Adding and subtracting decimals explained for parents (Australia)

Here's a homework answer that turns up in a lot of Year 6 books: 3.4 + 2.15 = 5.19. It looks reasonable at a glance. Your child added the whole numbers (3 + 2 = 5), then treated the bits after the point as their own little whole numbers (4 + 15 = 19). The true answer is 5.55, and the gap between the two tells you exactly what's missing: a feel for what each digit after the point is actually worth.

The good news is that adding and subtracting decimals uses the same column method your child already knows for whole numbers. There's really only one new habit — line up the decimal points so tenths sit under tenths and hundredths sit under hundredths — plus a couple of tidy-up moves like writing 5 as 5.00 before you take something away from it.

Below: why that habit works, worked examples, mental shortcuts, estimating, and real-life uses. If tenths and hundredths still feel wobbly, start with the overview of decimals.

The one habit that matters: point under point

With whole numbers, children learn to line sums up on the right edge. That rule quietly breaks once a decimal point arrives:

How it's set out	Working	Result
Lined up on the right edge (wrong)	3.4 sits over the 15 of 2.15	2.49 — nonsense, smaller than 3.4
Each side added separately (wrong)	3 + 2 and 4 + 15	5.19
Points lined up (right)	3.40 + 2.15, column by column	5.55

The dot itself isn't the clever part. What matters is matching digits that mean the same thing: the 4 in 3.4 is four tenths, the 1 in 2.15 is one tenth, and 3.4 has no hundredths at all. Once the points sit in a vertical line, each column holds one kind of value and ordinary column addition takes over.

Quick check: "What's the 4 worth?" If "four tenths" doesn't come easily, spend ten minutes on place value with coins or a ruler first.

Empty places and the zeros that fill them

Uneven numbers — one with a single decimal place, one with two — cause most of the trouble. Writing 3.4 as 3.40 doesn't change its value at all (four tenths is the same amount as forty hundredths), but it gives the hundredths column something to hold, so nothing gets lost.

Whole numbers work the same way: 5 can be written 5.00. If that feels like cheating to your child, use coins — 40 cents and four ten-cent pieces are the same money. It's the placeholder job described in zero holds the place, and it matters most in subtraction.

Adding decimals, step by step

Once the points line up, add from the right as usual and carry the decimal point straight down into the answer.

4.75 + 2.6

Write 2.6 as 2.60. Hundredths: 5 + 0 = 5. Tenths: 7 + 6 = 13, so write 3 and carry 1 into the ones. Ones: 4 + 2 + 1 = 7. Answer: 7.35.

Ten tenths make one whole, just as ten ones make a ten. If carries keep vanishing, see forgetting the carry.

0.8 + 0.5

Thirteen tenths is one whole and three tenths: 1.3. The classic wrong answer, 0.13, tucks the 13 behind the point. Counting in tenths out loud ("point eight, point nine, one, one point one…") fixes it fast.

12.36 + 7.9

Line the points up and treat 7.9 as 7.90. Hundredths: 6. Tenths: 3 + 9 = 12, write 2, carry 1. Ones: 2 + 7 + 1 = 10, write 0, carry 1. Tens: 1 + 1 = 2. Answer: 20.26.

6.05 + 3.98

Hundredths: 5 + 8 = 13, carry into the tenths; that column then reaches 10, which carries into the ones. The answer is 10.03 — a good test of whether your child trusts the columns.

Subtracting decimals (and why 5 becomes 5.00)

Same plan: points lined up, empty places filled, subtract from the right and trade when the top digit is too small — exactly like regrouping in subtraction, only now a tenth swaps for ten hundredths.

5 − 2.37

Write 5 as 5.00. You can't take 7 hundredths from 0, so trade: the 5 ones become 4 ones and 10 tenths, then one of those tenths becomes 10 hundredths, leaving 9 tenths. Hundredths: 10 − 7 = 3. Tenths: 9 − 3 = 6. Ones: 4 − 2 = 2. Answer: 2.63.

Without the zeros, plenty of children copy the .37 straight down and get 3.37.

8.4 − 3.65

Write 8.40. Hundredths: trade a tenth, 10 − 5 = 5. Tenths: 3 left, too few for 6, so trade a one: 13 − 6 = 7. Ones: 7 − 3 = 4. Answer: 4.75.

10.2 − 4.85

Write 10.20. After the trades, hundredths: 10 − 5 = 5; tenths: 11 − 8 = 3; ones: 9 − 4 = 5. Answer: 5.35.

0.6 − 0.25

Some children believe 0.25 is bigger than 0.6 because 25 beats 6. Writing 0.60 shows sixty hundredths against twenty-five: 0.60 − 0.25 = 0.35. (Column subtraction sets out the full written method.)

Mental shortcuts worth knowing

Not every sum needs paper:

• Bridge through a whole number. 2.7 + 0.5: 2.7 needs 0.3 to reach 3, then add the remaining 0.2 to get 3.2. This is the decimal version of making ten.
• Round, then adjust. 6.4 − 1.9: take away 2 to get 4.4, then give back the 0.1 you took too much, so 4.5. Or 3.99 + 2.45: add 4 to get 6.45, then take away 0.01, so 6.44.
• Count up to subtract. Change from $10 for a $6.35 item: $6.35 to $6.40 is 5 cents, $6.40 to $7.00 is 60 cents, $7.00 to $10.00 is $3. Total: $3.65. Sketching the jumps on a line helps.

Estimate first, then check

A ten-second estimate catches most slips. For 7.8 + 4.15, round to 8 + 4 = 12; the exact answer is 11.95, so a written 4.93 or 119.5 would stand out instantly.

Another: 9.12 − 3.7 is close to 9 − 4 = 5, and the exact answer is 5.42. Rough answers like these lean on rounding, and the habit of guessing first is unpacked in estimate before you add.

Calculators are fine too — Year 6 students are expected to use digital tools where sensible and then judge whether the screen is believable.

Where decimal sums show up in real life

Money. A canteen order of $3.85, $12.40 and $0.95 comes to $17.20, so change from $20 is $2.80. See money maths at home for shopping-trip ideas.

Length. A 1.35 m bookshelf next to a 0.8 m cupboard takes up 2.15 m of wall. See length and distance and converting units (0.8 m is 80 cm).

Mass. A 2.5 kg bag of flour with 0.75 kg used leaves 1.75 kg — handy on a baking day.

Sport. If a swimmer clocks 32.45 seconds one week and 31.9 the next, she's improved by 0.55 seconds.

Where this sits in the curriculum

The Australian Curriculum: Mathematics (version 9) lists adding and subtracting decimals as a Year 6 skill. Students apply place-value knowledge to add and subtract decimals, use digital tools where appropriate, and use estimation and rounding to check that answers are reasonable.

The groundwork is laid earlier. Year 4 students meet tenths and hundredths and work with money amounts, and Year 5 students build on that place value and connect familiar percentages to their decimal and fraction equivalents. In Victoria, Curriculum 2.0 mirrors version 9, and each school still picks its own sequence.

The road to decimal sums, Prep to Year 6

Prep–Year 3: whole-number addition and subtraction, place value to the thousands, and plenty of dollars-and-cents talk without formal decimals.

Year 4: tenths and hundredths as fractions of a whole, decimal money amounts, and first rough sums like "two items at about $2.50". Overview: Year 4.

Year 5: decimals in measurement and money, linking them to fractions and percentages, and plenty of money and measurement problems. Overview: Year 5.

Year 6: formal adding and subtracting of decimals with different numbers of places, estimating and checking, plus multiplying and dividing them (see multiplying and dividing by powers of ten). Overview: Year 6.

Being a term ahead or behind these markers is completely ordinary.

Talking about it at home

Questions beat worksheets. Try:

• "Which digits are worth the same kind of thing? Can you point to the tenths?"
• "Is there an empty place we should fill with a zero?"
• "Before you work it out, about how big should the answer be?"
• "Did you carry or trade anywhere? What did the ten turn into?"
• "Does that answer match your guess?"

Three sums your child can explain beat twenty rushed ones. If tears start, stop for the day (homework without tears).

Five games that make decimals feel normal

1. Make a dollar. Call out an amount like 0.35 and your child names the partner that makes 1 (0.65).
2. Catalogue shopping. Give a $50 budget and a supermarket catalogue. Your child picks three or four items, estimates the total, then works it out exactly and finds the change.
3. Closest to ten. Each player draws four digit cards and arranges them as two numbers with one decimal place (like 4.7 + 5.2). Closest total to 10 wins the round.
4. Spot my mistake. You do a sum with a deliberate slip, such as 0.8 + 0.5 = 0.13, and your child plays teacher.
5. Personal best. Time a simple activity (ten star jumps, tying shoelaces) with a phone stopwatch over a few days and work out how much faster or slower each attempt was.

Mistakes that come up again and again

Right-edge lining up. Writing 3.4 + 2.15 as if the last digits belong together. Draw a vertical line through the points first, then write the digits around it.

Adding the two sides separately. 3.4 + 2.15 = 5.19. Ask what the 15 means — fifteen hundredths, not fifteen tenths.

Thirteen tenths behind the point. 0.8 + 0.5 = 0.13. Count in tenths out loud, or use ten-cent coins.

Skipping zeros in subtraction. 8.4 − 3.65 = 5.25, from copying the 5 down and doing 6 − 4 instead of 4 − 6. Writing 8.40 and trading fixes it.

Losing the point. 4.75 + 2.6 = 735. A quick estimate ("about 7") exposes this immediately.

Longer means larger. Believing 0.25 > 0.6. Fill to the same number of places and compare 0.25 with 0.60.

When to ask for more support

If weeks of calm practice haven't helped your child line up a decimal sum, take some of their work to the teacher and find out how the class talks about and models decimals.

For bigger worries, a sensible first read is Is my child behind in maths?, followed by guides on maths anxiety and when to worry about maths. This page offers general information and can't assess an individual child; ongoing difficulties deserve a look from the school or a qualified professional.

FAQ

How do you add decimals?

Line up the decimal points, fill any empty places with zeros, then add each column from the right just like whole numbers, carrying when a column reaches ten. Bring the point straight down.

Why do you line up the decimal points?

So digits with the same value share a column: tenths with tenths, hundredths with hundredths. The point is simply the marker that makes the line-up easy.

Can you add a zero to the end of a decimal?

Yes. 3.4 and 3.40 are equal, so adding zeros after the last decimal digit fills empty places without changing the value.

What year do kids learn to add and subtract decimals in Australia?

In the Australian Curriculum (v9) it's a Year 6 skill, built on tenths and hundredths from Years 4 and 5. Schools vary in exact timing.

One small step this week

Next time a receipt lands on the bench, hand it over and ask your child to check whether the total is right — estimate first, then add properly. Real numbers that matter to your family will do more for decimal confidence than a stack of practice sheets.

Curious about your child's broader number skills? Ziado's free check is an adaptive diagnostic of roughly ten minutes that you can run at home. Parents see part of the results straight away, with no account or payment details required, and the complete placement unlocks once you sign up. It isn't a test of decimal sums on their own, it's not NAPLAN practice, and it's not a medical or learning-difficulty assessment. For ongoing practice, the Ziado maths page explains how things work. There's a 14-day free trial on both the Individual and Family plans, and pricing lays out each one.