Decimals add/subtract

1Summary 重點摘要

Align decimal points, then add/subtract like integers.

2Vocabulary cards Vocabulary

3Step by step Steps

1. Part 1: Set up with the dots in lineFor 1.25 + 3.4, write the column form so the two decimal points line up, not the last digits. 3.4 has one decimal place, so add a 0 at the end to make 3.40. Now both numbers have two decimal places, ready to add. Lining up the dots really means lining up the places; only with the places matched is the calculation reliable.
2. Part 2: An addition exampleFor 1.25 + 3.40: hundredths 5 + 0 = 5; tenths 2 + 4 = 6; ones 1 + 3 = 4. The answer is 4.65, with its dot on the same vertical line as the two dots above. The extra 0 only helps lining up and never changes the value. Add place by place, carry in your head or in small writing, and set the dot at the very end.
3. Part 3: Subtraction with borrowingFor 5 − 2.4, write 5 as 5.0 first. The tenths 0 − 4 cannot be done, so borrow 1 from the ones: the tenths become 10 and 10 − 4 = 6; the ones are left 4 and 4 − 2 = 2. The answer is 2.6. Padding zeros comes first. After borrowing, remember to reduce the digit that lent the 1, or everything after goes wrong.
4. Part 4: Where the dot goesThe answer's decimal point must stand on the same vertical line as the two points above. In 1.25 + 3.40 = 4.65 the dot in 4.65 lines up exactly with the two above. A misplaced dot makes the value 10 or 100 times too big or too small. Before writing the answer, check the dot's alignment — one second of care that can save the whole question.
5. Part 5: Estimate to checkEstimate before calculating: 1.25 is near 1 and 3.4 is near 3, so the answer should be a little over 4. That makes 4.65 sensible; 46.5 or 0.465 would mean the dot went in the wrong place. Estimating is the fastest check for decimals. The habit of 'estimate first, verify after' catches careless slips on the spot in a test.
6. Part 6: Money applicationBread costs 6.5 dollars and milk 12.3 dollars, so together 6.5 + 12.3 = 18.8 dollars. Pay 20 and the change should be 20 − 18.8 = 1.2 dollars. Money sums are decimal sums, so the position of the dot matters most. A receipt can serve as your check too — add the items one by one to confirm the total, the handiest review of all.

4Diagrams Diagrams

5Worked example Example

6Common mistakes Mistakes

7Quick check Quick check

8Recap Recap

• Step one: line up the decimal points, not the last digits
• Pad zeros to match: 3.4 = 3.40
• Carrying and borrowing work like whole numbers
• The answer's dot sits in the same column
• Estimate first to sanity-check the result