Multiplying by Multiples of 10

Section 1

Why Do We Multiply by Multiples of 10?

People have been grouping things into tens for thousands of years. Why tens? Because we have 10 fingers! Counting by tens is one of the oldest ideas in math. Let's see how this idea grew over time.

Long, Long Ago

Ancient people counted on their fingers. They made groups of 10 to keep track of things like sheep, fish, and tools.

About 5,000 Years Ago

People in Egypt and Mesopotamia wrote numbers using a system based on tens. They used special marks for 10, 100, and 1,000.

About 1,500 Years Ago

Mathematicians in India invented the digits 0 through 9 and the idea of place value. The spot where a digit sits tells you its value!

Today

We use place value every day! It helps us add, subtract, and multiply quickly — especially when one number is a multiple of 10 like 20, 50, or 90.

Here is the big question this lesson answers: How can you multiply a one-digit number (like 5) by a multiple of 10 (like 60) without having to count one by one? The answer comes from understanding place value!

Section 2

Key Ideas You Need

Before we learn the trick, let's make sure we understand four important ideas. These are the building blocks!

Multiples of 10

A multiple of 10 is what you get when you multiply a whole number by 10. Examples: 10, 20, 30, 40, 50, 60, 70, 80, 90. They all end in zero!

Place Value

Place value means that where a digit sits in a number tells you how much it is worth. In the number 40, the 4 is in the tens place, so it means 4 tens.

Groups of Ten

The number 30 is the same as 3 groups of 10. The number 70 is 7 groups of 10. Every multiple of 10 is really just "some number of tens."

Multiplication Facts

You already know basic facts like 3 × 4 = 12 and 5 × 6 = 30. We will use these same facts to solve bigger problems!

✦ Key Takeaway

Think of a multiple of 10 like a bag of marbles — each bag always holds exactly 10 marbles. So 60 is like having 6 bags with 10 marbles in each bag. If you want 5 × 60, you are asking: "What if I had 5 groups of those 6 bags?" That's 5 × 6 = 30 bags, and each bag has 10 marbles, so 30 × 10 = 300 marbles!

Section 3

See It: What Does 3 × 40 Look Like?

Let's picture the problem 3 × 40. This means 3 groups of 40. Since 40 is the same as 4 tens, we can draw 3 groups of 4 tens. Look at the picture below!

Diagram showing 3 groups of 40 as ten-blocks. Each group has 4 bars of 10, totaling 120.

Do you see it? We just counted 3 groups of 4 bars. That's 3 × 4 = 12 bars. Each bar is worth 10. So 12 bars of 10 is 120. That's the whole trick!

Section 4

The Place-Value Trick

Here is the secret shortcut. When you multiply a one-digit number by a multiple of 10, you can break it into two easy steps.

Step 1 — Ignore the Zero

5 × 60 → first do 5 × 6 = 30

Multiply the one-digit number by the tens digit

Step 2 — Put the Zero Back

30 → 300

Add a zero to the end, because you were really multiplying by tens

The Answer

5 × 60 = 300

Why does this work? Because 60 really means 6 × 10. So 5 × 60 is the same as 5 × 6 × 10. You do the small multiplication first (5 × 6 = 30), then multiply by 10 — and multiplying by 10 just means adding a zero at the end!

Why It Works

5 × 60 = 5 × (6 × 10) = (5 × 6) × 10 = 30 × 10 = 300

We use the fact that you can group multiplication any way you want

✦ Key Takeaway

Think of the zero in a multiple of 10 like a backpack you set down. You take it off (ignore it), do the easy multiplication, and then put the backpack back on (add the zero). That's all there is to it!

Section 5

Spot the Pattern

Let's look at a whole bunch of these problems side by side. See if you notice the pattern!

Problem	Basic Fact	Add the Zero	Answer
`2 × 30`	`2 × 3 = 6`	6 → 60	60
`4 × 50`	`4 × 5 = 20`	20 → 200	200
`7 × 20`	`7 × 2 = 14`	14 → 140	140
`6 × 80`	`6 × 8 = 48`	48 → 480	480
`9 × 90`	`9 × 9 = 81`	81 → 810	810
`5 × 60`	`5 × 6 = 30`	30 → 300	300

Did you see it? Every answer ends in zero. That's because you are always multiplying by a multiple of 10. The first part of the answer is just the basic multiplication fact you already know!

Visual showing how 4 × 70 breaks down: 70 is 7 tens, so 4 groups of 7 tens equals 28 tens, which is 280.

The picture above shows how we split the problem 4 × 70 into two smaller steps. First we do 4 × 7 = 28. Then we multiply by 10, which gives us 280. Easy!

Section 6

Worked Example: 9 × 80

Let's solve 9 × 80 step by step, nice and slow.

9 × 80 — Step by Step

Step 1 — Read the ProblemWe need to find 9 × 80. That means 9 groups of 80.

Step 2 — Break Apart the Multiple of 10The number 80 is a multiple of 10. We can write it as 8 × 10. So our problem becomes: 9 × 80 = 9 × (8 × 10)

Step 3 — Multiply the Basic FactNow ignore the × 10 part for a moment. Just multiply the two one-digit numbers:

9 × 8 = 72

Step 4 — Multiply by 10 (Add the Zero!)Now bring back the × 10. That means we put a zero at the end of 72:

72 × 10 = 720

Final Answer9 × 80 = 720. We had 9 groups of 80, and that gives us 720. Nice work!

Section 7

Helpful Tips & Common Mistakes

This strategy is really powerful, but there are a few things to watch out for. Let's look at what works well and what can trip you up.

✅ What Helps	❌ Watch Out For
Know your basic facts (times tables). The better you know them, the faster this goes!	Forgetting to add the zero at the end. If you get 9 × 80 = 72, you forgot the zero — it should be 720!
Remember that every multiple of 10 ends in 0. That zero is your clue to use this trick.	Adding too many zeros. 9 × 80 is 720, not 7200. You only add one zero because there is one zero in 80.
Check your answer by skip-counting. For 3 × 40, count: 40, 80, 120. ✓	Mixing up the digits. Be careful: 7 × 60 uses 7 × 6 = 42, not 7 × 5 or 6 × 6.
Use this trick for mental math — you can do these in your head once you practice!	Thinking you can only use this with small numbers. It works with any one-digit number × any multiple of 10!

✦ Key Takeaway

Think of the zero like a parking spot. The zero in 80 is "parked" at the end. You move it aside, do your multiplication (9 × 8 = 72), and then drive the zero right back into its parking spot at the end: 720. Just one zero goes back — not two, not zero!

Section 8

What Comes Next?

You just learned how to multiply by multiples of 10 in the range 10–90. That's awesome! But this is just the beginning. This same idea gets you ready for even bigger math.

What You Learned Today	What's Coming Later
`5 × 60 = 300` — One-digit × multiples of 10	`5 × 600 = 3,000` — One-digit × multiples of 100
Adding 1 zero at the end	Adding 2 zeros (for hundreds) or 3 zeros (for thousands)
Using basic facts like 5 × 6	Using the same basic facts for bigger numbers!
Place value: tens place	Place value: hundreds, thousands, and beyond

In 4th grade, you'll multiply two-digit numbers by two-digit numbers, like 23 × 45. Guess what? You'll break those apart using the same place-value ideas you practiced today. So every time you practice 7 × 30 or 9 × 80, you're building a superpower you'll use for years!

Section 9

Practice Problems

Time to try it yourself! Start with the first problem and work your way up. Click "Show Answer" when you're ready to check.

PROBLEM 1 — THINK ABOUT IT

What does 4 × 30 mean? Describe it using the words "groups" and "tens."

PROBLEM 2 — BASIC CALCULATION

Solve: 6 × 50 = ?

PROBLEM 3 — A BIT TRICKIER

Solve: 8 × 70 = ? Then check your answer by solving it a different way: What is 7 × 80?

PROBLEM 4 — WORD PROBLEM

A school is buying pencils. Each box holds 20 pencils. The school buys 9 boxes. How many pencils is that in all?

PROBLEM 5 — CHALLENGE!

Maria says: "I know that 7 × 6 = 42. So I also know the answers to 7 × 60 and 6 × 70 and 60 × 7 without doing any more work!" Is Maria right? What are those three answers, and why does knowing 7 × 6 help her find all of them?

Summary

Lesson Summary

In this lesson you learned how to multiply a one-digit number by a multiple of 10 (like 10, 20, 30, … 90). The big idea is place value: every multiple of 10 is really just "some number of tens." For example, 80 = 8 tens. So when you solve 9 × 80, you're really finding 9 groups of 8 tens, which is 72 tens, which equals 720.

The shortcut is simple: multiply the one-digit number by the tens digit (the basic fact you already know), then add a zero at the end. This works because multiplying by 10 just moves every digit one place to the left. You used strategies based on place value and the properties of multiplication (like being able to multiply in any order) to make big problems feel small. Keep practicing your basic facts, and these problems will become super fast!