Write multiplication and division equations from word problems
Use logic to solve for unknown values (like x)
Understand the relationship between multiplication and division
Apply math to real-world situations
Prepare for early algebra and deeper problem solving
Have you ever faced a word problem and wondered how to turn it into an equation?
That’s exactly what this worksheet helps you do!
Writing equations with unknowns is like turning real-world stories into short, meaningful math sentences. When you see a word problem like “3 times a number is 12,” your brain learns to translate it into 3 × n = 12 — where n is the unknown number you’re solving for.
This printable worksheet makes it easy to master that translation process through guided examples, visual modeling, and problem-based practice. Students learn how to use multiplication and division to represent and solve real situations using variables.
In math, the unknown is the part of an equation we’re trying to find.
It’s like a missing puzzle piece. We often use letters like x, n, or y to stand for that unknown number.
For example:
“A number times 4 equals 20.”
Equation: 4 × n = 20
Here, n is the unknown.
Solving it means finding what number makes that sentence true:
4 × 5 = 20
→ n = 5
This idea builds the foundation for algebra, where letters replace missing numbers so we can explore mathematical relationships more deeply.
Before writing equations, it’s important to understand how multiplication and division are connected. They’re inverse operations, meaning one undoes the other.
If 4 × 5 = 20, then 20 ÷ 4 = 5.
So, when you’re writing or solving equations, you can use division to find the unknown in a multiplication problem—or vice versa.
That’s why this worksheet helps students build both directions of thinking:
Writing multiplication equations when quantities are grouped or repeated.
Writing division equations when quantities are shared or separated equally.
An equation is a math statement that shows two sides are equal, using the = sign.
When there’s an unknown value, it means we need to find the number that makes the equation true.
Example:
“8 times a number equals 56.”
→ 8 × x = 56
→ x = 56 ÷ 8
→ x = 7
Historically, the concept of using symbols for unknowns dates back to early Arabic mathematicians like Al-Khwarizmi (the father of algebra). Today, it’s a skill taught from middle school onward — connecting arithmetic with the logical world of algebra.
Step 1 : Read the Problem
Understand what’s happening. Look for words that signal multiplication (“times,” “groups of,” “each”) or division (“shared,” “split,” “each part”).
Example:
“5 groups of a number equals 20.”
Step 2 : Choose a Variable
Use a letter to stand for the unknown number — usually x or n.
→ 5 × n = 20
Step 3 : Write the Equation
Translate the sentence into math language.
→ “5 times a number equals 20” becomes 5 × n = 20
Step 4: Solve for the Unknown
Use the opposite operation to find the missing number.
→ n = 20 ÷ 5
→ n = 4
Step 5: Check Your Answer
Always verify by plugging the number back in.
→ 5 × 4 = 20 True!
This logical process helps learners build both reasoning and confidence in problem solving.
Example 1:
“A number times 6 equals 42.”
Equation: 6 × x = 42
Solution: x = 42 ÷ 6 = 7
Answer: x = 7
Example 2:
“36 divided by a number equals 9.”
Equation: 36 ÷ x = 9
Solution: Multiply both sides by x → 36 = 9x → x = 4
Answer: x = 4
Example 3:
“A box has 8 candies in each pack. If there are 48 candies in total, how many packs are there?”
Equation: 8 × p = 48
Solution: p = 48 ÷ 8 = 6
There are 6 packs.
Example 4 (Real-Life Connection):
“Each pencil costs $2. If you spend $16, how many pencils did you buy?”
Equation: 2 × n = 16
Solution: n = 16 ÷ 2 = 8
You bought 8 pencils.
The worksheet begins with guided examples showing how to convert word problems into equations.
Students start with simple one-step problems and gradually move to real-world examples that require reasoning.
Later, learners write their own equations using sentence prompts like:
“A number times 9 is 27.”
“48 divided by a number equals 6.”
“A number times 3 equals 15.”
By the final section, they’ll be designing and solving their own real-world problems using multiplication and division with unknowns.
Visual learners can also use algebra tiles or counters to model multiplication and division.
For instance:
3 × x = 12 → Place 3 groups of unknown tiles equal to 12 total tiles.
Divide equally → Each group = 4 → x = 4.
This hands-on approach helps students see how multiplication and division balance out both sides of the equation.
Equations with unknowns aren’t just for math class — they appear everywhere in life!
Students will recognize them in:
Budgeting: “How many hours must I work to earn $120 if I make $15 per hour?”
→ 15 × h = 120
Shopping: “If 5 shirts cost $60, how much is one shirt?”
→ 60 ÷ 5 = 12
Cooking: “Each tray holds 9 cupcakes. If you bake 81 cupcakes, how many trays do you need?”
→ 9 × t = 81
This helps learners connect algebra to the decisions they make daily — from saving money to solving puzzles.
Before finalizing your answer, check reasonableness by estimating.
If a number feels too big or small for the situation, something might be off.
Example:
“8 × n = 400” → You expect n to be close to 50 (because 8 × 50 = 400).
So if your solution gives 5 or 500, you know it’s unreasonable.
Building this habit strengthens logical thinking — a key life skill beyond math.
Learning to write equations with unknowns transforms students into math detectives.
Each problem is a story waiting to be decoded with multiplication and division.
Once they grasp how to represent unknowns, they gain the confidence to solve more complex algebraic challenges in the future.
This worksheet isn’t just about finding answers — it’s about understanding how math works and why it matters.
Printable Worksheet PDF:
Includes:
20 step-by-step word problems
Equation writing space
Visual modeling area
Self-check section for reasonableness
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