Adding and Subtracting Decimal Numbers and Whole Numbers
Adding and subtracting decimal numbers and whole numbers requires writing the whole number with a decimal point and appending zeros so that decimal points align vertically. In Grade 6 Saxon Math Course 1 (Chapter 4: Number, Operations, and Measurement), students treat the whole number as a decimal (e.g., 7 becomes 7.00) before stacking the numbers. For 7 + 3.45: rewrite as 7.00 + 3.45 = 10.45. For 15 - 2.6: rewrite as 15.0 - 2.6 = 12.4. The rule is always align the decimal points, then add or subtract column by column as with any decimal problem.
Key Concepts
Property To add or subtract a whole number and a decimal, write the whole number with a decimal point and align the decimal points vertically. This ensures that you are combining digits with the same place value, like ones with ones and tenths with tenths.
Examples $15. + 9.5 + 15. + 9.5 = 49.0$ $25.75 8.00 = 17.75$ Find the total cost of a 5 dollars snack and a 2.50 dollars drink: $5.00 + 2.50 = 7.50$ dollars.
Explanation Think of a whole number as a celebrity trying to sneak into the decimal party. To fit in, it needs a disguise: a decimal point and a zero cape! By writing 7 as 7.0, you can line it up perfectly with other decimals like 3.14. This trick ensures everyone lines up correctly, preventing mathematical chaos and making your calculations neat and tidy.
Common Questions
How do you add a whole number and a decimal?
Write the whole number with a decimal point and enough trailing zeros to match the decimal's places. Align decimal points vertically, then add normally.
Add 7 and 3.45.
Rewrite 7 as 7.00. Stack: 7.00 + 3.45 = 10.45.
Subtract 2.6 from 15.
Rewrite 15 as 15.0. Stack: 15.0 - 2.6 = 12.4.
Why is it necessary to add zeros after the decimal point to a whole number?
Zeros ensure that all columns contain a digit, allowing correct place-value alignment. Without them, you might subtract tenths from ones.
Add 100 and 4.75.
Rewrite 100 as 100.00. Stack: 100.00 + 4.75 = 104.75.