Adding and Subtracting Decimals
Adding and subtracting decimals requires aligning decimal points vertically so tenths line up with tenths and hundredths with hundredths. In Saxon Math Course 1 (Grade 6), students stack numbers with decimal points aligned, pad empty places with zeros, then add or subtract from right to left. For example, 54.6 + 13.75 becomes 54.60 + 13.75 = 68.35, and 68.35 − 8.20 = 60.15. This technique mirrors adding money — dollars align with dollars and cents with cents — making it a familiar entry point for all decimal computation.
Key Concepts
Property We line up decimal numbers for addition or subtraction by lining up the decimal points. The decimal point in the answer is aligned with the other decimal points. Empty places are treated as zeros.
Examples The sum of $3.46 + 0.2$ is found by aligning the points: $3.46 + 0.20 = 3.66$. To find the difference for $8.28 6.1$, calculate it as $8.28 6.10 = 2.18$. For multiple numbers like $3.4 + 0.26 + 0.3$, stacking them gives a total of $3.96$.
Explanation Forget lining up the last digit! When decimals enter the party, the decimal point is the VIP. You must line them up vertically. This ensures you’re adding apples to apples (tenths to tenths, hundredths to hundredths). It's the golden rule of decimal math that prevents your numbers from becoming a chaotic jumble of wrong answers.
Common Questions
Why must decimal points be lined up when adding decimals?
Aligning decimal points ensures tenths add to tenths and hundredths to hundredths, preserving place value exactly as in whole-number column addition.
How do you add 2.5 and 1.38?
Pad 2.5 as 2.50, then add: 2.50 + 1.38 = 3.88. The decimal point in the answer is directly below the other decimal points.
What does padding with zeros mean?
Adding zeros after the last decimal digit (e.g., 2.5 → 2.50) so both numbers have the same number of decimal places, making column alignment error-free.
Can subtraction of decimals use the same alignment rule?
Yes. Stack with decimal points aligned, pad shorter decimals with zeros, then subtract right to left with borrowing as needed.
What error happens when decimal points are not aligned?
Digits shift into wrong columns, causing tenths to be added to ones or hundredths to tenths, producing completely wrong answers.
How is decimal addition like adding money?
Money naturally aligns dollars with dollars and cents with cents at the decimal point — the same principle as decimal column addition.