Multiplying & Dividing Integers Partner Matching Activity - Free Printable

Let's solve this step-by-step by following the flowchart from START to END, filling in each circle with the correct value based on the operations.

We'll go through each column (left, middle, right) and compute values as we move through the operations.

---

🔹 Left Column (Start at -8)

We begin at -8.

1. -8 × (-2)
= +16
→ First circle: +16

2. +16 × (+3)
= +48
→ Second circle: +48

3. +48 × (-3)
= -144
→ Third circle: -144

4. -144 ÷ (+2)
= -72
→ Fourth circle: -72

5. -72 × (+5)
= -360
→ Fifth circle: -360

Now, from this last result, we go to the middle column via:
> -360 ÷ (-9) → +40 ✔ (This matches the checkpoint)

So far so good.

---

🔹 Middle Column (Checkpoint: +40)

We start from +40 at the bottom of the middle column and go upward, reversing the operations (since arrows point upward).

Operations are:

1. +40 ← x (-5)
So, what number × (-5) = 40?
→ Let’s reverse:
40 ÷ (-5) = -8
→ Circle above: -8

2. -8 ← ÷ (+2)
So, what number ÷ (+2) = -8?
→ Reverse: -8 × (+2) = -16
→ Next circle: -16

3. -16 ← x (-4)
So, what × (-4) = -16?
→ Reverse: -16 ÷ (-4) = +4
→ Next circle: +4

4. +4 ← x (+3)
So, what × (+3) = +4?
→ Reverse: +4 ÷ (+3) = +4/3 ≈ 1.333...
But wait — let's check if this makes sense.

Wait! This suggests a fractional number, but the rest are integers. Let's double-check.

But hold on — we're going upward, so we’re applying reverse operations.

Let’s list them again carefully:

From bottom to top:

- Start: +40
- Operation before it: × (-5) → So previous value is: 40 ÷ (-5) = -8
- Then: ÷ (+2) → So previous value: -8 × (+2) = -16
- Then: × (-4) → So previous value: -16 ÷ (-4) = +4
- Then: × (+3) → So previous value: +4 ÷ (+3) = +4/3 ✘ Not integer.

Hmm — this seems problematic. But let’s see if there’s a mistake.

Wait — maybe we need to follow the flow properly.

Let’s re-express the middle column from bottom to top:

The operations are applied in reverse order because arrows go up.

But the operations are written between circles, so we must apply them correctly.

Let’s define the sequence:

We have:

```
[ ] ← ÷ (+2)
↑
[ ] ← x (-4)
↑
[ ] ← x (+3)
↑
[ ] ← ÷ (-4)
↑
[ ] ← ÷ (+2)
↑
-150 ← ÷ (+2)
```

Wait — no, the top of the middle column connects to -150 via ÷ (+2).

Let’s look at the structure:

- The top circle is connected to -150 by ÷ (+2) → So:
Top circle ÷ (+2) = -150
→ Therefore, top circle = -150 × (+2) = -300

So, top circle = -300

Now work downward from there.

But wait — the arrows in the middle column go upward, so we should go from bottom to top?

Actually, let's trace the flow.

From the right column, we know that -150 is a checkpoint, and it feeds into the middle column.

But the arrow from the middle column goes to -150 via ÷ (+2).

So:
Middle column top circle → ÷ (+2) → -150
→ So: top circle = -150 × (+2) = -300

So, top of middle column = -300

Now, below it: operation is ÷ (-4)

So:
-300 ÷ (-4) = +75 → next circle down

Then: × (+3)
+75 × (+3) = +225

Then: × (-4)
+225 × (-4) = -900

Then: ÷ (+2)
-900 ÷ (+2) = -450

Then: × (-5)
-450 × (-5) = +2250

But wait — this doesn't match the checkpoint at +40.

Wait — something is wrong.

Hold on — the bottom of the middle column is +40, and the top connects to -150.

And the arrows go upward from +40 to the top.

So the operations are:

- From bottom to top:
+40 → × (-5) → ?
→ ÷ (+2) → ?
→ × (-4) → ?
→ × (+3) → ?
→ ÷ (-4) → ?
→ ÷ (+2) → -150

Wait — but the last operation before -150 is ÷ (+2)

So:
Let’s define variables from bottom to top.

Let’s denote the circles from bottom to top as:

A → B → C → D → E → F → G

With:

- A = +40 (given)
- A → × (-5) → B
- B → ÷ (+2) → C
- C → × (-4) → D
- D → × (+3) → E
- E → ÷ (-4) → F
- F → ÷ (+2) → G = -150

So we can work backward from G = -150.

Let’s do that.

---

🔁 Work Backward from Middle Column (Top to Bottom)

We know:

- G = -150
- G = F ÷ (+2) → So F = -150 × (+2) = -300

- F = E ÷ (-4) → So E = F × (-4) = -300 × (-4) = +1200

- E = D × (+3) → So D = E ÷ (+3) = 1200 ÷ 3 = +400

- D = C × (-4) → So C = D ÷ (-4) = 400 ÷ (-4) = -100

- C = B ÷ (+2) → So B = C × (+2) = -100 × 2 = -200

- B = A × (-5) → So A = B ÷ (-5) = -200 ÷ (-5) = +40

✔ Matches the given checkpoint: +40

Perfect!

So now we can fill in the middle column from bottom to top:

- Bottom: +40
- × (-5) → -200
- ÷ (+2) → -100
- × (-4) → +400
- × (+3) → +1200
- ÷ (-4) → -300
- ÷ (+2) → -150

So the middle column (from bottom to top):

- +40
- -200
- -100
- +400
- +1200
- -300
- -150

Now, the top of the middle column is -300, which connects to the right column via ÷ (+2) → -150 ✔

Now, let’s go to the right column.

---

🔹 Right Column (Starts at -150)

We know:

- Start: -150
- ↓ × (-5)
- ↓ ÷ (-5)
- ↓ ÷ (-2)
- ↓ × (-4)
- ↓ ÷ (-3)
- End: 100

Let’s compute step by step:

1. -150 × (-5) = +750

2. +750 ÷ (-5) = -150

3. -150 ÷ (-2) = +75

4. +75 × (-4) = -300

5. -300 ÷ (-3) = +100

✔ Ends at 100 → Correct!

So right column values:

- -150
- +750
- -150
- +75
- -300
- +100

---

🔹 Left Column (We already did it earlier)

Let’s verify again:

Start: -8

1. × (-2): -8 × (-2) = +16

2. × (+3): +16 × 3 = +48

3. × (-3): +48 × (-3) = -144

4. ÷ (+2): -144 ÷ 2 = -72

5. × (+5): -72 × 5 = -360

Now: -360 ÷ (-9) = +40 ✔ (matches checkpoint)

So left column:

- -8
- +16
- +48
- -144
- -72
- -360

---

✔ Final Answer: Fill in all circles

#### Left Column (from top to bottom):
- -8
- +16
- +48
- -144
- -72
- -360

#### Middle Column (from bottom to top):
- +40
- -200
- -100
- +400
- +1200
- -300
- -150

(But in the diagram, the middle column has circles from bottom to top: +40 → ↑ → ... → -150)

So the circles (from bottom to top):

1. +40
2. -200
3. -100
4. +400
5. +1200
6. -300
7. -150

#### Right Column (from top to bottom):
- -150
- +750
- -150
- +75
- -300
- +100

---

🧩 Summary of All Values

Let’s write the full solution:

---

Left Column (Vertical Flow Down):

```
-8
↓ ×(-2)
+16
↓ ×(+3)
+48
↓ ×(-3)
-144
↓ ÷(+2)
-72
↓ ×(+5)
-360
→ ÷(-9) → +40
```

---

Middle Column (Vertical Flow Up):

```
-150 ← ÷(+2) ← -300
↑ ÷(-4)
↑ ×(+3)
↑ ×(-4)
↑ ÷(+2)
↑ ×(-5)
↑
+40
```

So from bottom to top:

- +40
- -200
- -100
- +400
- +1200
- -300
- -150

---

Right Column (Vertical Flow Down):

```
-150
↓ ×(-5)
+750
↓ ÷(-5)
-150
↓ ÷(-2)
+75
↓ ×(-4)
-300
↓ ÷(-3)
+100
```

---

✔ Verification

- Left end: -8 → -360 → ÷(-9) = +40 ✔
- Middle: +40 → … → -150 → ÷(+2) = -150 ✔
- Right: -150 → … → +100 ✔

All checkpoints match.

---

✔ Final Answer: Fill the Circles

Here is the complete filled-in chart:

#### Left Column (Top to Bottom):
- -8
- +16
- +48
- -144
- -72
- -360

#### Middle Column (Bottom to Top):
- +40
- -200
- -100
- +400
- +1200
- -300
- -150

#### Right Column (Top to Bottom):
- -150
- +750
- -150
- +75
- -300
- +100

All values are consistent and satisfy the operations.

✔ Problem Solved!