Whole Number Operations

➕ Whole Number Operations

Part 1 of 5 — Concept Introduction

Whole numbers are the numbers $0, 1, 2, 3, 4, 5,$ and so on. They are the counting numbers plus zero. There are no fractions, no decimals, and no negative numbers in this group — just clean, complete numbers.

In this lesson you will master the four basic operations you use every day:

• Addition $(+)$ — putting amounts together
• Subtraction $(-)$ — taking away or finding a difference
• Multiplication $(\times)$ — fast repeated addition of equal groups
• Division $(\div)$ — splitting into equal parts

By the end you will know not just how to compute, but which operation to choose in a real situation.

The Four Operations at a Glance 🔢

Two helpful pairs of "opposites":

• Addition and subtraction undo each other. Since $653 + 347 = 1{,}000$, we know $1{,}000 - 347 = 653$.
• Multiplication and division undo each other. Since $12 \times 12 = 144$, we know $144 \div 12 = 12$.

These inverse relationships let you check your work: redo the problem with the opposite operation and you should land back where you started.

Properties That Make Math Easier 🧠

Some operations follow special rules called properties.

• Commutative Property (for $+$ and $\times$): order doesn't matter.
  • $5 + 3 = 3 + 5 = 8$
  • $4 \times 6 = 6 \times 4 = 24$
• Associative Property (for $+$ and $\times$): grouping doesn't matter.
  • $(2 + 3) + 4 = 2 + (3 + 4) = 9$

Watch out: subtraction and division are not commutative! $8 - 3$ is $5$, but $3 - 8$ is not $5$. Order really matters for those two.

Order of Operations — PEMDAS

When several operations appear in one expression, follow PEMDAS:

1. Parentheses
2. Exponents
3. Multiplication and Division (left to right)
4. Addition and Subtraction (left to right)

For example, $2 + 3 \times 4 = 2 + 12 = 14$ — you multiply before you add.

Concept Check 🎯

Which property is being used below?

📝 Worked Examples

Part 2 of 5 — Worked Examples

Let's slow down and work through one problem of each type, step by step.

Example 1: Addition with Regrouping → $456 + 789$

Line up the place values and add right to left, carrying when a column is $10$ or more.

• Ones: $6 + 9 = 15$ → write $5$, carry $1$
• Tens: $5 + 8 = 13$, plus the carried $1$ is $14$ → write $4$, carry $1$
• Hundreds: $4 + 7 = 11$, plus the carried $1$ is $12$ → write $12$

$456 + 789 = 1{,}245$

Example 2: Subtraction with Borrowing → $1{,}000 - 347$

Subtract right to left, borrowing when the top digit is too small.

$1{,}000 - 347 = 653$

Check it: $653 + 347 = 1{,}000$ ✅. The inverse operation confirms the answer.

Example 3: Multiplication → $24 \times 15$

Break the second factor apart: $15 = 10 + 5$.

• $24 \times 10 = 240$
• $24 \times 5 = 120$
• Add the partial products: $240 + 120 = 360$

$24 \times 15 = 360$

Example 4: Division → $144 \div 12$

Ask: "$12$ times what equals $144$?"

Because $12 \times 12 = 144$, the answer is:

$144 \div 12 = 12$

Check it: $12 \times 12 = 144$ ✅. Multiplication undoes the division. 🎉

Your Turn 🧮

Compute each one and type the whole number into the box.

1. Add: $327 + 596$

2. Subtract: $800 - 245$

3. Multiply: $32 \times 14$

🧭 Guided Practice

Part 3 of 5 — Guided Practice

Work each problem carefully. Remember to use PEMDAS when more than one operation appears.

Fill In the Steps 🔍

Evaluate the expression $(8 + 2) \times 3$ using the order of operations.

🌍 Application & Word Problems

Part 4 of 5 — Real-World Problems

The hardest part of a word problem is choosing the right operation. Use these clues:

Field Trip Example 🚌

A school is taking $156$ students on a field trip. Each bus holds $40$ students. How many full buses can they fill, and how many students are left over?

This is a division problem: $156 \div 40$.

• $40 \times 3 = 120$ and $40 \times 4 = 160$ (too big).
• So 3 full buses, using $120$ students.
• Left over: $156 - 120 = 36$ students still need a ride (a 4th bus!).

Solve the Word Problem 🧮

A bakery sells muffins in boxes of $6$. On Monday they bake $18$ boxes.

1. How many muffins did they bake in total? (Multiply boxes by muffins per box.)

2. On Tuesday they baked $90$ muffins. How many muffins did they bake over the two days? (Add the two days.)

3. If $48$ of the Monday muffins were sold, how many Monday muffins were left? (Subtract from your answer to question 1.)

Choose the Operation 🤔

🏆 Review & Challenge

Part 5 of 5 — Review & Challenge

You've mastered all four operations and the rules that organize them. Here is the big picture:

Remember: multiplication and division come before addition and subtraction, and you always work parentheses first. Time for the final challenge! 🚀

Final Challenge 🎓

Mix everything you've learned. Take your time with each one.