Add, Subtract, and Multiply Multi-Digit Decimals

Lesson 1 of 2

In this lesson:

• Add and subtract decimals by aligning the points
• Multiply decimals by counting and placing the point
• Estimate first to catch off-by-ten errors

What You Will Be Able to Do

By the end, you will:

1. Align decimal points to add and subtract
2. Multiply decimals using count-and-place
3. Estimate to confirm reasonableness
4. Spot decimal-point misplacement errors

A Receipt You Need to Get Right

A grocery receipt: $43.87 + $12.59 + $7.45.

The dollars are easy: 43 + 12 + 7 = 62. But the cents matter — half a cent times a million transactions is real money.

How does the standard algorithm handle the decimal point?

Recap: How You Stack Whole Numbers

You already do this with whole numbers:

Columns align: ones under ones, tens under tens. Add right to left.

Aligning Points Means Aligning Places

Decimal points line up — and so do tenths, hundredths.

Add Column by Column, Drop the Point

Add right to left: (carry), (carry), , .

The decimal point in the answer drops straight down.

Different Lengths? Add Trailing Zeros

When decimals have different decimal-place counts, append zeros so columns match.

• (same value, more zeros visible)
• Trailing zeros do not change a decimal's value
• They make the place-value columns line up

Worked Subtraction: Step by Step

Estimate: . Answer 62.024 is right.

Mixing Decimals and Whole Numbers

Write as . All three decimal points align.

Estimate: . Answer 21.05 is right.

Predict: What If You Right-Justify?

Stack and with rightmost digits aligned (ignore the points).

What answer would that give? Try it before advancing.

• A.
• B.
• C.

Right-Justify Gives a Nonsense Answer

Estimate matches , not .

Quick Check:

Estimate first, then compute.

Pause. Estimate. Compute. Then advance.

Does the Decimal Drop Down for Multiplication?

For , where does the decimal point go?

• A. It drops straight down (like addition)
• B. It needs a different rule

Predict before advancing.

Multiply: Ignore Points, Then Place

The multiplication rule has three steps:

1. Ignore decimal points; multiply as integers
2. Count total decimal places in the factors
3. Place the point so the answer has that many places

Worked:

Estimate confirms .

Why the Count-and-Place Rule Works

The two zeros below come from the two factors of .

Worked:

Multiply . Count places: . Place: .

Estimate: . Answer matches.

Surprise: Smaller Than Both Factors

When both factors are less than , the product shrinks.

• — less than , less than
• A fraction of a fraction is smaller than either piece
• Multiplication does not always make things bigger

Trailing Zeros Drop in Answers

Compute . Count places: . Place: .

Drop the trailing zeros: .

Your Turn:

Estimate first, then compute, then check.

Pause. Estimate. Compute. Check.

Mixed Practice: Three Operations Together

Estimate first, then compute:

Pause and try each. Estimates next slide; full answers follow.

Answers and the Common Errors to Watch

1. (estimate )
2. (estimate )
3. (estimate )

Watch out: right-justifying (); miscounting places ( or ).

Key Takeaways from Today's Lesson

✓ Add/subtract: align the decimal points
✓ Multiply: ignore, multiply, count-and-place
✓ Estimate first, every time

Watch out:

• Don't right-justify when adding
• Don't drop down for multiplication
• Don't miscount decimal places
• Less-than-1 factors shrink products

Coming Up Next: Dividing Decimals

In Lesson 2, you will divide multi-digit decimals — first by a whole number (point goes up first), then by a decimal (shift both points equally).

The estimate-first habit travels forward.