Lesson 3: Unknown Numbers in Addition, Subtraction, Multiplication, and Division

New Concept

An equation is a statement that two quantities are equal. Here we show two equations:

What’s next

This is just the start of your journey with equations. Next, you'll tackle worked examples for finding unknowns in addition, subtraction, multiplication, and division problems.

Property

An equation is a statement that two quantities are equal, like $5+a=9$.

Examples

An addition equation with an unknown addend: $x + 10 = 25$.
An subtraction equation with an unknown subtrahend: $50 - y = 30$.
A multiplication equation with an unknown factor: $8k = 64$.

Explanation

Think of an equation as a perfectly balanced scale. Whatever is on the left side must equal the right side. If a number is missing (represented by a variable), your job is to figure out what that number must be to keep the scale from tipping. It’s all about finding that magic number to maintain balance!

Property

We can find an unknown addend by subtracting the known addend from the sum.

Examples

Find the unknown number: $a + 25 = 70 \implies a = 70 - 25 \implies a = 45$.
Find the unknown number: $10 + n + 20 = 55 \implies 30 + n = 55 \implies n = 55 - 30 \implies n = 25$.

Explanation

Think of this as a number mystery! You know the final total (the sum) and one of the pieces (an addend). To find the secret number, simply subtract the known piece from the total. Subtraction is the inverse of addition, making it the perfect tool to work backward and solve for the unknown value!

Property

To find an unknown factor, we divide the product by the known factor(s).

Examples

Find the unknown number: $9k = 81 \implies k = 81 \div 9 \implies k = 9$.
Find the unknown number: $m \times 6 = 120 \implies m = 120 \div 6 \implies m = 20$.

Explanation

When a number is hiding in a multiplication problem, division is your secret weapon! Since division is the inverse of multiplication, you can undo the problem by dividing the total product by the factor you already know. This powerful move isolates the mystery factor and reveals its true identity every single time.