V.3 Add and subtract decimal numbers: word problems
What are decimal numbers?
Decimal numbers are numbers that show a part of a whole. They use a decimal point (.) to separate the whole number part from the fractional part. For example, in 3.25, the 3 is the whole number, and the 25 is the fractional part (twenty-five hundredths).
- 0.5 is the same as one-half (12).
- 1.75 is one whole and seventy-five hundredths.
- 4.00 is the same as the whole number 4.
When you add or subtract decimals, always line up the decimal points. This keeps the place values correct: ones with ones, tenths with tenths, hundredths with hundredths.
Adding decimals
Adding decimals means combining two or more decimal numbers to find the total. First, write the numbers in a column so the decimal points are aligned. Then, add each place value starting from the right. Finally, bring the decimal point straight down into your answer.
- Step 1: Line up the decimal points.
- Step 2: Add hundredths: 2 + 8 = 10 hundredths. Write 0 in the hundredths place and carry 1 to the tenths place.
- Step 3: Add tenths: 4 + 5 + 1 (carried) = 10 tenths. Write 0 in the tenths place and carry 1 to the ones place.
- Step 4: Add ones: 0 + 0 + 1 (carried) = 1.
- Step 5: Bring down the decimal point.
So, 0.42 + 0.58 = 1.00 (which is just 1).
If a decimal number does not show a digit in a place, imagine a zero there. For example, 0.4 is the same as 0.40. This makes adding easier.
Subtracting decimals
Subtracting decimals means finding the difference between two decimal numbers. Write the numbers in a column with decimal points lined up. Subtract starting from the rightmost place. If the top digit is smaller, regroup (borrow) from the left. Then bring the decimal point straight down.
- Step 1: Line up the decimal points: 1.25 and 0.47.
- Step 2: Hundredths: 5 − 7? You cannot. Borrow 1 tenth from the 2 tenths. The 2 becomes 1 tenth; the 5 becomes 15 hundredths. Now 15 − 7 = 8 hundredths.
- Step 3: Tenths: Now you have 1 tenth (after borrowing) minus 4 tenths? You cannot. Borrow 1 one from the 1 one. The 1 one becomes 0; the 1 tenth becomes 11 tenths. Now 11 − 4 = 7 tenths.
- Step 4: Ones: 0 − 0 = 0.
- Step 5: Bring down the decimal point.
So, 1.25 − 0.47 = 0.78.
Always check that your answer makes sense. If you subtract a smaller number from a larger number, your answer should be positive. If you subtract a larger number from a smaller number, you will get a negative decimal (which you will learn in later grades).
Solving word problems with decimals: addition
Word problems tell a short story with numbers. To solve a decimal addition word problem, look for keywords like total, together, sum, in all, combined, or how much altogether. Then, write the decimal numbers in a column, line up the decimal points, and add.
Maya bought a notebook for $3.25 and a pen for $1.75. How much did she spend in total?
- Step 1: Identify the numbers: $3.25 and $1.75.
- Step 2: Decide the operation: “in total” means addition.
- Step 3: Line up decimals and add.
Step 4: Write the answer with the correct unit: Maya spent $5.00 (or $5).
Always include the unit (like dollars, meters, or liters) in your final answer. Word problems expect a complete sentence or labeled number.
Solving word problems with decimals: subtraction
Subtraction word problems often use keywords like difference, how much more, how much less, remain, left, or how much farther. Write the larger number on top, line up the decimals, and subtract.
Leo ran 2.75 kilometers on Monday and 1.9 kilometers on Tuesday. How many more kilometers did he run on Monday than on Tuesday?
- Step 1: Identify the numbers: 2.75 km and 1.9 km.
- Step 2: “How many more” means subtraction: 2.75 − 1.9.
- Step 3: Write 1.9 as 1.90 to match place values.
- Step 4: Line up and subtract.
Step 5: Answer: Leo ran 0.85 kilometers more on Monday.
If a decimal in a word problem has fewer digits after the decimal point, add zeros to make the numbers the same length. This prevents mistakes.
Two-step word problems with adding and subtracting decimals
Some word problems need more than one step. You might add first, then subtract. Or subtract twice. Read carefully, decide the order, and solve one part at a time.
Ella had $20.00. She bought a book for $7.99 and a game for $5.49. How much money does she have left?
- Step 1: Add the costs: $7.99 + $5.49.
- Step 2: Subtract the total cost from the money she had: $20.00 − $13.48.
Step 3: Ella has $6.52 left.
Always show your work step by step. If you make a mistake in step 1, step 2 will also be wrong. Check each small calculation.
Estimating decimal sums and differences in word problems
Estimation helps you check if your answer is reasonable. Round each decimal to the nearest whole number or to the nearest tenth. Then add or subtract. Your exact answer should be close to your estimate.
A recipe needs 2.35 cups of flour and 1.82 cups of sugar. About how many cups total? Then find the exact total.
- Estimate: Round 2.35 to 2, round 1.82 to 2. Estimate total ≈ 4 cups.
- Exact addition:
Exact total = 4.17 cups. The estimate (4 cups) is very close, so the answer is reasonable.
Estimation is not guessing. It is a quick math check. If your exact answer is far from your estimate, re-add or re-subtract.
Avoiding common mistakes with decimal word problems
Students often make the same mistakes. Knowing them ahead of time helps you avoid them.
- Mistake: Not lining up decimal points.
Fix: Write numbers in a column, one above the other, with decimal points in a straight line. - Mistake: Forgetting to write the decimal point in the answer.
Fix: Bring the decimal point straight down before you write the digits. - Mistake: Adding or subtracting without regrouping when needed.
Fix: Work from right to left and borrow or carry carefully. - Mistake: Ignoring the unit (dollars, kg, miles).
Fix: Write the unit from the problem into your final answer.
Slow down. Decimal word problems are easy to rush. Read the problem twice before writing any numbers.
Common Core alignment: CCSS.MATH.CONTENT.4.NF.C.5 – Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with denominators 10 and 100. CCSS.MATH.CONTENT.4.NBT.B.4 – Fluently add and subtract multi-digit whole numbers using the standard algorithm, including decimals to hundredths.
Notes for teachers
This lesson is aligned with CCSS.MATH.CONTENT.4.NF.C.5 and 4.NBT.B.4. All content is 100% free; use it for whole-class instruction, independent study and practice, or homework. Emphasize place value, lining up decimal points, and reading word problems for keywords.