Adding and Subtracting Decimals

What Are Decimals? 🔢

A decimal is another way to show parts of a whole — just like a fraction does.

The little dot in the middle is called the decimal point ( . ). It separates the whole number part (on the left) from the part that is less than one (on the right).

Example: $3.5$ means 3 and 5 tenths, which is the same as the mixed number $3\frac{5}{10}$.

You already use decimals every day:

• Money: a candy bar costs $1.25
• Sports: a runner finished in 9.8 seconds
• Cooking: a recipe needs 2.5 cups of flour

Decimals let us measure and count things that don't land on a nice whole number.

Place Value Is the Key 🗝️

Understanding place value is the secret to adding and subtracting decimals. Each spot to the right of the decimal point is ten times smaller than the one before it.

Let's look at the number 3.45:

So $3.45$ is:

• 3 ones
• 4 tenths (that's $\frac{4}{10}$)
• 5 hundredths (that's $\frac{5}{100}$)

The first digit after the point is tenths. The second digit after the point is hundredths. Lining these places up correctly is what makes our math work.

⭐ The Golden Rule: Line Up the Decimal Points!

The most important rule for adding and subtracting decimals is this:

Always line up the decimal points, one right on top of the other!

When the points are lined up, the tenths sit under the tenths and the hundredths sit under the hundredths. That keeps every digit in its correct place.

Correct way to add $4.3 + 2.6$:

  4.3
+ 2.6
-----
  6.9   ✓  (points lined up!)

If you slide the numbers around so the points are not lined up, you will mix up tenths with ones and get the wrong answer. Keep those points stacked!

Quick Concept Check ✅

Let's make sure the big idea is clear.

Adding Decimals: Step by Step ➕

Let's add $5.4 + 3.8$ together, one step at a time.

Step 1 — Line up the decimal points.

  5.4
+ 3.8
-----

Step 2 — Add from right to left, just like whole numbers.

Start with the tenths: $4 + 8 = 12$ tenths. That is more than 9, so we write the 2 and carry the 1 to the ones place.

Then the ones: $1 + 5 + 3 = 9$.

   $ {}^{1}$
  5.4
+ 3.8
-----
  9.2

Step 3 — Bring the decimal point straight down into the answer.

$5.4 + 3.8 = 9.2 \;✓$

Adding Numbers with Different Decimal Places 🧩

What if the numbers have a different number of digits, like $6.5 + 2.34$?

Trick: add a placeholder zero so both numbers have the same number of decimal places. Adding a zero on the end of a decimal does not change its value ($6.5 = 6.50$).

Step 1 — Line up the points and add a zero:

  6.50   ← added a zero
+ 2.34
------

Step 2 — Add each column from the right:

• Hundredths: $0 + 4 = 4$
• Tenths: $5 + 3 = 8$
• Ones: $6 + 2 = 8$

  6.50
+ 2.34
------
  8.84   ✓

So $6.5 + 2.34 = 8.84$. The placeholder zero keeps every digit in the right column.

Your Turn: Add These ✍️

Use the line-up rule (and a placeholder zero when you need one). Type each answer as a decimal number, like 7.5.

1. $3.2 + 4.5 = \;?$
2. $5.6 + 2.7 = \;?$
3. $4.3 + 1.85 = \;?$

Subtracting Decimals ➖

Subtracting works the exact same way as adding: line up the points, subtract right to left, and bring the point straight down.

Example: $8.7 - 3.2$

  8.7
- 3.2
-----
  5.5   ✓

Borrowing (regrouping): Sometimes the top digit is too small. For $5.4 - 2.8$, you can't take $8$ tenths from $4$ tenths, so borrow 1 one (which is 10 tenths) from the ones place.

• $5.4$ becomes $4$ ones and $14$ tenths.
• Tenths: $14 - 8 = 6$
• Ones: $4 - 2 = 2$

$5.4 - 2.8 = 2.6 \;✓$

Now answer the questions below.

Multiple Choice 🎯

Fill in the Blanks 🔽

Choose the correct answer for each problem.

Decimals in the Real World 🌎

Decimals show up most often with money and measuring. The same line-up rule works every time.

Money example: Maya buys a juice for $1.75 and a muffin for $2.40. How much does she spend?

  1.75
+ 2.40
------
  4.15   ✓

She spends $4.15.

Change example: She pays with a $5.00 bill. How much change does she get?

  5.00
- 4.15
------
  0.85   ✓

She gets $0.85 back. Notice how the placeholder zeros in 5.00 keep the columns lined up. Now try some yourself!

Word Problem Practice 💵

Type each answer as a decimal number (no dollar sign needed), like 3.50 or 3.5.

1. Ben jogs 2.4 km in the morning and 1.5 km at night. How many km total?
2. A water bottle holds 0.75 L. Sam drinks 0.5 L. How many liters are left?
3. A pencil costs $0.60 and an eraser costs $0.85. What is the total cost?

One More Word Problem 🧠

Review: Everything You Learned 📋

You are now a decimal pro! Here is a quick summary of the steps.

Remember the Golden Rule: Line up the decimal points! If you do that one thing, the rest is just whole-number math.

Ready for the final challenge? Let's go! 🚀

Final Challenge 🏆