In this Grade 6 lesson from Big Ideas Math, Advanced 1 (Chapter 2: Fractions and Decimals), students learn how to add and subtract decimals by lining up decimal points vertically and inserting placeholder zeros to match decimal places. The lesson uses base ten block models and place value charts to build understanding before moving to standard algorithm practice with tenths, hundredths, and thousandths. It aligns with Common Core standard 6.NS.3 and includes real-life applications such as calculating costs and making change.
Section 1
Decimal Place Value Foundation
Each place represents 10 times the place just to the right, including decimal places. In decimal numbers, places to the right of the decimal point represent fractions of powers of ten. For example:
This can also be written using negative exponents:
Section 2
Adding and Subtracting Decimals - Core Algorithm
The algorithms for the arithmetic operations are the same for multi-digit decimals as the algorithm for whole numbers, with one additional ingredient: the placement of the decimal point in the answer.
For addition and subtraction this is a simple task: it goes in the same position as that for the given numbers.
If the numbers have different size decimal parts, we make them the same by filling in the empty spaces with zeroes.
Section 3
Regrouping in Decimal Subtraction
When subtracting decimals, if a digit in the minuend (top number) is smaller than the corresponding digit in the subtrahend (bottom number), you must regroup from the place value to the left.
One unit from the higher place value becomes ten units in the current place value, just like with whole numbers.
For decimal subtraction like :
Regroup from tenths to hundredths, then from ones to tenths:
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Section 1
Decimal Place Value Foundation
Each place represents 10 times the place just to the right, including decimal places. In decimal numbers, places to the right of the decimal point represent fractions of powers of ten. For example:
This can also be written using negative exponents:
Section 2
Adding and Subtracting Decimals - Core Algorithm
The algorithms for the arithmetic operations are the same for multi-digit decimals as the algorithm for whole numbers, with one additional ingredient: the placement of the decimal point in the answer.
For addition and subtraction this is a simple task: it goes in the same position as that for the given numbers.
If the numbers have different size decimal parts, we make them the same by filling in the empty spaces with zeroes.
Section 3
Regrouping in Decimal Subtraction
When subtracting decimals, if a digit in the minuend (top number) is smaller than the corresponding digit in the subtrahend (bottom number), you must regroup from the place value to the left.
One unit from the higher place value becomes ten units in the current place value, just like with whole numbers.
For decimal subtraction like :
Regroup from tenths to hundredths, then from ones to tenths:
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter