Primary - Stage 3 (Year 5 & 6) Stage 3 (Year 5 & 6) Addition & Subtraction

Add whole numbers (written strategies) - With regrouping

20 practice questions 0 video lessons Theory + worked examples

Every question with a fully worked solution.

Theory

When a column adds to ten or more, carry the extra ten into the next column — this is regrouping. Add each column from the ones, write the ones digit of any total that reaches ten, and carry the rest.

The column algorithm adds numbers written one under the other, lined up by place value.

Regrouping (carrying) happens when a column adds to ten or more: write the ones digit of the total and carry the ten into the next column to the left.

Ten ones become one ten and ten tens become one hundred, so the value is kept — just regrouped into a higher place.

$2758 + 1467 = 4225$. The ones make $15$: write $5$, carry $1$. Carry wherever a column reaches ten.

When a column total reaches ten, the extra ten is regrouped into the next column as a single carried digit.

Column	Add	Write	Carry
Ones	$8+7=15$	$5$	$1$
Tens	$5+6+1=12$	$2$	$1$
Hundreds	$7+4+1=12$	$2$	$1$
Thousands	$2+1+1=4$	$4$	—

Ten of one place makes one of the next. Ten ones make a ten, ten tens make a hundred — the value is regrouped, not lost.

How to add with regrouping

Line up the numbers by place value and add the ones first.
Carry when a column reaches ten: write the ones digit, carry the ten.
Add the carried digit into the next column and continue to the left.

Example 1 — One carry

Calculate $148 + 236$.

Solution

Ones: $8+6=14$, write $4$ carry $1$.

$148 + 236$

$=$

$384$

Example 2 — Two carries

Calculate $367 + 285$.

Solution

Ones $7+5=12$; tens $6+8+1=15$.

$367 + 285$

$=$

$652$

Example 3 — Chained carries

Calculate $2758 + 1467$.

Solution

Every column from the ones reaches ten, so it carries each time.

$2758 + 1467$

$=$

$4225$

Example 4 — Money

Two prizes are $1875 and $2360. What is the total?

Solution

$1875 + 2360$

$=$

$4235$

The total is $4235.

Common pitfalls

Forgetting the carried digit. It is easy to leave out the little $1$ when adding the next column.

Writing the whole total. From $8+7=15$, write the $5$ and carry the $1$ ten — do not write $15$ in the column.

Missing a chained carry. A carry can push the next column to ten as well, so it carries again.

Frequently asked questions

What is regrouping in addition?

Regrouping, or carrying, is what you do when a column adds to ten or more: you write the ones digit and carry the ten into the next column. $8+7=15$ means write $5$, carry $1$.

How do you carry when adding?

Add a column; if the total is ten or more, write its ones digit underneath and place the tens digit as a small carry above the next column, then add it in.

Why do you carry the 1?

Ten ones make one ten, so the extra ten is regrouped into the tens column as a single $1$. The value is not lost, just moved to a higher place.

Can a carry happen more than once?

Yes. A carried digit can push the next column to ten as well, so it carries again. This can chain across several columns.

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Add whole numbers (written strategies) - 5-7 digit numbers