Adding and Subtracting 10 or 100 in Your Head!

SECTION 1

Where Did Mental Math Come From?

People have been adding and subtracting in their heads for a very long time! Before we had phones and calculators, people had to do math using just their brains. Let's look at some cool moments in the story of mental math.

Long, Long Ago

People in ancient times used their fingers to count and add. They grouped things by 10s because we have 10 fingers!

About 2,000 Years Ago

People invented the abacus — a frame with beads you slide. It helped them add and subtract by moving groups of 10.

About 1,400 Years Ago

Mathematicians in India created the place-value system we use today. That means the spot where a digit sits tells us if it means ones, tens, or hundreds!

Today

You are learning to add and subtract 10 and 100 in your head — just like mathematicians have been doing for hundreds of years. You're part of the story!

Here is the big question we will answer today: How can you add or subtract 10 or 100 from a number without writing anything down? The secret is understanding place value — knowing what each digit in a number means.

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The Big Ideas You Need to Know

Before we start adding and subtracting, let's learn four important ideas. These are like your super-power tools!

Hundreds, Tens, and Ones

Every number has places. In the number 365, the 3 is in the hundreds place, the 6 is in the tens place, and the 5 is in the ones place.

Adding 10 Changes the Tens Digit

When you add 10, only the tens digit goes up by 1. The hundreds and ones stay the same!

Adding 100 Changes the Hundreds Digit

When you add 100, only the hundreds digit goes up by 1. The tens and ones stay the same!

Subtracting Works the Same Way — Backwards!

Subtracting 10 makes the tens digit go down by 1. Subtracting 100 makes the hundreds digit go down by 1.

✦ KEY TAKEAWAY

Think of a number like a house with three rooms. The hundreds room is on the left, the tens room is in the middle, and the ones room is on the right. When you add 10, you only visit the tens room and put 1 more in it. When you add 100, you only visit the hundreds room. The other rooms don't change at all!

SECTION 3

See It in a Picture!

Let's look at the number 254 and watch what happens when we add 10, add 100, subtract 10, and subtract 100. Look at which digit changes!

Look at the picture above. The number 254 is in the middle. When we add 10, the tens digit goes from 5 to 6, and we get 264. When we subtract 10, the tens digit goes from 5 to 4, and we get 244. The hundreds and ones digits stay put!

The same idea works for 100. When we add 100, the hundreds digit goes from 2 to 3, giving us 354. When we subtract 100, it goes from 2 to 1, giving us 154. The tens and ones digits don't move at all!

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How Does the Trick Work?

Here are the four simple rules. Think of them as magic spells for your brain!

RULE 1 — ADD 10

Number + 10 → Tens digit goes UP by 1

Example: 370 + 10 = 380 (the 7 becomes an 8)

RULE 2 — SUBTRACT 10

Number − 10 → Tens digit goes DOWN by 1

Example: 530 − 10 = 520 (the 3 becomes a 2)

RULE 3 — ADD 100

Number + 100 → Hundreds digit goes UP by 1

Example: 462 + 100 = 562 (the 4 becomes a 5)

RULE 4 — SUBTRACT 100

Number − 100 → Hundreds digit goes DOWN by 1

Example: 817 − 100 = 717 (the 8 becomes a 7)

That's it! You only need to look at one digit. If you're adding or subtracting 10, look at the tens place (the middle digit). If you're adding or subtracting 100, look at the hundreds place (the first digit). The other digits stay exactly the same.

✦ KEY TAKEAWAY

Imagine you have three jars on a shelf. The left jar holds hundreds, the middle jar holds tens, and the right jar holds ones. When someone says "add 10," you walk to the middle jar and drop in 1 more bead. You don't touch the other jars! That's exactly what happens to the digits in your number.

SECTION 5

The Hundreds Chart — See the Pattern!

A hundreds chart helps you see what happens when you add or subtract 10 and 100. Look at the chart below. When you move down one row, you add 10. When you move up one row, you subtract 10.

On the chart, moving down one row is the same as adding 10. Moving up one row is the same as subtracting 10. If you could jump down 10 whole rows, that would be the same as adding 100! The ones digit always stays the same because you are only changing tens or hundreds.

START	+ 10	− 10	+ 100	− 100
`340`	`350`	`330`	`440`	`240`
`572`	`582`	`562`	`672`	`472`
`815`	`825`	`805`	—	`715`
`200`	`210`	`190`	`300`	`100`

Look at the table above. Notice how the pattern is always the same! The ones digit never changes. For 815 + 100, we'd get 915 (the 8 goes to 9). We put a dash because 915 is at the edge of our range.

SECTION 6

Let's Solve One Together!

Let's work through a full problem step by step. Ready? Here we go!

Problem: What is 438 + 100? Then what is 538 − 10?

Step 1 — Break Apart 438The number 438 has three digits. The 4 is in the hundreds place. The 3 is in the tens place. The 8 is in the ones place.

Step 2 — Add 100We are adding 100, so we look at the hundreds digit. The hundreds digit is 4. We add 1 to it: 4 + 1 = 5. The tens and ones stay the same.

438 + 100 = 538

Step 3 — Now Subtract 10 from 538Now we have 538. We need to subtract 10. That means we look at the tens digit. The tens digit is 3. We subtract 1 from it: 3 − 1 = 2. The hundreds and ones stay the same.

538 − 10 = 528

Step 4 — Check Our WorkLet's double-check. 438 + 100 = 538 ✓. Then 538 − 10 = 528 ✓. We did it!

The final answer is 528. Great job!

SECTION 7

When Is This Easy? When Is It Tricky?

Most of the time, adding and subtracting 10 or 100 in your head is super easy. But there are a few times it can feel a little tricky. Let's look at both!

SITUATION	EASY OR TRICKY?	EXAMPLE
Middle digits (2–8)	Easy!	`350 + 10 = 360`
Tens digit is 9 and you add 10	A little tricky	`190 + 10 = 200`
Tens digit is 0 and you subtract 10	A little tricky	`400 − 10 = 390`
Hundreds digit is 9 and you add 100	Edge of range	`900 + 100 = 1000`
Hundreds digit is 1 and you subtract 100	Edge of range	`100 − 100 = 0`

The tricky part is when a digit "rolls over." For example, 190 + 10 is like the tens digit going from 9 to 10, which means the tens digit becomes 0 and the hundreds digit goes up by 1. So 190 becomes 200. It's just like when a clock goes from 59 minutes to 00 minutes and the hour goes up by 1!

✦ KEY TAKEAWAY

Think about an odometer in a car (the number that counts miles). When the tens place hits 9 and you add 1 more, it rolls back to 0 and the hundreds digit goes up. It's the same thing with our numbers! Most of the time, only one digit changes. But when a digit rolls over from 9 to 0, the digit to its left goes up by 1 too.

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What Will You Learn Next?

Right now, you are learning to add and subtract 10 and 100 in your head. This is an amazing skill! As you keep learning math, you will build on this skill in bigger and bigger ways.

WHAT YOU KNOW NOW	WHAT COMES NEXT
Add/subtract 10	Add/subtract 20, 30, 40 (multiples of 10)
Add/subtract 100	Add/subtract 200, 300, 400 (multiples of 100)
Numbers 100–900	Numbers up to 1,000 and beyond!
Change one digit at a time	Add two-digit and three-digit numbers together

The skill you are learning today is like a building block. When you can add 10 really fast, adding 20 is just adding 10 twice. Adding 30 is adding 10 three times. And adding 200 is just adding 100 twice! So keep practicing — you are building a strong math brain.

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Practice Time! 🎉

Now it's your turn! Try these five problems. Think about which digit changes, then click "Show Answer" to check your work.

PROBLEM 1 — THINK ABOUT IT

When you add 10 to a number, which digit changes — the hundreds, the tens, or the ones?

PROBLEM 2 — QUICK MATH

What is 340 + 100 ?

PROBLEM 3 — A LITTLE HARDER

What is 672 − 10 ? And then what is the answer − 100 ?

PROBLEM 4 — WORD PROBLEM

Emma has 450 stickers. Her friend gives her 10 more. Then her mom gives her 100 more. How many stickers does Emma have now?

PROBLEM 5 — BRAIN STRETCH 🧠

I start with a number. I add 100, and I get 783. What number did I start with? Then, if I subtract 10 from that starting number, what do I get?

SUMMARY

What You Learned Today

Today you learned how to add 10, subtract 10, add 100, and subtract 100 from numbers between 100 and 900 — all in your head! The secret is place value. Every number has a hundreds place, a tens place, and an ones place. When you add or subtract 10, only the tens digit changes. When you add or subtract 100, only the hundreds digit changes. The other digits stay exactly the same.

You also saw this on a hundreds chart, where moving down one row means +10 and moving up one row means −10. You practiced with tables, pictures, and word problems. Remember: this skill is like a building block. Once you are fast at adding 10 and 100, you can add 20, 30, 200, 300, and even bigger numbers! Keep practicing, and your math brain will get stronger every day. 🌟