Ratios (6.RP.A.1 .2 .3 .a .b .c .d) - Printable Worksheets - The - Free Printable

Let’s solve each section of the “Find the Ratios” worksheet step by step. We’ll count the symbols carefully and simplify the ratios where possible.

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## Section 1: Hearts (♥) and Plus Signs (+)

Image has:
- Rows of hearts and plus signs.
- Count the ♥ and + in the entire grid.

Looking at the image:

There are 6 rows, each with:
- 4 ♥ and 8 + → so per row: 4 hearts, 8 pluses.

Total:
- ♥ = 6 × 4 = 24
- + = 6 × 8 = 48

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Question 1: What is the ratio of ♥ to +?

→ 24 : 48

Simplify by dividing both by 24:
→ 24 ÷ 24 : 48 ÷ 24 = 1 : 2

✔ Answer: 24 : 48 = 1 : 2

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Question 2: What is the ratio of + to (♥ + +)?

First, find total number of symbols: ♥ + + = 24 + 48 = 72

Ratio of + to total = 48 : 72

Simplify by dividing both by 24:
→ 48 ÷ 24 : 72 ÷ 24 = 2 : 3

✔ Answer: 48 : 72 = 2 : 3

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## Section 2: Black Circles (●) and Orange Pluses (+)

Image has:
- Grid of black circles and orange pluses.
- Let’s count:

Rows: 8 rows total.

Each row has:
- First 6 columns: ●
- Last 2 columns: +

So per row: 6 ●, 2 +

Total:
- ● = 8 × 6 = 48
- + = 8 × 2 = 16

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Question 1: What is the ratio of ● to +?

→ 48 : 16

Simplify by dividing both by 16:
→ 48 ÷ 16 : 16 ÷ 16 = 3 : 1

✔ Answer: 48 : 16 = 3 : 1

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Question 2: What is the ratio of + to (● + +)?

Total symbols = 48 + 16 = 64

Ratio of + to total = 16 : 64

Simplify by dividing both by 16:
→ 16 ÷ 16 : 64 ÷ 16 = 1 : 4

✔ Answer: 16 : 64 = 1 : 4

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## Section 3: Diamonds (◆) and Triangles (▲)

Image has:
- Grid of diamonds and triangles.
- 5 rows.

Each row:
- First 6 columns: ◆
- Last 8 columns: ▲

So per row: 6 ◆, 8 ▲

Total:
- ◆ = 5 × 6 = 30
- ▲ = 5 × 8 = 40

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Question 1: What is the ratio of ◆ to ▲?

→ 30 : 40

Simplify by dividing both by 10:
→ 30 ÷ 10 : 40 ÷ 10 = 3 : 4

✔ Answer: 30 : 40 = 3 : 4

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Question 2: What is the ratio of ▲ to (◆ + ▲)?

Total symbols = 30 + 40 = 70

Ratio of ▲ to total = 40 : 70

Simplify by dividing both by 10:
→ 40 ÷ 10 : 70 ÷ 10 = 4 : 7

✔ Answer: 40 : 70 = 4 : 7

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## Section 4: Orange Pluses (+) and Red Circles (●)

Image has:
- Grid of orange pluses and red circles.
- 5 rows.

Each row:
- First 8 columns: +
- Last 4 columns: ●

So per row: 8 +, 4 ●

Total:
- + = 5 × 8 = 40
- ● = 5 × 4 = 20

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Question 1: What is the ratio of + to ●?

→ 40 : 20

Simplify by dividing both by 20:
→ 40 ÷ 20 : 20 ÷ 20 = 2 : 1

✔ Answer: 40 : 20 = 2 : 1

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Question 2: What is the ratio of ● to (+ + ●)?

Total symbols = 40 + 20 = 60

Ratio of ● to total = 20 : 60

Simplify by dividing both by 20:
→ 20 ÷ 20 : 60 ÷ 20 = 1 : 3

✔ Answer: 20 : 60 = 1 : 3

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## ✔ Final Answers Summary:

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Section 1:
- Ratio of ♥ to + = 24 : 48 = 1 : 2
- Ratio of + to (♥ + +) = 48 : 72 = 2 : 3

Section 2:
- Ratio of ● to + = 48 : 16 = 3 : 1
- Ratio of + to (● + +) = 16 : 64 = 1 : 4

Section 3:
- Ratio of ◆ to ▲ = 30 : 40 = 3 : 4
- Ratio of ▲ to (◆ + ▲) = 40 : 70 = 4 : 7

Section 4:
- Ratio of + to ● = 40 : 20 = 2 : 1
- Ratio of ● to (+ + ●) = 20 : 60 = 1 : 3

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You can now fill in the worksheet with these answers! Let me know if you’d like a printable version or explanation for students.