Assorted Venn diagrams worksheet for practicing number classification and set logic.

Let’s solve each Venn diagram one by one. We’ll go step by step and check our work carefully.

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Top Left: Numbers less than 20 vs. Numbers greater than 30

We have these numbers to place:
14, 51, 25, 32, 34, 29, 20, 100

First, understand the circles:
- Left circle: numbers less than 20
- Right circle: numbers greater than 30
- Middle (overlap): numbers that are BOTH less than 20 AND greater than 30 → impossible! So overlap is empty.
- Outside both: numbers that are NOT less than 20 AND NOT greater than 30 → so between 20 and 30 inclusive? Wait — let’s be precise.

Actually, “less than 20” means < 20
“Greater than 30” means > 30
So numbers from 20 to 30 inclusive go outside both circles.

Now sort each number:

- 14 → < 20 → left circle only
- 51 → > 30 → right circle only
- 25 → between 20 and 30 → outside both
- 32 → > 30 → right circle only
- 34 → > 30 → right circle only
- 29 → between 20 and 30 → outside both
- 20 → not less than 20, not greater than 30 → outside both
- 100 → > 30 → right circle only

Wait — what about 20? The condition is “less than 20” — so 20 is NOT included. Similarly, “greater than 30” — 30 is not included. So 20 to 30 inclusive go outside.

So:

Left circle (<20): 14
Right circle (>30): 51, 32, 34, 100
Outside both: 25, 29, 20
Overlap: none

But wait — we have 8 numbers total. Let’s list them again:

Given: 14, 51, 25, 32, 34, 29, 20, 100 → yes, 8 numbers.

Assigned:
- Left: 14 → 1 number
- Right: 51, 32, 34, 100 → 4 numbers
- Outside: 25, 29, 20 → 3 numbers
Total: 1+4+3 = 8 ✔️

Good.

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Top Right: Even numbers vs. Numbers greater than 20

Numbers given:
24, 18, 20, 27, 4, 16, 26, 21, 14, 29

Left circle: even numbers
Right circle: numbers > 20
Overlap: even AND > 20
Outside: neither even nor > 20 → odd and ≤ 20

Let’s go one by one:

- 24 → even AND >20 → overlap
- 18 → even, but 18 ≤ 20 → left only
- 20 → even, but 20 is NOT >20 → left only
- 27 → odd, >20 → right only
- 4 → even, ≤20 → left only
- 16 → even, ≤20 → left only
- 26 → even, >20 → overlap
- 21 → odd, >20 → right only
- 14 → even, ≤20 → left only
- 29 → odd, >20 → right only

Now group:

Left only (even, ≤20): 18, 20, 4, 16, 14 → 5 numbers
Right only (odd, >20): 27, 21, 29 → 3 numbers
Overlap (even, >20): 24, 26 → 2 numbers
Outside (neither): any left? All accounted for? Total numbers: 10

Check: 5 + 3 + 2 = 10 ✔️

No number is both odd and ≤20? Let’s see: 18,20,4,16,14 are even; 27,21,29 are odd>20; 24,26 even>20. What about odd ≤20? None in the list. So outside is empty? But according to logic, outside should be numbers that are NOT even AND NOT >20 → i.e., odd and ≤20. In this set, there are no such numbers. So outside is empty. That’s fine.

Wait — let me double-check the list: 24,18,20,27,4,16,26,21,14,29 — all covered. No odd numbers ≤20. So outside = empty.

Okay.

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Bottom Left: Multiples of 2 vs. Multiples of 3

Numbers: 2, 3, 6, 8, 12, 15, 18, 21

Left circle: multiples of 2 → divisible by 2
Right circle: multiples of 3 → divisible by 3
Overlap: multiples of both → multiples of 6
Outside: neither multiple of 2 nor 3

Go one by one:

- 2 → multiple of 2 only → left
- 3 → multiple of 3 only → right
- 6 → multiple of 2 and 3 → overlap
- 8 → multiple of 2 only → left
- 12 → multiple of 2 and 3 → overlap
- 15 → multiple of 3 only → right
- 18 → multiple of 2 and 3 → overlap
- 21 → multiple of 3 only → right

Now group:

Left only (mult 2, not mult 3): 2, 8 → 2 numbers
Right only (mult 3, not mult 2): 3, 15, 21 → 3 numbers
Overlap (mult 6): 6, 12, 18 → 3 numbers
Outside: any? Check if any number is not mult of 2 or 3.

List: 2,3,6,8,12,15,18,21 — all are either mult of 2 or 3 or both. So outside = empty.

Total: 2+3+3=8 ✔️

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Bottom Right: Numbers less than 1 vs. Numbers greater than 0.7

Numbers: 0.08, 0.8, 1.8, 2.8, 1/2, 1, 6/10, 10

Note: 1/2 = 0.5, 6/10 = 0.6

So rewrite decimals:

0.08, 0.8, 1.8, 2.8, 0.5, 1, 0.6, 10

Left circle: < 1
Right circle: > 0.7
Overlap: <1 AND >0.7 → so between 0.7 and 1 (not including 0.7 or 1)
Outside: not <1 and not >0.7 → so ≥1 and ≤0.7 → impossible? Wait:

Not <1 → ≥1
Not >0.7 → ≤0.7
So outside: numbers that are ≥1 AND ≤0.7 → impossible. So outside should be empty? But let’s think:

Actually, outside = numbers that are NOT in left AND NOT in right → so NOT (<1) AND NOT (>0.7) → which is ≥1 AND ≤0.7 → no number can satisfy that. So outside is always empty? Not necessarily — if a number is exactly 1, it’s not <1, and if it’s 0.7, it’s not >0.7. But here, we need to check each number.

Better to assign each number:

Define:

- Left: x < 1
- Right: x > 0.7
- Overlap: 0.7 < x < 1
- Outside: x ≥ 1 OR x ≤ 0.7? No — outside is NOT left AND NOT right → so x ≥ 1 AND x ≤ 0.7 → impossible. So actually, every number must be in at least one circle? Let’s test.

Take x = 1:
Is 1 < 1? No → not in left
Is 1 > 0.7? Yes → in right → so in right circle only

x = 0.5:
<1? Yes → left
>0.7? No → not in right → so left only

x = 0.8:
<1? Yes → left
>0.7? Yes → right → overlap

x = 0.08:
<1? Yes → left
>0.7? No → left only

x = 1.8:
<1? No
>0.7? Yes → right only

x = 2.8: same → right only

x = 10: same → right only

x = 0.6:
<1? Yes → left
>0.7? No → left only

Now list all:

Numbers: 0.08, 0.8, 1.8, 2.8, 0.5, 1, 0.6, 10

Assign:

- Left only (<1 and ≤0.7): 0.08, 0.5, 0.6 → because they are <1 but not >0.7
- Right only (≥1 and >0.7): 1.8, 2.8, 10, and also 1? 1 is ≥1 and >0.7 → yes, so 1 goes to right only
- Overlap (0.7 < x < 1): 0.8 → since 0.8 is >0.7 and <1
- Outside: any number that is not <1 and not >0.7? As discussed, impossible. But let’s check: is there a number that is ≥1 and ≤0.7? No. So outside = empty.

Wait — what about 1? It’s not <1, but it is >0.7 → so in right circle.

What about 0.7 itself? Not in list.

So:

Left only: 0.08, 0.5, 0.6 → 3 numbers
Right only: 1.8, 2.8, 10, 1 → 4 numbers
Overlap: 0.8 → 1 number
Outside: none? But total numbers: 8 → 3+4+1=8 ✔️

But wait — 1 is equal to 1, so not <1, but >0.7 → correct, right only.

And 0.8 is between 0.7 and 1 → overlap.

Perfect.

But note: 6/10 = 0.6, 1/2=0.5 — already used.

So final assignment:

Left only: 0.08, 1/2, 6/10 → which are 0.08, 0.5, 0.6
Right only: 1.8, 2.8, 10, 1
Overlap: 0.8
Outside: none

But the problem says "numbers less than 1" and "numbers greater than 0.7". So 1 is not less than 1, but is greater than 0.7 → right circle. Correct.

Now, to write the answer clearly.

Since the user wants the final answer with placements, I’ll summarize each diagram.

But the instruction says: “Place the numbers in the correct positions on the Venn diagrams.” So for each diagram, we need to say which numbers go where.

Since it’s text, I’ll describe for each diagram:

For Top Left:
- Left circle (less than 20): 14
- Right circle (greater than 30): 51, 32, 34, 100
- Outside both: 25, 29, 20
- Overlap: none

For Top Right:
- Left circle (even): 18, 20, 4, 16, 14
- Right circle (greater than 20): 27, 21, 29
- Overlap (even and greater than 20): 24, 26
- Outside: none

Wait — earlier I said left only is even and ≤20, but the circle is just "even numbers", so all evens go in left circle, regardless of size. Similarly, right circle is "numbers greater than 20", so all >20 go in right, regardless of parity.

In my initial assignment, I put:

Left circle (even): includes those that are even, whether >20 or not. But in Venn diagram, the left circle contains ALL even numbers, so 24 and 26 should also be in left circle, but they are also in right circle, so they go in overlap.

Similarly, right circle contains all numbers >20, so 24,26,27,21,29 are in right circle, but 24,26 are also even, so overlap.

So for Top Right:

Left circle (even numbers): 24, 18, 20, 4, 16, 26, 14 → all evens
But in Venn, we split into:
- Only left: even but not >20 → 18,20,4,16,14
- Only right: >20 but not even → 27,21,29
- Overlap: even and >20 → 24,26
- Outside: neither → none

Yes.

Similarly for others.

Now for Bottom Left:

Multiples of 2: 2,6,8,12,18
Multiples of 3: 3,6,12,15,18,21
Overlap: multiples of 6: 6,12,18
Left only: multiples of 2 not 3: 2,8
Right only: multiples of 3 not 2: 3,15,21
Outside: none

Bottom Right:

Less than 1: 0.08, 0.8, 0.5, 0.6, and also 1? No, 1 is not less than 1. So <1: 0.08, 0.8, 0.5, 0.6
Greater than 0.7: 0.8, 1.8, 2.8, 1, 10
Overlap: <1 and >0.7: 0.8
Left only: <1 and ≤0.7: 0.08, 0.5, 0.6
Right only: ≥1 and >0.7: 1.8, 2.8, 1, 10
Outside: none

All good.

Now, to present the final answer as per requirement.

The user didn't specify format, but since it's "place the numbers", I'll list for each diagram the sets.

But perhaps better to write:

Final Answer:

Top Left Diagram:
- Less than 20 only: 14
- Greater than 30 only: 51, 32, 34, 100
- Both: (empty)
- Neither: 25, 29, 20

Top Right Diagram:
- Even only (not >20): 18, 20, 4, 16, 14
- Greater than 20 only (not even): 27, 21, 29
- Both (even and >20): 24, 26
- Neither: (empty)

Bottom Left Diagram:
- Multiples of 2 only (not multiple of 3): 2, 8
- Multiples of 3 only (not multiple of 2): 3, 15, 21
- Both (multiples of 6): 6, 12, 18
- Neither: (empty)

Bottom Right Diagram:
- Less than 1 only (not >0.7): 0.08, 1/2, 6/10
- Greater than 0.7 only (not <1): 1.8, 2.8, 1, 10
- Both (between 0.7 and 1): 0.8
- Neither: (empty)

Note: 1/2 = 0.5, 6/10 = 0.6, so we can write as fractions or decimals, but since input has mixed, keep as given.

In the box, it's written as 1/2 and 6/10, so use those.

Also, for bottom right, "numbers less than 1" includes 0.8, but 0.8 is also >0.7, so in overlap.

I think this is accurate.

Let me verify one more time for bottom right:

Numbers: 0.08, 0.8, 1.8, 2.8, 1/2 (0.5), 1, 6/10 (0.6), 10

- <1: 0.08, 0.8, 0.5, 0.6 → four numbers
- >0.7: 0.8, 1.8, 2.8, 1, 10 → five numbers
- Intersection: 0.8 → one number
- Left only: <1 and not >0.7 → 0.08, 0.5, 0.6 → three
- Right only: >0.7 and not <1 → 1.8, 2.8, 1, 10 → four (since 1 is not <1)
- Total: 3+4+1=8 ✔️

Perfect.

Now, for the final answer section, since the user said "provide only the final correct answer", but it's multiple diagrams, I need to present it clearly.

Perhaps list each diagram's content.

Since it's a worksheet, maybe they expect the numbers placed in regions.

I'll write it as:

Final Answer:

Diagram 1 (Top Left):
- Left circle only: 14
- Right circle only: 51, 32, 34, 100
- Intersection:
- Outside: 25, 29, 20

Diagram 2 (Top Right):
- Left circle only: 18, 20, 4, 16, 14
- Right circle only: 27, 21, 29
- Intersection: 24, 26
- Outside:

Diagram 3 (Bottom Left):
- Left circle only: 2, 8
- Right circle only: 3, 15, 21
- Intersection: 6, 12, 18
- Outside:

Diagram 4 (Bottom Right):
- Left circle only: 0.08, \frac{1}{2}, \frac{6}{10}
- Right circle only: 1.8, 2.8, 1, 10
- Intersection: 0.8
- Outside:

To make it neat.

In the original, numbers are given as is, so for bottom right, use fractions as given.

Also, in top right, 20 is even and not greater than 20, so in left only — correct.

I think this is solid.

So final answer below.