Division arrays online exercise for - Free Printable

Let’s solve each row step by step.

We are given arrays of dots. First, count how many dots are in each array — that’s the total number being divided.

Then, for each column:
- Left column: divide the total into groups of a certain size (the number of dots *per group*), and find how many such groups you get.
- Right column: divide the same total into a different group size, and find how many groups.

The format is:
“___ divided into groups of ___ is ___ groups.”
Then the division sentence: “___ ÷ ___ = ___”

Let’s go row by row.

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Row 2:
Array: 2 rows × 5 columns = 10 dots

Left: We need to choose a group size. Look at pattern from Row 1:
In Row 1, 12 dots → left: groups of 3 → 4 groups (12 ÷ 3 = 4)
Right: groups of 4 → 3 groups (12 ÷ 4 = 3)

So for Row 2 (10 dots), common group sizes could be 2 and 5 (since 10 = 2×5). Let’s verify visually:

The array is:
• • • • •
• • • • •
→ 2 rows, 5 columns → 10 dots.

If we group by 2, how many groups? 10 ÷ 2 = 5 groups.
If we group by 5, how many groups? 10 ÷ 5 = 2 groups.

That matches the pattern (like Row 1: 12 ÷ 3 = 4, 12 ÷ 4 = 3 — swapped group size and number of groups).

So:
Left: 10 divided into groups of 2 is 5 groups. → 10 ÷ 2 = 5
Right: 10 divided into groups of 5 is 2 groups. → 10 ÷ 5 = 2

✔ Good.

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Row 3:
Array: 3 rows × 5 columns = 15 dots

Look for factor pairs of 15: (3,5), (5,3), (1,15), etc. Likely using 3 and 5 again.

15 ÷ 3 = 5
15 ÷ 5 = 3

So:
Left: 15 divided into groups of 3 is 5 groups. → 15 ÷ 3 = 5
Right: 15 divided into groups of 5 is 3 groups. → 15 ÷ 5 = 3

✔ Matches pattern.

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Row 4:
Array: Let's count. It's 4 rows × 2 columns = 8 dots

Factor pairs of 8: (2,4), (4,2), (1,8), etc.

Try 2 and 4:
8 ÷ 2 = 4
8 ÷ 4 = 2

So:
Left: 8 divided into groups of 2 is 4 groups. → 8 ÷ 2 = 4
Right: 8 divided into groups of 4 is 2 groups. → 8 ÷ 4 = 2

✔ Makes sense.

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Row 5:
Array: 3 rows × 3 columns = 9 dots

Factor pairs: (3,3), (1,9), (9,1). Since both sides need different group sizes (like earlier rows), but 9 = 3×3 — only one nontrivial pair.

Wait — look at visual: it's a 3×3 grid → 9 dots.

Possibility: left: groups of 3 → 3 groups (9 ÷ 3 = 3)
right: groups of ? Maybe 1? But earlier rows used two different divisors.

But in Row 1, they used 3 and 4 (both divisors of 12). For 9, possible divisors: 1, 3, 9.

Maybe they intend:
Left: 9 ÷ 3 = 3
Right: 9 ÷ 1 = 9? But grouping into groups of 1 is trivial.

Wait — double-check the image description. The user said: “The first one is done for you.” In row 1, 12 dots, they used 3 and 4 — which are not symmetric; 12 ÷ 3 = 4, 12 ÷ 4 = 3 — they swapped divisor and quotient.

So the pattern is: pick two numbers a and b such that a × b = total, then write:
total ÷ a = b
total ÷ b = a

So for each row, total = rows × columns.

Let’s tabulate all arrays:

1) 3×4 = 12 → used (3,4)
2) 2×5 = 10 → use (2,5)
3) 3×5 = 15 → use (3,5)
4) 4×2 = 8 → use (2,4) — same as (2,4)
5) 3×3 = 9 → only (3,3) — but then both sides would be same: 9 ÷ 3 = 3 and 9 ÷ 3 = 3. Is that allowed?

Let’s see if the blank expects different numbers. The template has two separate blanks — maybe it's okay if same.

But maybe I miscounted row 5. Let me re-evaluate:

Row 5 array shown as:
• • •
• • •
• • •
→ yes, 3 rows, 3 columns = 9.

So likely:
Left: 9 divided into groups of 3 is 3 groups → 9 ÷ 3 = 3
Right: same? But the problem shows two columns — maybe they still want 9 ÷ 3 = 3 on both? Unlikely — perhaps it's 9 ÷ 1 = 9 and 9 ÷ 9 = 1? That also fits a × b = 9.

Check row 6 to infer pattern.

Row 6:
Array: 2 rows × 6 columns = 12 dots
Wait — same as row 1? But row 1 was 3×4=12. This is 2×6=12.

So total = 12 again.

Then possible pairs: (2,6), (3,4), (4,3), (6,2)

Row 1 used (3,4). Row 6 likely uses (2,6):

12 ÷ 2 = 6
12 ÷ 6 = 2

Yes — that fits the pattern: use the dimensions of the array as the group size and number of groups.

Aha! Key insight:

In each array, the grid is R rows × C columns = total dots.

Then:
- Left column: total divided into groups of R is C groups. Because you can think of grouping by rows → each group has R dots (one per row in a column), and there are C such groups (columns).
- Right column: total divided into groups of C is R groups.

Let’s verify with Row 1:
Array: 3 rows × 4 columns = 12
Left: groups of 3 (rows) → 4 groups (columns) → 12 ÷ 3 = 4 ✔
Right: groups of 4 (columns) → 3 groups (rows) → 12 ÷ 4 = 3 ✔

Perfect! So rule:
- Left: total ÷ (number of rows) = number of columns
- Right: total ÷ (number of columns) = number of rows

Now apply this to all rows.

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Row 2:
Array: 2 rows × 5 columns
Total = 10
Left: 10 ÷ 2 = 5 → “10 divided into groups of 2 is 5 groups.”
Right: 10 ÷ 5 = 2 → “10 divided into groups of 5 is 2 groups.”

✔

Row 3:
3 rows × 5 columns = 15
Left: 15 ÷ 3 = 5
Right: 15 ÷ 5 = 3

✔

Row 4:
How many rows/columns? Visual: looks like 4 rows × 2 columns
Yes: vertical stack of 4 pairs → 4 rows, 2 columns
Total = 8
Left: 8 ÷ 4 = 2
Right: 8 ÷ 2 = 4

Wait! Earlier I assumed left = ÷ rows, but in row 1, rows = 3, left used ÷3. So left is ÷ rows.

So for row 4: rows = 4, columns = 2
Left: 8 ÷ 4 = 2 groups
Right: 8 ÷ 2 = 4 groups

So:
Left: 8 divided into groups of 4 is 2 groups. → 8 ÷ 4 = 2
Right: 8 divided into groups of 2 is 4 groups. → 8 ÷ 2 = 4

I had swapped earlier — correction needed!

Let’s confirm with row 1 again:
Rows = 3, columns = 4
Left: ÷ rows = ÷3 → 4 groups = columns ✔
Right: ÷ columns = ÷4 → 3 groups = rows ✔

So general:
- Left: total ÷ (rows) = columns
- Right: total ÷ (columns) = rows

Thus for row 4 (4 rows, 2 columns):
Left: 8 ÷ 4 = 2
Right: 8 ÷ 2 = 4

Good.

Row 5:
3 rows × 3 columns = 9
Left: 9 ÷ 3 = 3
Right: 9 ÷ 3 = 3
So both are same — acceptable.

Row 6:
2 rows × 6 columns = 12
Left: 12 ÷ 2 = 6
Right: 12 ÷ 6 = 2

Now fill all blanks:

Row 2:
- Left: 10 divided into groups of 2 is 5 groups. → 10 ÷ 2 = 5
- Right: 10 divided into groups of 5 is 2 groups. → 10 ÷ 5 = 2

Wait — no! According to rule: left = ÷ rows. Rows = 2, so ÷2 → 5 groups (columns = 5) → yes, that matches.

But in row 4, rows = 4, so left = ÷4 → 2 groups. So consistent:

Row 2: rows=2, cols=5 → left: ÷2 = 5, right: ÷5 = 2
Row 3: rows=3, cols=5 → left: ÷3 = 5, right: ÷5 = 3
Row 4: rows=4, cols=2 → left: ÷4 = 2, right: ÷2 = 4
Row 5: rows=3, cols=3 → left: ÷3 = 3, right: ÷3 = 3
Row 6: rows=2, cols=6 → left: ÷2 = 6, right: ÷6 = 2

Now write all answers clearly:

2)
10 divided into groups of 2 is 5 groups.
10 ÷ 2 = 5
10 divided into groups of 5 is 2 groups.
10 ÷ 5 = 2

3)
15 divided into groups of 3 is 5 groups.
15 ÷ 3 = 5
15 divided into groups of 5 is 3 groups.
15 ÷ 5 = 3

4)
8 divided into groups of 4 is 2 groups.
8 ÷ 4 = 2
8 divided into groups of 2 is 4 groups.
8 ÷ 2 = 4

5)
9 divided into groups of 3 is 3 groups.
9 ÷ 3 = 3
9 divided into groups of 3 is 3 groups.
9 ÷ 3 = 3

6)
12 divided into groups of 2 is 6 groups.
12 ÷ 2 = 6
12 divided into groups of 6 is 2 groups.
12 ÷ 6 = 2

All checked.

Final Answer:
2) 10 divided into groups of 2 is 5 groups. 10 ÷ 2 = 5; 10 divided into groups of 5 is 2 groups. 10 ÷ 5 = 2
3) 15 divided into groups of 3 is 5 groups. 15 ÷ 3 = 5; 15 divided into groups of 5 is 3 groups. 15 ÷ 5 = 3
4) 8 divided into groups of 4 is 2 groups. 8 ÷ 4 = 2; 8 divided into groups of 2 is 4 groups. 8 ÷ 2 = 4
5) 9 divided into groups of 3 is 3 groups. 9 ÷ 3 = 3; 9 divided into groups of 3 is 3 groups. 9 ÷ 3 = 3
6) 12 divided into groups of 2 is 6 groups. 12 ÷ 2 = 6; 12 divided into groups of 6 is 2 groups. 12 ÷ 6 = 2