Adding Decimals with Same Number of Decimal Places

Calculate $3.45 + 2.31$

Line up the decimal points: Write the numbers vertically with decimal points aligned = $\begin{array}{r} 3.45 \\ +2.31 \end{array}$

Add the hundredths column: $5 + 1 = 6$ = 6 hundredths

Add the tenths column: $4 + 3 = 7$ = 7 tenths

Add the ones column: $3 + 2 = 5$ = 5 ones

Bring down the decimal point: Place the decimal between ones and tenths = $5.76$

Answer: $3.45 + 2.31 = 5.76$

Subtracting Decimals with Borrowing

Calculate $8.25 - 3.48$

Line up the decimal points: Write the numbers vertically with decimal points aligned = $\begin{array}{r} 8.25 \\ -3.48 \end{array}$

Subtract hundredths (need to borrow): Cannot do $5 - 8$, so borrow from tenths: $15 - 8 = 7$ = 7 hundredths

Subtract tenths (after borrowing): $1 - 4$ still needs borrowing from ones: $11 - 4 = 7$ = 7 tenths

Subtract ones (after borrowing): $7 - 3 = 4$ = 4 ones

Bring down the decimal point: Place the decimal between ones and tenths = $4.77$

Answer: $8.25 - 3.48 = 4.77$

Adding Decimals with Different Decimal Places

Calculate $12.6 + 4.35$

Line up the decimal points: Write numbers vertically, aligning decimal points = $\begin{array}{r} 12.6\phantom{0} \\ +\phantom{0}4.35 \end{array}$

Add a zero placeholder: $12.6$ becomes $12.60$ to match decimal places = $\begin{array}{r} 12.60 \\ +\phantom{0}4.35 \end{array}$

Add the hundredths: $0 + 5 = 5$ = 5 hundredths

Add the tenths: $6 + 3 = 9$ = 9 tenths

Add the ones and tens: $2 + 4 = 6$ ones, bring down the $1$ in tens = $16.95$

Answer: $12.6 + 4.35 = 16.95$

Mistake: Not lining up the decimal points

Why: When decimals are not aligned, you end up adding digits with different place values, like adding tenths to hundredths.

Correct: Always write the numbers vertically with decimal points directly above each other before calculating.

Mistake: Forgetting to add zero placeholders

Why: Without placeholders, it's easy to misalign digits. For example, adding $2.5 + 1.25$ without writing $2.50$ can cause errors.

Correct: Add zeros at the end of decimals so all numbers have the same number of decimal places: $2.50 + 1.25$

Mistake: Forgetting to bring down the decimal point

Why: The answer looks correct but is actually 10, 100, or 1000 times too large!

Correct: Always place the decimal point in your answer directly below the decimal points in the problem.

Shopping and Money

Every time you buy multiple items or calculate change, you use decimal addition and subtraction.

A notebook costs 4.99 dollars and a pen costs 2.50 dollars. The total is $4.99 + 2.50 = 7.49$ dollars.

Sports and Timing

In racing events, times are measured in decimals of seconds. Athletes compare times to see improvement.

A swimmer's time dropped from $28.45$ seconds to $27.82$ seconds. The improvement is $28.45 - 27.82 = 0.63$ seconds.

Q: Why do we need to line up the decimal points?

A: Lining up decimal points ensures that digits with the same place value are in the same column. This means ones are added to ones, tenths to tenths, hundredths to hundredths, and so on.

Q: Can I add zeros at the end of a decimal without changing its value?

A: Yes! Adding zeros at the end of a decimal does not change its value. $3.5 = 3.50 = 3.500$. This is helpful for aligning decimal places when adding or subtracting.

Q: What if one number has no decimal and the other does?

A: Add a decimal point and zeros to the whole number. For example, to add $7 + 2.35$, rewrite $7$ as $7.00$, then line up and add.