Add or subtract decimals accurately.

SECTION 1

Why Do We Use Decimals?

Have you ever bought something at a store? Prices like $3.49 or $12.75 use decimals. Decimals are numbers that show parts of a whole, like cents in a dollar. People needed a way to write amounts that were not whole numbers.

Long ago, people used fractions for everything. Over time, mathematicians invented decimals to make math easier. Let's see how decimals came to be!

1400s

Early Decimal Ideas

Mathematicians in the Middle East began using a system like decimals to handle tricky fractions.

1585

Simon Stevin's Book

A Dutch math teacher named Simon Stevin wrote a famous book explaining how decimals work. He showed people that decimals make adding and subtracting much simpler.

1600s

The Decimal Point Appears

The little dot we use today (the decimal point) became common. It separates the whole-number part from the fractional part.

Today

Decimals Are Everywhere

We use decimals for money, measurements, sports stats, and so much more. The ISEE test loves to ask about adding and subtracting decimals!

So here's the big question: how do you add or subtract decimals without making mistakes? The secret is all about lining up the decimal points. Let's learn exactly how!

SECTION 2

Core Principles of Decimal Addition & Subtraction

Adding and subtracting decimals is a lot like adding and subtracting whole numbers. You just need to follow a few important rules. Let's look at the big ideas!

Line Up the Decimal Points

Always write numbers so the decimal points are directly above and below each other. This keeps ones with ones, tenths with tenths, and so on.

Use Placeholder Zeros

If one number has more decimal places, add zeros to the shorter number. For example, write 3.5 as 3.50 so it matches 2.75.

Add or Subtract Column by Column

Start from the right side. Work one column at a time, just like you do with whole numbers. Don't forget to regroup (carry or borrow) when needed!

Bring Down the Decimal Point

Drop the decimal point straight down into your answer. It should be right below the decimal points you lined up.

✦ KEY TAKEAWAY

KEY TAKEAWAY

SECTION 3

See It: Lining Up Decimal Points

Let's look at a picture that shows why lining up decimals matters. We'll add 4.53 + 2.7. Watch how the columns stay neat!

The left side shows what happens when you don't line up the decimals — the columns are a mess. The right side shows the correct way. Notice the cyan line showing the decimal points perfectly stacked.

See how we wrote 2.7 as 2.70? That placeholder zero doesn't change the value. It just helps us keep our columns straight. This trick is super helpful on the ISEE!

ISEE Test Tip

SECTION 4

The Steps for Adding and Subtracting Decimals

Here are the exact steps you should follow every time. Whether you're adding or subtracting, the process is the same!

STEP 1 — LINE UP

Write the numbers vertically with decimal points aligned.

Stack the numbers so each decimal point is in the same column. Put ones above ones, tenths above tenths, and hundredths above hundredths.

STEP 2 — ADD PLACEHOLDER ZEROS

Fill empty spots with zeros so both numbers have the same length.

Example: If you have 6.4 and 3.85, change 6.4 to 6.40. The zero after the 4 does not change the value, but it keeps your columns even.

STEP 3 — COMPUTE COLUMN BY COLUMN

Start from the rightmost column. Add or subtract. Regroup if needed.

Work just like with whole numbers. If a column adds up to 10 or more, carry the 1. If you can't subtract, borrow from the column to the left.

STEP 4 — DROP THE DECIMAL POINT

Bring the decimal point straight down into your answer.

The decimal point in your answer should be directly below the decimal points above it. Check this before you choose your answer on the test!

✦ KEY TAKEAWAY

REMEMBER THIS RHYME

SECTION 5

Watch Out! Common Decimal Mistakes

The ISEE test makers know the mistakes students make. They put wrong answers (called trap answers) that match those mistakes. If you know what to avoid, you won't fall into their traps!

The top row shows three common mistakes in red, yellow, and orange. The bottom row shows the correct solutions in green. Always add placeholder zeros and bring down the decimal point!

ISEE Strategy

SECTION 6

Worked Example: Step by Step

Let's solve a subtraction problem together. Follow along with each step. You've got this!

Problem: What is 12.5 − 7.83?

Step 1 — Write Vertically & Line Up DecimalsWrite 12.5 on top and 7.83 below it. Make sure the decimal points are in a straight line.

12.5 − 7.83

Step 2 — Add a Placeholder ZeroThe top number (12.5) has one decimal place. The bottom number (7.83) has two. Add a zero to 12.5 so it becomes 12.50. Now both numbers have two decimal places.

12.50 − 7.83

Step 3 — Subtract the Hundredths ColumnHundredths: 0 − 3. You can't take 3 from 0! Borrow 1 from the tenths place. Now it's 10 − 3 = 7.

Hundredths digit: 7

Step 4 — Subtract the Tenths ColumnThe tenths place was 5, but we borrowed 1, so now it's 4. Then 4 − 8. We can't do that! Borrow 1 from the ones place. Now it's 14 − 8 = 6.

Tenths digit: 6

Step 5 — Subtract the Ones and Tens ColumnsOnes: The 2 became 1 after borrowing. 1 − 7 can't be done, so borrow from the tens place. 11 − 7 = 4. Tens: The 1 became 0, and there's nothing to subtract. So the tens digit is 0 (we don't write a leading zero).

Ones digit: 4, Tens digit: (nothing)

Step 6 — Bring Down the Decimal PointPlace the decimal point in the answer directly below the other decimal points.

12.50 − 7.83 = 4.67

Let's check: 4.67 + 7.83 should equal 12.50. And it does! Checking your work is a great habit for the ISEE.

SECTION 7

Tips and Tricks for the ISEE

Let's compare different strategies and see what works best. These tips will help you save time and avoid errors on test day!

Helpful strategies for decimal problems on the ISEE

Strategy	When to Use It	Why It Helps
Estimate first	Every decimal problem	Round to whole numbers. If 3.82 + 5.19 ≈ 4 + 5 = 9, your answer should be near 9.
Add placeholder zeros	When numbers have different decimal lengths	Keeps columns even. Prevents the most common mistake!
Use scratch paper	Always (no calculator on ISEE!)	Writing vertically is much easier than doing it in your head.
Eliminate wrong answers	When you're unsure	If your estimate is 9, cross out choices like 0.9 or 90. Then pick from what's left.

✦ KEY TAKEAWAY

KEY TAKEAWAY

SECTION 8

Decimals Now and Later

Adding and subtracting decimals is a skill you'll use for years. Here's how what you learn now connects to what comes next!

How decimal skills build over time

What You Learn Now	What You'll Learn Later
Adding decimals like 3.25 + 1.40	Multiplying decimals like 3.25 × 1.4
Subtracting decimals with borrowing	Working with negative decimals
Lining up decimal points	Counting decimal places when multiplying
Estimating decimal sums	Using estimation to check algebra

Every math skill you build is like a brick in a wall. Right now, you're building a strong foundation with decimal addition and subtraction. Later, multiplication and division of decimals will feel easy because you already understand how decimals work. Great job sticking with it!

SECTION 9

Practice Problems

Now it's your turn! Try these five problems. They start easy and get a little harder. Remember: line up the decimal points, use placeholder zeros, and bring the point straight down. You've got this!

What is 3.2 + 1.5?

What is 9.4 − 4.1?

What is 2.45 + 3.38?

What is 8.32 − 1.75?

Maria had $12.50. She spent $4.85 on a book. How much money does she have left?