with addition. First, determine what we are asked to find. Then write a phrase that gives the information to find it, translate the phrase into math notation, simplify, and finally answer the question with a complete sentence using the appropriate units.

Example. The temperature in Chicago one morning was $73$ degrees Fahrenheit. A cold front arrived, and by noon the temperature was $27$ degrees Fahrenheit. What was the difference between the morning and noon temperatures?

We are asked to find the difference between the two temperatures. The phrase is the difference of $73$ and $27$, which translates to $73 - 27$. Subtracting (borrow $1$ ten: $13 - 7 = 6$, then $6 - 2 = 4$) gives $46$. The difference in temperatures was $46$ degrees Fahrenheit.

Example. A washing machine is on sale for $399. Its regular price is $588. What is the difference between the regular price and the sale price?

The phrase is the difference between $588$ and $399$, which translates to $588 - 399$. Subtracting gives $189$, so the difference between the regular price and the sale price is $189.

Key terms

difference — the result of subtracting one number from another. inverse operations — operations that undo each other; addition and subtraction are inverse operations, which is why a subtraction can be checked by adding. borrowing — exchanging $1$ from the place to the left for $10$ in the current place so a column can be subtracted.

This section is adapted from Prealgebra 2e, Section 1.3: Subtract Whole Numbers by Lynn Marecek, MaryAnne Anthony-Smith, and Andrea Honeycutt Mathis, © OpenStax, licensed under CC BY-NC-SA 4.0. Access the original for free at openstax.org. Changes: condensed prose, redrew the base-10 block model as an accessible inline graphic and described the remaining models in prose, and converted practice problems (“Try Its”) into interactive exercises with instant feedback.