For parents and teachers
DecimalsGrades 4–6
Decimals Across Grades 4 to 6: Choose the Right Method
Decimal problems can look similar even when they need different methods. This guide shows how to identify the job, choose suitable steps and check whether an answer makes sense.
At 4:15, I am sitting beside Maya at her kitchen table. She has to work out 4.6 + 2.35, but she cannot decide whether to line up the final digits or the decimal points. She tries both ways and gets two different answers.
Start by naming the job
The decimal point is not an instruction by itself. First ask what the question wants: compare, add, subtract, multiply or divide. The answer changes the method.
For comparing, adding and subtracting, the position of each digit matters. A digit in the tenths place must be compared or calculated with tenths. A digit in the hundredths place belongs with hundredths.
Multiplication and division need different thinking. In multiplication, you can first calculate with whole numbers and then restore the decimal places. When dividing by a decimal, you can change both numbers by the same amount until the number you are dividing by is whole.
Which method fits this question?
1. Are you comparing or ordering decimals?
- Yes: Write the numbers with decimal points underneath one another. Add zeros at the right when they help you see matching places, then compare from left to right.
- No: go to question 2
2. Are you adding or subtracting?
- Yes: Put the decimal points in one vertical line. Fill any empty end places with zeros, then calculate one column at a time.
- No: go to question 3
3. Are you multiplying two decimals?
- Yes: Multiply as whole numbers first. Count all the decimal places in the two starting numbers, then put that many places in the product.
- No: go to question 4
4. Are you dividing by a decimal?
- Yes: Multiply both numbers by 10, 100 or 1000, the same one for each, until the number you are dividing by is whole. Then divide.
- No: Read the question again and identify the operation before calculating.
See how the methods differ
Suppose the question is 0.8 compared with 0.75. Writing 0.80 beside 0.75 shows eight tenths against seven tenths and five hundredths. The extra zero does not change the value; it only makes the places easier to see.
For 4.6 + 2.35, matching the final digits would put tenths under hundredths. Matching the decimal points instead gives 4.60 + 2.35. This is why Maya needs the decimal-point option at the kitchen table.
Now consider 1.2 × 0.4. Lining up points is not the multiplication rule. Calculate 12 × 4 = 48, count two decimal places across the starting numbers, and write 0.48.
For 3.6 ÷ 0.6, counting decimal places in the answer is not suitable either. Change both numbers by multiplying by 10, so the calculation becomes 36 ÷ 6. The answer is 6.
Use paper columns when places are hard to see
Draw one vertical line through the decimal points. Add faint column lines on either side, then write one digit in each space. This gives tenths, hundredths and whole-number digits their own positions.
Use these columns for comparing, adding or subtracting. Do not carry the layout into decimal multiplication or division, because those operations use the other methods in the decision guide.
If a number ends sooner, place a zero in the empty space at the right. When matching decimal places, add zeros at the right end of the decimal part, where needed. For example, write 4.6 as 4.60. A zero inserted between digits can change the number's value, so never add one there just to fill a column.
Work through Maya’s addition
4.6 + 2.35
- Make a quick estimate. The answer should be more than 6 and less than 7.
Show step 2
Rewrite 4.6 as 4.60. Put 4.60 above 2.35 with the decimal points in one line.Show step 3
Add the hundredths: 0 + 5 = 5.Show step 4
Add the tenths: 6 + 3 = 9.Show step 5
Add the ones: 4 + 2 = 6. Keep the decimal point in its column.
Answer: 6.95
Check the size as well as the digits
A written calculation can be neat and still use the wrong decimal position. Before accepting an answer, compare its size with the starting numbers.
For addition, the result should be larger than either positive starting number. For subtraction, ask whether the result is a sensible distance between the numbers. When multiplying by a positive decimal below 1, the result should be smaller than the other positive factor.
This size check does not replace the calculation. It catches answers such as 69.5 for Maya’s problem, which cannot fit the estimate between 6 and 7.
Avoid using one shortcut for every problem
Do not tell a child simply to move the decimal point. That wording can leave it unclear which digits change position, how far they change or whether both numbers must change.
Do not add zeros until the operation is clear. A zero at the right can help match places for comparison, addition and subtraction, but they are not needed for multiplication, where you count decimal places instead.
Also avoid correcting several different skills at once. If the trouble is lining up addition, stay with addition until the columns are secure. Bring in multiplication or division during a separate piece of practice.
Choose a page that matches the current problem
The Grade 4 decimal pages include reading, comparing, ordering, addition, subtraction and links between decimals and fractions. A learner who is unsure why 0.8 is greater than 0.75 can begin with comparison before returning to written calculation.
The Grade 5 collection adds work with whole-number multiplication and division, powers of ten and rounding. The Grade 6 collection also includes multiplying two decimals, dividing by a decimal and mixed calculations.
Choose by the skill shown in the child’s work, not just by the number printed at the top of a school page. If comparison is secure but multiplication is not, use multiplication steps rather than repeating comparison.
When to talk to the teacher
Talk to the teacher when it is not clear which method is being taught in class, especially if the written layout looks different from the one used here. Bring one completed example so the teacher can see where the steps changed.
Ask the school for more help if the child cannot tell what each digit is worth after calm practice with a few numbers, or if several decimal operations are becoming mixed together. The teacher can help choose one starting skill and keep home practice in step with classroom work.
Return to the kitchen-table choice
Back at the table, I ask Maya to circle the addition sign before touching the numbers. That rules out the multiplication and division methods. She draws a line through the decimal points, changes 4.6 to 4.60 and gets 6.95.
Her estimate gives one final check: 6.95 lies between 6 and 7. The useful choice was not the quickest-looking layout. It was the method that matched addition.
Quick review, once each skill has been practised
1Which is greater: 0.7 or 0.68?
0.7 is greater because it can be written as 0.70.
1. Which is greater: 0.7 or 0.68?
Answer: 0.7 is greater because it can be written as 0.70.
2Work out 3.4 + 1.25.
4.65
2. Work out 3.4 + 1.25.
Answer: 4.65
3Work out 5.00 − 2.36.
2.64
3. Work out 5.00 − 2.36.
Answer: 2.64
Questions parents ask
Why can a zero be added to the end of a decimal?
A zero at the far right after the decimal point does not change the value. It can make matching places easier to see, as in 0.7 and 0.70.
Should decimal points always be lined up?
Line them up for comparing, adding and subtracting. For multiplication, calculate with whole numbers and then restore the required decimal places. For division by a decimal, change both numbers by the same power of ten first.
What if the child gets the calculation right but puts the decimal point in the wrong place?
Use an estimate before calculating and compare the final answer with it. Then revisit only the method for that operation rather than mixing several decimal skills together.
From KidosLab
Was this guide helpful?
Related guides
Ready to practice?
Put it into practice with a free printable worksheet, Kindergarten to Grade 8. No account, no sign-up.
Find a worksheet