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Mom's Basement University

Addition & Subtraction of Whole Numbers

What You’ll Learn

Section titled “What You’ll Learn”

In this lesson you’ll start with the basics of addition and subtraction using small numbers, then build up to multi-digit problems with carrying (regrouping) and borrowing.

The Basics

Section titled “The Basics”

Addition means combining two amounts into one total. Think of it as putting groups together.

If you have 3 apples and someone gives you 5 more, you now have 3+5=83 + 5 = 8 apples. That’s addition, counting how many you have altogether.

Here are a few single-digit examples to get comfortable:

  • 2+4=62 + 4 = 6
  • 7+1=87 + 1 = 8
  • 5+5=105 + 5 = 10
  • 6+3=96 + 3 = 9

Subtraction means taking one amount away from another. It tells you what’s left.

If you have 9 cookies and eat 4, you have 9 − 4 = 5 cookies left. Subtraction answers “how many remain?” or “what’s the difference?”

  • 8−3=58 - 3 = 5
  • 7−2=57 - 2 = 5
  • 10−6=410 - 6 = 4
  • 9−9=09 - 9 = 0

A helpful way to think about it: addition and subtraction are opposites. If 3+5=83 + 5 = 8, then 8−5=38 - 5 = 3. You can always check subtraction by adding back.

Multi-Digit Addition & Subtraction

Section titled “Multi-Digit Addition & Subtraction”

Once you’re comfortable with single digits, the same idea scales up. You just work one column at a time, starting from the right.

Addition with larger numbers works from right to left:

  • Add each column starting from the ones place.
  • If the sum is 10 or more, write the ones digit and carry 1 to the next column.

Example: 456+789456 + 789

111456+7891245\begin{array}{rrrr} \scriptsize{1} & \scriptsize{1} & \scriptsize{1} & \\ & 4 & 5 & 6 \\ {+} & 7 & 8 & 9 \\ \hline 1 & 2 & 4 & 5 \end{array}
  • Ones: 6+9=156 + 9 = 15 → write 5, carry 1
  • Tens: 5+8+1=145 + 8 + 1 = 14 → write 4, carry 1
  • Hundreds: 4+7+1=124 + 7 + 1 = 12 → write 12

Result: 1,2451{,}245

Subtraction takes one number from another. When the top digit is smaller than the bottom digit, borrow from the next column:

  • Borrowing adds 10 to the current column and subtracts 1 from the column to the left.

Example: 1,000−3781{,}000 - 378

0991000−378622\begin{array}{rrrr} \scriptsize{0} & \scriptsize{9} & \scriptsize{9} & \scriptsize{} \\ 1 & 0 & 0 & 0 \\ {-} & 3 & 7 & 8 \\ \hline & 6 & 2 & 2 \end{array}
  • Ones: 0−80 - 8 → borrow → 10−8=210 - 8 = 2
  • Tens: 9−7=29 - 7 = 2 (after borrow)
  • Hundreds: 9−3=69 - 3 = 6 (after borrow)

Result: 622622

Check your work: Add the answer back to the number you subtracted. It should equal the original number.

Worked Examples

Section titled “Worked Examples”

Add 2,847+1,5692{,}847 + 1{,}569

1112847+15694416\begin{array}{rrrrr} & \scriptsize{1} & \scriptsize{1} & \scriptsize{1} & \\ & 2 & 8 & 4 & 7 \\ {+} & 1 & 5 & 6 & 9 \\ \hline & 4 & 4 & 1 & 6 \end{array}
  • Ones: 7+9=167 + 9 = 16 → write 6, carry 1
  • Tens: 4+6+1=114 + 6 + 1 = 11 → write 1, carry 1
  • Hundreds: 8+5+1=148 + 5 + 1 = 14 → write 4, carry 1
  • Thousands: 2+1+1=42 + 1 + 1 = 4

Result: 4,4164{,}416

Now subtract 3,416−1,9283{,}416 - 1{,}928

213103416−19281488\begin{array}{rrrrr} & \scriptsize{2} & \scriptsize{13} & \scriptsize{10} & \scriptsize{} \\ & 3 & 4 & 1 & 6 \\ {-} & 1 & 9 & 2 & 8 \\ \hline & 1 & 4 & 8 & 8 \end{array}
  • Ones: 6−86 - 8 → borrow → 16−8=816 - 8 = 8
  • Tens: 0−20 - 2 → borrow → 10−2=810 - 2 = 8
  • Hundreds: 3−93 - 9 → borrow → 13−9=413 - 9 = 4
  • Thousands: 2−1=12 - 1 = 1

Result: 1,4881{,}488

Check: 1,488+1,928=3,4161{,}488 + 1{,}928 = 3{,}416 ✓

Real-World Applications

Section titled “Real-World Applications”

Addition tracks total income, shopping totals, or hours worked. Subtraction figures change due, remaining budget, or debt payoff. Example: Paycheck of 2,150 dollars minus rent of 1,200 dollars = 950 dollars left for bills and food. Simple subtraction keeps finances on track without surprises.

Quiz

Section titled “Quiz”
What is 567 + 389?
Subtract 742 - 385.
A bill is 458 dollars. You pay with 500 dollars. How much change?
Add 1,234 + 567 + 89.
Subtract 5,003 - 2,478.