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Subtract Whole Numbers

Use subtraction notation

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

\[7-3\]

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

Example

Try it.

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

Solution

ⓐ We read this as eight minus one. The result is the difference of eight and one.
ⓑ 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 will use $\text{base-10}$ blocks. Remember a block represents 1 and a rod represents 10. Let’s start by modeling the subtraction expression we just considered, $7-3.$

We start by modeling the first number, 7.
Now take away the second number, 3. We'll circle 3 blocks to show that we are taking them away.
Count the number of blocks remaining.
There are 4 ones blocks left.	We have shown that $7-3=4$.

Example

Try it.

Model the subtraction: $8-2.$

Solution

$8-2$ means the difference of 8 and 2.
Model the first, 8.
Take away the second number, 2.
Count the number of blocks remaining.
There are 6 ones blocks left.	We have shown that $8-2=6$.

Example

Try it.

Model the subtraction: $13-8.$

Solution

Model the first number, 13. We use 1 ten and 3 ones.
Take away the second number, 8. However, there are not 8 ones, so we will exchange the 1 ten for 10 ones.
Now we can take away 8 ones.
Count the blocks remaining.
There are five ones left.	We have shown that $13-8=5$.

As we did with addition, we can describe the models as ones blocks and tens rods, or we can simply say ones and tens.

Example

Try it.

Model the subtraction: $43-26.$

Solution

Because $43-26$ means $43$ take away $26,$ we begin by modeling the $43.$

Now, we need to take away $26,$ which is $2$ tens and $6$ ones. We cannot take away $6$ ones from $3$ ones. So, we exchange $1$ ten for $10$ ones.

Now we can take away $2$ tens and $6$ ones.

Count the number of blocks remaining. There is $1$ ten and $7$ ones, which is $17.$

$43-26=17$

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 all the addition number facts will help with subtraction. Then we can check subtraction by adding. In the examples above, our subtractions can be checked by addition.

\[\begin{array}{lllllll}\ 7-3=4 & & & \text{because} & & & \ 4+3=7 \\ 13-8=5 & & & \text{because} & & & \ 5+8=13 \\ 43-26=17 & & & \text{because} & & & 17+26=43\end{array}\]

Example

Try it.

Subtract and then check by adding:

ⓐ $9-7$
ⓑ $8-3.$

Solution

ⓐ
	$9-7$
Subtract 7 from 9.	$2$
Check with addition. $2+7=9✓$

ⓑ
	$8-3$
Subtract 3 from 8.	$5$
Check with addition. $5+3=8✓$

To subtract numbers with more than one digit, it is usually easier to write the numbers vertically in columns just as we did for addition. Align the digits by place value, and then subtract each column starting with the ones and then working to the left.

Example

Try it.

Subtract and then check by adding: $89-61.$

Solution

Write the numbers so the ones and tens digits line up vertically.	$\begin{array}{l}89\ \\ \underset{\text{____}}{-61}\end{array}$
Subtract the digits in each place value. Subtract the ones: $9-1=8$ Subtract the tens: $8-6=2$	$\begin{array}{l}89\ \\ \underset{\text{____}}{-61} \\ 28\ \end{array}$
Check using addition. $\begin{array}{l}28\ \\ \underset{\text{____}}{+61} \\ 89\ \end{array}$

Our answer is correct.

When we modeled subtracting $26$ from $43,$ we exchanged $1$ ten for $10$ ones. When we do this without the model, we say we borrow $1$ from the tens place and add $10$ to the ones place.

Condensed — the full section is in OpenStax Prealgebra 2e.

Translate Word Phrases to Math Notation

As with addition, word phrases can tell us to operate on two numbers using subtraction. To translate from a word phrase to math notation, we look for key words that indicate subtraction. Some of the words that indicate subtraction are listed in .

Operation	Word Phrase	Example	Expression
Subtraction	minus	$5$ minus $1$	$5-1$
	difference	the difference of $9$ and $4$	$9-4$
	decreased by	$7$ decreased by $3$	$7-3$
	less than	$5$ less than $8$	$8-5$
	subtracted from	$1$ subtracted from $6$	$6-1$

Example

Try it.

Translate and then simplify:

ⓐ the difference of $13$ and $8$
ⓑ subtract $24$ from $43$

Solution

ⓐ
The word difference tells us to subtract the two numbers. The numbers stay in the same order as in the phrase.

the difference of 13 and 8
Translate. $13-8$
Simplify. 5
ⓑ
The words subtract from tells us to take the first number away from the second. We must be careful to get the order correct.

subtract 24 from 43
Translate. $43-24$
Simplify. 19

Subtract Whole Numbers in Applications

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

Example

Try it.

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 temperature in the morning and the temperature at noon?

Solution

We are asked to find the difference between the morning temperature and the noon temperature.

Write a phrase.	the difference of 73 and 27
Translate to math notation. Difference tells us to subtract.	$73-27$
Then we do the subtraction.
Write a sentence to answer the question.	The difference in temperatures was 46 degrees Fahrenheit.

Example

Try it.

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

Solution

We are asked to find the difference between the regular price and the sale price.

Write a phrase.	the difference between 588 and 399
Translate to math notation.	$588-399$
Subtract.
Write a sentence to answer the question.	The difference between the regular price and the sale price is $189.

Key Concepts

Operation	Notation	Expression	Read as	Result
Subtraction	$-$	$7-3$	seven minus three	the difference of $7$ and $3$

Subtract 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.

Subtract Whole Numbers

Use Subtraction Notation

In the following exercises, translate from math notation to words.

Try it.

$15-9$

Solution

fifteen minus nine; the difference of fifteen and nine

Try it.

$18-16$

Try it.

$42-35$

Solution

forty-two minus thirty-five; the difference of forty-two and thirty-five

Try it.

$83-64$

Try it.

$675-350$

Solution

six hundred seventy-five minus three hundred fifty; the difference of six hundred seventy-five and three hundred fifty

Try it.

$790-525$

Model Subtraction of Whole Numbers

In the following exercises, model the subtraction.

Try it.

$5-2$

Solution

Try it.

$8-4$

Try it.

$6-3$

Solution

Try it.

$7-5$

Try it.

$18-5$

Solution

Try it.

$19-8$

Try it.

$17-8$

Solution

Try it.

$17-9$

Try it.

$35-13$

Solution

Try it.

$32-11$

Try it.

$61-47$

Solution

Try it.

$55-36$

Subtract Whole Numbers

In the following exercises, subtract and then check by adding.

Try it.

$9-4$

Solution

Try it.

$9-3$

Try it.

$8-0$

Solution

Try it.

$2-0$

Try it.

$38-16$

Solution

Try it.

$45-21$

Try it.

$85-52$

Solution

Try it.

$99-47$

Try it.

$493-370$

Solution

123

Try it.

$268-106$

Try it.

$5,946-4,625$

Solution

1,321

Try it.

$7,775-3,251$

Try it.

$75-47$

Solution

Try it.

$63-59$

Try it.

$461-239$

Solution

222

Try it.

$486-257$

Try it.

$525-179$

Solution

346

Try it.

$542-288$

Try it.

$6,318-2,799$

Solution

3,519

Try it.

$8,153-3,978$

Try it.

$2,150-964$

Solution

1,186

Try it.

$4,245-899$

Try it.

$43,650-8,982$

Solution

34,668

Try it.

$35,162-7,885$

Translate Word Phrases to Algebraic Expressions

In the following exercises, translate and simplify.

Try it.

The difference of $10$ and $3$

Solution

10 − 3; 7

Try it.

The difference of $12$ and $8$

Try it.

The difference of $15$ and $4$

Solution

15 − 4; 11

Try it.

The difference of $18$ and $7$

Try it.

Subtract $6$ from $9$

Solution

9 − 6; 3

Try it.

Subtract $8$ from $9$

Try it.

Subtract $28$ from $75$

Solution

75 − 28; 47

Try it.

Subtract $59$ from $81$

Try it.

$45$ decreased by $20$

Solution

45 − 20; 25

Try it.

$37$ decreased by $24$

Try it.

$92$ decreased by $67$

Solution

92 − 67; 25

Try it.

$75$ decreased by $49$

Try it.

$12$ less than $16$

Solution

16 − 12; 4

Try it.

$15$ less than $19$

Try it.

$38$ less than $61$

Solution

61 − 38; 23

Try it.

$47$ less than $62$

Mixed Practice

In the following exercises, simplify.

Try it.

$76-47$

Solution

Try it.

$91-53$

Try it.

$256-184$

Solution

Try it.

$305-262$

Try it.

$719+341$

Solution

1,060

Try it.

$647+528$

Try it.

$2,015-1,993$

Solution

Try it.

$2,020-1,984$

In the following exercises, translate and simplify.

Try it.

Seventy-five more than thirty-five

Solution

75 + 35; 110

Try it.

Sixty more than ninety-three

Try it.

$13$ less than $41$

Solution

41 − 13; 28

Try it.

$28$ less than $36$

Try it.

The difference of $100$ and $76$

Solution

100 − 76; 24

Try it.

The difference of $1,000$ and $945$

Subtract Whole Numbers in Applications

In the following exercises, solve.

Try it.

Temperature The high temperature on June $2$ in Las Vegas was $80$ degrees and the low temperature was $63$ degrees. What was the difference between the high and low temperatures?

Solution

The difference between the high and low temperature was 17 degrees

Try it.

Temperature The high temperature on June $1$ in Phoenix was $97$ degrees and the low was $73$ degrees. What was the difference between the high and low temperatures?

Try it.

Class size Olivia’s third grade class has $35$ children. Last year, her second grade class had $22$ children. What is the difference between the number of children in Olivia’s third grade class and her second grade class?

Solution

The difference between the third grade and second grade was 13 children.

Try it.

Class size There are $82$ students in the school band and $46$ in the school orchestra. What is the difference between the number of students in the band and the orchestra?

Try it.

Shopping A mountain bike is on sale for $\text{\$399}.$ Its regular price is $\text{\$650}.$ What is the difference between the regular price and the sale price?

Solution

The difference between the regular price and sale price is $251.

Try it.

Shopping A mattress set is on sale for $\text{\$755}.$ Its regular price is $\text{\$1,600}.$ What is the difference between the regular price and the sale price?

Try it.

Savings John wants to buy a laptop that costs $\text{\$840}.$ He has $\text{\$685}$ in his savings account. How much more does he need to save in order to buy the laptop?

Solution

John needs to save $155 more.

Try it.

Banking Mason had $\text{\$1,125}$ in his checking account. He spent $\text{\$892}.$ How much money does he have left?

Condensed — the full section is in OpenStax Prealgebra 2e.

Practice (40)

Try each one on paper first. Reveal the answer to check; verified ones can be opened in the solver for every step.

Model $3+4$ using base-ten blocks.
If you missed this problem, review .
Add: $324+586.$
If you missed this problem, review .

Rivela la risposta

$910$
Translate from math notation to words: ⓐ $8-1$ ⓑ $26-14$.
Rivela la risposta
- ⓐ We read this as eight minus one. The result is the difference of eight and one.
- ⓑ We read this as twenty-six minus fourteen. The result is the difference of twenty-six and fourteen.
1. ⓐ $12-4$
2. ⓑ $29-11$
Rivela la risposta
1. ⓐ twelve minus four; the difference of twelve and four
2. ⓑ twenty-nine minus eleven; the difference of twenty-nine and eleven
1. ⓐ $11-2$
2. ⓑ $29-12$
Rivela la risposta
1. ⓐ eleven minus two; the difference of eleven and two
2. ⓑ twenty-nine minus twelve; the difference of twenty-nine and twelve
Model the subtraction: $8-2.$

Rivela la risposta

$8-2$ means the difference of 8 and 2.
Model the first, 8.
Take away the second number, 2.
Count the number of blocks remaining.
There are 6 ones blocks left. We have shown that $8-2=6$.
Model: $9-6.$

Rivela la risposta
Model: $6-1.$

Rivela la risposta

Model the subtraction: $13-8.$

Rivela la risposta

Model the first number, 13. We use 1 ten and 3 ones.
Take away the second number, 8. However, there are not 8 ones, so we will exchange the 1 ten for 10 ones.
Now we can take away 8 ones.
Count the blocks remaining.
There are five ones left.	We have shown that $13-8=5$.

As we did with addition, we can describe the models as ones blocks and tens rods, or we can simply say ones and tens.

Model the subtraction: $12-7.$

Rivela la risposta
Model the subtraction: $14-8.$

Rivela la risposta
Model the subtraction: $43-26.$

Rivela la risposta

Because $43-26$ means $43$ take away $26,$ we begin by modeling the $43.$

Now, we need to take away $26,$ which is $2$ tens and $6$ ones. We cannot take away $6$ ones from $3$ ones. So, we exchange $1$ ten for $10$ ones.

Now we can take away $2$ tens and $6$ ones.

Count the number of blocks remaining. There is $1$ ten and $7$ ones, which is $17.$
$43-26=17$
Model the subtraction: $42-27.$

Rivela la risposta
Model the subtraction: $45-29.$

Rivela la risposta
Subtract and then check by adding:
1. ⓐ $9-7$
2. ⓑ $8-3.$
Rivela la risposta

ⓐ
$9-7$
Subtract 7 from 9. $2$
Check with addition.
$2+7=9✓$
ⓑ
$8-3$
Subtract 3 from 8. $5$
Check with addition.
$5+3=8✓$
Subtract and then check by adding:
$7-0$

Rivela la risposta

7 − 0 = 7; 7 + 0 = 7
Subtract and then check by adding:
$6-2$

Rivela la risposta

6 − 2 = 4; 2 + 4 = 6

Subtract and then check by adding: $89-61.$

Rivela la risposta

Write the numbers so the ones and tens digits line up vertically.	$\begin{array}{l}89\ \\ \underset{\text{____}}{-61}\end{array}$
Subtract the digits in each place value. Subtract the ones: $9-1=8$ Subtract the tens: $8-6=2$	$\begin{array}{l}89\ \\ \underset{\text{____}}{-61} \\ 28\ \end{array}$
Check using addition. $\begin{array}{l}28\ \\ \underset{\text{____}}{+61} \\ 89\ \end{array}$

Our answer is correct.

Subtract and then check by adding: $86-54.$

Rivela la risposta

86 − 54 = 32 because 54 + 32 = 86
Subtract and then check by adding: $99-74.$

Rivela la risposta

99 − 74 = 25 because 74 + 25 = 99

Subtract: $43-26.$

Rivela la risposta

Write the numbers so each place value lines up vertically.
Subtract the ones. We cannot subtract 6 from 3, so we borrow 1 ten. This makes 3 tens and 13 ones. We write these numbers above each place and cross out the original digits.
Now we can subtract the ones. $13-6=7.$ We write the 7 in the ones place in the difference.
Now we subtract the tens. $3-2=1.$ We write the 1 in the tens place in the difference.
Check by adding. Our answer is correct.

Subtract and then check by adding: $93-58.$

Rivela la risposta

93 − 58 = 35 because 58 + 35 = 93
Subtract and then check by adding: $81-39.$

Rivela la risposta

81 − 39 = 42 because 42 + 39 = 81

Subtract and then check by adding: $207-64.$

Rivela la risposta

Write the numbers so each place value lines up vertically.
Subtract the ones. $7-4=3.$ Write the 3 in the ones place in the difference.
Subtract the tens. We cannot subtract 6 from 0 so we borrow 1 hundred and add 10 tens to the 0 tens we had. This makes a total of 10 tens. We write 10 above the tens place and cross out the 0. Then we cross out the 2 in the hundreds place and write 1 above it.
Now we subtract the tens. $10-6=4.$ We write the 4 in the tens place in the difference.
Finally, subtract the hundreds. There is no digit in the hundreds place in the bottom number so we can imagine a 0 in that place. Since $1-0=1,$ we write 1 in the hundreds place in the difference.
Check by adding. Our answer is correct.

Subtract and then check by adding: $439-52.$

Rivela la risposta

439 − 52 = 387 because 387 + 52 = 439
Subtract and then check by adding: $318-75.$

Rivela la risposta

318 − 75 = 243 because 243 + 75 = 318

Subtract and then check by adding: $910-586.$

Rivela la risposta

Write the numbers so each place value lines up vertically.
Subtract the ones. We cannot subtract 6 from 0, so we borrow 1 ten and add 10 ones to the 0 ones we had. This makes 10 ones. We write a 0 above the tens place and cross out the 1. We write the 10 above the ones place and cross out the 0. Now we can subtract the ones. $10-6=4.$
Write the 4 in the ones place of the difference.
Subtract the tens. We cannot subtract 8 from 0, so we borrow 1 hundred and add 10 tens to the 0 tens we had, which gives us 10 tens. Write 8 above the hundreds place and cross out the 9. Write 10 above the tens place.
Now we can subtract the tens. $10-8=2$.
Subtract the hundreds place. $8-5=3$ Write the 3 in the hundreds place in the difference.
Check by adding. Our answer is correct.

Subtract and then check by adding: $832-376.$

Rivela la risposta

832 − 376 = 456 because 456 + 376 = 832
Subtract and then check by adding: $847-578.$

Rivela la risposta

847 − 578 = 269 because 269 + 578 = 847

Subtract and then check by adding: $2,162-479.$

Rivela la risposta

Write the numbers so each place value lines up vertically.
Subtract the ones. Since we cannot subtract 9 from 2, borrow 1 ten and add 10 ones to the 2 ones to make 12 ones. Write 5 above the tens place and cross out the 6. Write 12 above the ones place and cross out the 2.
Now we can subtract the ones.	$12-9=3$
Write 3 in the ones place in the difference.
Subtract the tens. Since we cannot subtract 7 from 5, borrow 1 hundred and add 10 tens to the 5 tens to make 15 tens. Write 0 above the hundreds place and cross out the 1. Write 15 above the tens place.
Now we can subtract the tens.	$15-7=8$
Write 8 in the tens place in the difference.
Now we can subtract the hundreds.
Write 6 in the hundreds place in the difference.
Subtract the thousands. There is no digit in the thousands place of the bottom number, so we imagine a 0. $1-0=1.$ Write 1 in the thousands place of the difference.
Check by adding. $\begin{array}{l} \\ \overset{1}{1},\overset{1}{6}\overset{1}{8}3 \\ \underset{\text{______}}{+\ 479} \\ 2,\ 162✓\end{array}$

Our answer is correct.

Subtract and then check by adding: $4,585-697.$

Rivela la risposta

4,585 − 697 = 3,888 because 3,888 + 697 = 4,585
Subtract and then check by adding: $5,637-899.$

Rivela la risposta

5,637 − 899 = 4,738 because 4,738 + 899 = 5,637
Translate and then simplify:
1. ⓐ the difference of $13$ and $8$
2. ⓑ subtract $24$ from $43$
Rivela la risposta
- ⓐ
  The word difference tells us to subtract the two numbers. The numbers stay in the same order as in the phrase.
  
  the difference of 13 and 8
  Translate. $13-8$
  Simplify. 5
- ⓑ
  The words subtract from tells us to take the first number away from the second. We must be careful to get the order correct.
  
  subtract 24 from 43
  Translate. $43-24$
  Simplify. 19
Translate and simplify:
1. ⓐ the difference of $14$ and $9$
2. ⓑ subtract $21$ from $37$
Rivela la risposta
1. ⓐ 14 − 9 = 5
2. ⓑ 37 − 21 = 16
Translate and simplify:
1. ⓐ $11$ decreased by $6$
2. ⓑ $18$ less than $67$
Rivela la risposta
1. ⓐ 11 − 6 = 5
2. ⓑ 67 − 18 = 49

Rivela la risposta

We are asked to find the difference between the morning temperature and the noon temperature.

Write a phrase.	the difference of 73 and 27
Translate to math notation. Difference tells us to subtract.	$73-27$
Then we do the subtraction.
Write a sentence to answer the question.	The difference in temperatures was 46 degrees Fahrenheit.

The high temperature on $\text{June}\ {1}^{\text{st}}$ in Boston was $77$ degrees Fahrenheit, and the low temperature was $58$ degrees Fahrenheit. What was the difference between the high and low temperatures?

Rivela la risposta

The difference is 19 degrees Fahrenheit.
The weather forecast for June $2$ in St Louis predicts a high temperature of $90$ degrees Fahrenheit and a low of $73$ degrees Fahrenheit. What is the difference between the predicted high and low temperatures?

Rivela la risposta

The difference is 17 degrees Fahrenheit.

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

Rivela la risposta

We are asked to find the difference between the regular price and the sale price.

Write a phrase.	the difference between 588 and 399
Translate to math notation.	$588-399$
Subtract.
Write a sentence to answer the question.	The difference between the regular price and the sale price is $189.

A television set is on sale for $\text{\$499}.$ Its regular price is $\text{\$648}.$ What is the difference between the regular price and the sale price?

Rivela la risposta

The difference is $149.

Symbols used here

\pm

plus or minus
Both signs at once: x = 3 ± 2 means 5 and 1.

\neq

not equal
The two sides are different.

\leq,\ \geq

less/greater than or equal
Inequalities that allow equality; < and > exclude it.

\approx

approximately equal
Equal to the precision shown, not exactly.

\sqrt{x},\ \sqrt[n]{x}

square root, n-th root
The non-negative number whose square (n-th power) is x.

a \bmod n

remainder
What is left after dividing a by n.

per cent
Per hundred: 15% = 15/100.

a : b,\ \frac{a}{b}

ratio, fraction
a for every b; a divided by b.

How to: Subtract Whole Numbers

Use subtraction notation
Model subtraction of whole numbers
Subtract whole numbers
Translate word phrases to math notation
Subtract whole numbers in applications
Write the numbers so each place value lines up vertically.
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.
Continue subtracting each place value from right to left, borrowing if needed.

Questions people ask

Why does the order of operations matter?

Because 2 + 3 × 4 would otherwise be two different numbers. The convention (brackets, exponents, multiplication and division, addition and subtraction) exists so every reader gets the same value from the same expression.

How do I check an arithmetic answer?

Estimate first (round every number and compute roughly), then compare. If the estimate and the exact answer disagree by more than a little, one of them is wrong. The solver shows every operation, so you can find which line went astray.

Why are fractions harder than decimals?

They are not harder, they are more exact: 1/3 is a precise number, 0.333 is an approximation. Fractions need a common denominator to add, which is the one extra step people trip on.

Prova il tuo

Parts of this page are adapted from OpenStax Prealgebra 2e (CC BY-NC-SA 4.0). Condensed and re-explained here; errors are ours.

Più in Arithmetic

Order of operations Fractions Percentages Powers and roots

ⓐ
	\(9-7\)
Subtract 7 from 9.	\(2\)
Check with addition. \(2+7=9✓\)

ⓑ
	\(8-3\)
Subtract 3 from 8.	\(5\)
Check with addition. \(5+3=8✓\)

Write the numbers so the ones and tens digits line up vertically.	\(\begin{array}{l}89\ \\ \underset{\text{____}}{-61}\end{array}\)
Subtract the digits in each place value. Subtract the ones: \(9-1=8\) Subtract the tens: \(8-6=2\)	\(\begin{array}{l}89\ \\ \underset{\text{____}}{-61} \\ 28\ \end{array}\)
Check using addition. \(\begin{array}{l}28\ \\ \underset{\text{____}}{+61} \\ 89\ \end{array}\)

ⓐ
	\(9-7\)
Subtract 7 from 9.	\(2\)
Check with addition. \(2+7=9✓\)

ⓑ
	\(8-3\)
Subtract 3 from 8.	\(5\)
Check with addition. \(5+3=8✓\)

\(8-2\) means the difference of 8 and 2.
Model the first, 8.
Take away the second number, 2.
Count the number of blocks remaining.
There are 6 ones blocks left.	We have shown that \(8-2=6\).

Write the numbers so each place value lines up vertically.
Subtract the ones. We cannot subtract 6 from 3, so we borrow 1 ten. This makes 3 tens and 13 ones. We write these numbers above each place and cross out the original digits.
Now we can subtract the ones. \(13-6=7.\) We write the 7 in the ones place in the difference.
Now we subtract the tens. \(3-2=1.\) We write the 1 in the tens place in the difference.
Check by adding. Our answer is correct.

Write the numbers so each place value lines up vertically.
Subtract the ones. \(7-4=3.\) Write the 3 in the ones place in the difference.
Subtract the tens. We cannot subtract 6 from 0 so we borrow 1 hundred and add 10 tens to the 0 tens we had. This makes a total of 10 tens. We write 10 above the tens place and cross out the 0. Then we cross out the 2 in the hundreds place and write 1 above it.
Now we subtract the tens. \(10-6=4.\) We write the 4 in the tens place in the difference.
Finally, subtract the hundreds. There is no digit in the hundreds place in the bottom number so we can imagine a 0 in that place. Since \(1-0=1,\) we write 1 in the hundreds place in the difference.
Check by adding. Our answer is correct.

	the difference of 13 and 8
Translate.	\(13-8\)
Simplify.	5

	subtract 24 from 43
Translate.	\(43-24\)
Simplify.	19

	the difference of 13 and 8
Translate.	\(13-8\)
Simplify.	5

	subtract 24 from 43
Translate.	\(43-24\)
Simplify.	19