Adding and Subtracting Decimals

🔢 Adding and Subtracting Decimals

Part 1 of 5 — Concept Introduction

You already know how to add and subtract whole numbers. Adding and subtracting decimals works almost exactly the same way — you just have to be careful about one thing.

The Golden Rule

Always line up the decimal points! 🎯

When the decimal points are stacked in a straight vertical line, every digit lands in the correct place: tenths under tenths, ones under ones, and so on. If the points are lined up, the rest is just normal adding or subtracting.

Look how the points form a perfect vertical line:

$\begin{array}{r} 3.45 \\ + 12.80 \\ \hline 16.25 \end{array}$

The decimal point in the answer drops straight down into the same column.

Why Lining Up Matters

Each spot in a decimal number has a place value. You can only add or subtract digits that share the same place value — tenths with tenths, hundredths with hundredths.

See how the $8$ and the $4$ (the tenths) line up in the same column? That only happens when the decimal points are stacked.

The Zero Trick 🪄

Numbers can have a different number of decimal places. To make them match, add zeros as placeholders on the right side.

• $12.8$ becomes $12.80$
• $7.3$ becomes $7.30$

Adding a zero at the end of a decimal does not change its value — $0.5$ and $0.50$ are exactly the same amount. But the extra zero gives every column a digit, which makes lining up easy.

A Worked Example

Let's add $3.45 + 12.8$ together.

Step 1 — Line up the decimal points and add a placeholder zero so both numbers have two decimal places:

$\begin{array}{r} 3.45 \\ + 12.80 \\ \hline \end{array}$

Step 2 — Add each column from right to left, just like whole numbers. Keep the decimal point in line:

$\begin{array}{r} 3.45 \\ + 12.80 \\ \hline 16.25 \end{array}$

So $3.45 + 12.8 = 16.25$. ✅

The decimal point in the answer comes straight down from the points above it.

Concept Check 🎯

Make sure you understand the Golden Rule.

📝 Worked Examples

Part 2 of 5 — Worked Examples

Let's slow down and walk through one addition and one subtraction, step by step.

Example 1: Adding — $5.6 + 2.74$

Step 1 — Line up the points and add a placeholder zero to $5.6$ so it becomes $5.60$:

$\begin{array}{r} 5.60 \\ + 2.74 \\ \hline \end{array}$

Step 2 — Add right to left. Hundredths: $0 + 4 = 4$. Tenths: $6 + 7 = 13$, so write $3$ and carry $1$. Ones: $5 + 2 + 1 = 8$.

$\begin{array}{r} 5.60 \\ + 2.74 \\ \hline 8.34 \end{array}$

So $5.6 + 2.74 = 8.34$. ✅

Example 2: Subtracting — $15.6 - 7.38$

Step 1 — Line up the points and add a placeholder zero to $15.6$ so it becomes $15.60$:

$\begin{array}{r} 15.60 \\ - 7.38 \\ \hline \end{array}$

Step 2 — Subtract right to left, borrowing when needed. Hundredths: $0 - 8$ needs a borrow, so $10 - 8 = 2$. Tenths becomes $5$, then $5 - 3 = 2$. Ones: $5 - 7$ needs a borrow → $15 - 7 = 8$. Tens: $0$.

$\begin{array}{r} 15.60 \\ - 7.38 \\ \hline 8.22 \end{array}$

So $15.6 - 7.38 = 8.22$. ✅

Your Turn 🧮

Add $4.7 + 3.25$ step by step. Type each answer in the box.

1. Rewrite $4.7$ with a placeholder zero so it has two decimal places. (Type it like $4.70$.)

2. Add the tenths and ones first, then finish. What is $4.7 + 3.25$? (Type it like $7.95$.)

3. Now subtract: what is $6.5 - 1.28$? (Type it like $5.22$.)

🧭 Guided Practice

Part 3 of 5 — Guided Practice

Line up the decimal points, use placeholder zeros, and work each column carefully.

Fill In the Steps 🔍

Complete the two steps for solving $8.4 + 5.16$.

🌍 Application & Word Problems

Part 4 of 5 — Real-World Problems

Decimals show up in real life all the time — especially with money! Dollars and cents are decimals, where the digits after the point are cents.

Money Example 💵

You have $20.00 and you spend $12.75. How much money is left?

This is a subtraction problem. Line up the points (the dollar amounts already have two decimal places):

$\begin{array}{r} 20.00 \\ - 12.75 \\ \hline 7.25 \end{array}$

You have $7.25 left. ✅

How to Tackle Word Problems

1. Read carefully to decide whether to add (combining or total) or subtract (difference, change, or "how much left").
2. Line up the decimal points and add placeholder zeros.
3. Check your answer — does it make sense? If you started with $20 and spent some, the answer should be less than $20.

Word Problem Practice 🧮

At the snack stand, Ava buys a juice for $1.50 and a granola bar for $2.35.

1. What is the total cost of both items? Add them. (Type it like $3.85$.)

2. Ava pays with a $5.00 bill. How much change does she get back? (Type it like $1.15$.)

3. Later she finds $0.40 in her pocket and adds it to her change. How much money does she have now? (Type it like $1.55$.)

Word Problem Check 📋

🏆 Review & Challenge

Part 5 of 5 — Review & Challenge

You made it! Here is everything you learned, all in one place.

Quick Summary Table

Remember:

• Adding a zero to the end of a decimal does not change its value: $0.5 = 0.50$.
• Money is just decimals — dollars and cents.
• For word problems, read carefully to decide whether to add or subtract.

Now try these mixed challenge problems!

Challenge Round 🎯

These mix everything together. Take your time!