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Multiplication: Whole Numbers

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Multiplication: Whole Numbers

Study Guide

Key Definition

Multiplication of whole numbers can be seen as repeated addition. For example, $3 \times 5$ equals adding $3$ five times or $5$ three times.

Important Notes

Multiplication is commutative: $a \times b = b \times a$
Use the rectangle model to visualize multiplication: arrange $a$ rows and $b$ columns
Remember to carry over when multiplying digits that sum to 10 or more: for example, with $37 \times 6$, compute $7 \times 6 = 42$, write down 2 and carry 4; then $3 \times 6 = 18$ plus the carried 4 gives $22$, so the result is $222$.
Multiplication by zero always results in zero: $a \times 0 = 0$
Multiplying by one leaves the number unchanged: $a \times 1 = a$

Mathematical Notation

$\times$ or $*$ represents multiplication

$+$ represents addition

Remember to use proper notation when solving problems

Why It Works

Multiplication leverages repeated addition, making it efficient for large numbers. For example, $3 \times 5$ simplifies repeated addition to a single operation.

Remember

Multiplication is an essential skill in math, used in various real-world applications, such as calculating areas and solving equations.

Quick Reference

Commutative Property:$a \times b = b \times a$

Understanding Multiplication: Whole Numbers

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

Multiplication is repeated addition. For example, to compute $3 \times 4$, you add $3$ four times: $3 + 3 + 3 + 3 = 12$. Use a simple table or counting dots to check your work.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is $3 \times 7$?

Real-World Problem

Question Exercise

Intermediate

Grocery Shopping Scenario

If each apple costs $2$ dollars, how much do $5$ apples cost?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

If a rectangle has $4$ rows and $6$ columns of dots, how many dots are in total? Visualize: * * * * * * * * * * * * * * * * * * * * * * * *

Practice Quiz

Single Choice Quiz

Intermediate

What is $12 \times 9$?

Recap

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Review key concepts and takeaways