Math worksheet for learning ratios using visual comparisons of shapes.

Let’s solve each question step by step.

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Question 1: What is the ratio of stars to squares?

Look at the shapes in the first row for this question:

Shapes:
□ □ ☆ ☆ ☆ □ □

Count:
- Stars (☆): 3
- Squares (□): 4

So, ratio of stars to squares = 3 : 4

This cannot be simplified further because 3 and 4 have no common factor other than 1.

✔ Answer: 3 : 4

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Question 2: What is the ratio of circles to triangles?

Second row:

Shapes:
● ● ● ● △ △

Count:
- Circles (●): 4
- Triangles (△): 2

Ratio of circles to triangles = 4 : 2

We can simplify this by dividing both numbers by their greatest common factor, which is 2.

4 ÷ 2 = 2
2 ÷ 2 = 1

Simplified ratio = 2 : 1

But the question asks for the ratio *before* simplifying? Let’s check:

Actually, looking back — Question 2 says “What is the ratio of circles to triangles?” — it doesn’t say “simplified”, so we give the raw count first.

Wait — let’s read carefully:

> 2) What is the ratio of circles to triangles? ___ : ___
> 3) What is the ratio of circles to triangles simplified? ___ : ___

Ah! So:

→ Q2 wants the unsimplified ratio → 4 : 2
→ Q3 wants the simplified version → 2 : 1

✔ Q2 Answer: 4 : 2
✔ Q3 Answer: 2 : 1

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Question 4: What is the ratio of triangles to circles?

Third row:

Shapes:
● ● ● △ △ △ ● ● △ △

Let’s count carefully:

Circles (●): positions 1,2,3,7,8 → that’s 5 circles
Triangles (△): positions 4,5,6,9,10 → that’s 5 triangles

Wait — let me recount:

Row:
● ● ● △ △ △ ● ● △ △

Breakdown:

1. ●
2. ●
3. ●
4. △
5. △
6. △
7. ●
8. ●
9. △
10. △

So:

Circles: 1,2,3,7,8 → 5
Triangles: 4,5,6,9,10 → 5

Ratio of triangles to circles = 5 : 5

✔ Q4 Answer: 5 : 5

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Question 5: What is the ratio of triangles to circles simplified?

From above: 5 : 5

Divide both by 5 → 1 : 1

✔ Q5 Answer: 1 : 1

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Question 6: What is the ratio of circles to triangles simplified?

Same group: circles = 5, triangles = 5

Ratio of circles to triangles = 5 : 5 → simplified = 1 : 1

✔ Q6 Answer: 1 : 1

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Now, double-check all answers:

Q1: stars to squares → 3 stars, 4 squares → 3:4 ✔️
Q2: circles to triangles (unsimplified) → 4:2 ✔️
Q3: same, simplified → 2:1 ✔️
Q4: triangles to circles → 5:5 ✔️
Q5: simplified → 1:1 ✔️
Q6: circles to triangles simplified → 1:1 ✔️

All correct.

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Final Answer:
1) 3 : 4
2) 4 : 2
3) 2 : 1
4) 5 : 5
5) 1 : 1
6) 1 : 1