Lesson 43: Adding and Subtracting Decimal Numbers, Part 1, Activity Adding and Subtracting Decimals

New Concept

We add or subtract decimal numbers by lining up the decimal points and then add or subtract.

Why it matters

This course is your training ground for algebra, where you'll learn to solve complex puzzles using the language of math. Starting with decimals teaches you the precision needed to handle any number, a core skill for unlocking powerful new problem-solving methods later on.

What’s next

Next, you’ll apply this rule to solve problems involving money and measurements, ensuring your calculations are precise every time.

Property

To add or subtract decimal numbers, we line up the decimal points. This action correctly aligns all the digits according to their place value, making sure you add tenths to tenths and hundredths to hundredths. This is the most important rule for decimal arithmetic!

Examples

To add $0.2$ and $0.5$, we line up the decimals:

$$
\begin{align*}
0.2 \\

• 0.5 \\

\hline
0.7
\end{align*}

Property

To add or subtract a whole number and a decimal, you must first convert the whole number into a decimal. Do this by placing a decimal point to its right and adding as many zeros as needed to match the other number's decimal places.

Examples

To solve $5.35 \text{ dollars} - 2 \text{ dollars}$, first change $2$ to $2.00$:

To add $6.32 \text{ dollars} + 5 \text{ dollars}$, change $5$ to $5.00$:

Explanation

Think of it as giving a whole number a disguise to fit in with the decimals! Adding a decimal point and some zeros does not change its value, but it allows the number to line up correctly for any addition or subtraction problem. This simple trick makes combining whole numbers and decimals easy.

Property

Before adding amounts of money, you must ensure they are all in the same format. Convert whole dollars to decimal form (e.g., 4 dollars becomes 4.00 dollars) and cents to their dollar equivalent (e.g., 15 cents becomes 0.15 dollars). This standardization is key.

Examples

To solve $3.75 \text{ dollars} + 4 \text{ dollars} + 15¢$, first convert to decimals:

Explanation

Mixing dollars, cents, and decimal amounts is like trying to add cats and dogs—it gets messy! By converting everything to the standard decimal format first, you make sure you are only adding like terms. This keeps your calculations clean, simple, and most importantly, correct every single time.