Seventh Grade Ratios, Rates, and Equivalency Practice - Free Printable

Since the user has not specified which option to activate (ExplainAnswer, TeachTopic, or GeneratePractice), and the request is simply to “solve the problem accurately” based on the uploaded image, I will assume the intent is to provide answers to all questions shown in the worksheet — treating it as a full homework solution.

However, per your instructions:
> If an option is false, completely omit that section.

And since all three options are set to `false`, I must omit Explanation, Teach Topic, and Practice Task sections entirely.

But then you also say:
> IMPORTANT: Complete ALL reasoning and explanations BEFORE writing the Final Answer.

This creates a conflict — if all options are false, do I still explain? The instruction says “if an option is true…”, implying if false, skip those sections. But then it also says “Complete ALL reasoning and explanations BEFORE writing the Final Answer.”

Given this ambiguity, I will interpret the core directive — “Solve the problem accurately” — as requiring me to work through each question step by step (as per CRITICAL rule), verify calculations, and only then give the final answer. Since no specific question was singled out, I’ll solve all 6 questions from the right-hand page (which appears to be the main focus).

Let’s go step by step.

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Question 1: What is the difference between a ratio and a rate?

- A ratio compares two quantities of the same kind (e.g., 3 apples to 5 oranges → 3:5).
- A rate compares two quantities of different kinds, often involving time or units (e.g., 60 miles per hour, $2 per pound).
→ So, key difference: ratios compare like things; rates compare unlike things (often with units).

✔ Verified.

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Question 2: What are the three ways to write a ratio?

Ratios can be written as:
1. Using a colon: 3 : 4
2. As a fraction: 3/4
3. With the word “to”: 3 to 4

✔ Standard curriculum answer.

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Question 3: Circle all the equivalent ratios in each set below.

We need to check which numbers in each set are proportional (i.e., simplify to same fraction).

Set 1: 1.3, 2.6, 2.6, 5.15, 7.9
Wait — these look like single numbers, not pairs. Probably typo? Looking back at left page, Set 1 there had pairs like (1,2), (2,4) etc. Here, likely meant to be pairs? But as written, they’re decimals.

Actually, looking again — perhaps these are meant to be simplified fractions? Or maybe it's listing values that should form ratios when paired?

Wait — let’s re-read: “Circle all the equivalent ratios in each set below.” And under Set 1: “1.3 2.6 2.6 5.15 7.9”

That doesn’t make sense unless we assume these are numerators or denominators? Alternatively, maybe it’s a misprint and should be pairs like (1,3), (2,6), etc.? Because 1:3 = 2:6 = 5:15, and 7.9 doesn’t fit.

Ah! Likely, the decimal points are typos — probably meant to be whole numbers: 1:3, 2:6, 2:6, 5:15, 7:9? But 7:9 isn't equivalent.

Alternatively, perhaps it's listing the second term assuming first term is 1? Like 1.3 means 1:3? That could be.

Assume:

Set 1: Ratios are 1:3, 2:6, 2:6, 5:15, 7:9

Simplify:
- 1:3 → 1/3
- 2:6 → 1/3
- 2:6 → 1/3
- 5:15 → 1/3
- 7:9 → 7/9 ≠ 1/3

So equivalent ones: 1:3, 2:6, 2:6, 5:15 → circle those.

But how are they presented? As “1.3” meaning 1:3? In many worksheets, yes — sometimes written without colon.

Similarly, Set 2: 1.5, 2.3, 2.6, 5.20, 6.9 → probably 1:5, 2:3, 2:6, 5:20, 6:9

Check:
- 1:5 = 0.2
- 2:3 ≈ 0.666
- 2:6 = 1/3 ≈ 0.333
- 5:20 = 1/4 = 0.25
- 6:9 = 2/3 ≈ 0.666 → so 2:3 and 6:9 are equivalent.

Set 3: 1.8, 4:28, 3:24, 5:35, 8:64

Write clearly:
- 1:8 = 0.125
- 4:28 = 1:7 ≈ 0.142...
- 3:24 = 1:8 = 0.125
- 5:35 = 1:7 ≈ 0.142...
- 8:64 = 1:8 = 0.125

So equivalent groups:
- Group A (1:8): 1:8, 3:24, 8:64
- Group B (1:7): 4:28, 5:35

So for Set 3, circle 1:8, 3:24, 8:64 together; and 4:28, 5:35 together — but since it says “circle all equivalent ratios”, probably group them.

But since it's one list, perhaps just identify which are equivalent to each other.

In practice, for Set 1: circle 1.3, 2.6, 2.6, 5.15 (assuming 1:3, 2:6, 2:6, 5:15)

For Set 2: circle 2.3 and 6.9 (since 2:3 and 6:9 both reduce to 2:3)

For Set 3: circle 1.8, 3:24, 8:64 (all 1:8); and separately 4:28, 5:35 (both 1:7) — but since it's one set, perhaps list which are equivalent.

To avoid overcomplicating, I'll state:

Set 1: Equivalent ratios are 1:3, 2:6, 2:6, 5:15 → so circle those four (ignoring 7:9)

Set 2: Equivalent are 2:3 and 6:9 → circle those

Set 3: Equivalent groups: (1:8, 3:24, 8:64) and (4:28, 5:35) — so circle accordingly.

But since the format is ambiguous, I'll proceed with standard interpretation.

✔ Verified logic.

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Question 4: Write an equivalent ratio to the one below: 5:3 = ___

Any multiple: e.g., multiply both by 2 → 10:6

Or by 3 → 15:9

Simplest: 10:6

✔ Correct.

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Question 5: Do the ratios below form a proportion? Prove your answer: 6:3 and 18:9

Proportion means they are equal.

Simplify 6:3 → 6÷3 : 3÷3 = 2:1

Simplify 18:9 → 18÷9 : 9÷9 = 2:1

Same → yes, they form a proportion.

Cross-multiply: 6×9 = 54, 3×18=54 → equal → proportion.

✔ Confirmed.

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Question 6: Name an example of a unit rate.

Unit rate: rate where second quantity is 1.

Examples:
- 60 miles per hour
- $2 per pound
- 3 words per minute

Pick one: 5 miles per hour

✔ Valid.

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Now, compiling final answers for all 6 questions:

Final Answer:
1. A ratio compares two similar quantities; a rate compares two different quantities, often with units.
2. Ratio can be written as a:b, a/b, or a to b.
3. Set 1: 1:3, 2:6, 2:6, 5:15; Set 2: 2:3, 6:9; Set 3: 1:8, 3:24, 8:64 and 4:28, 5:35
4. 10:6 (or any multiple like 15:9)
5. Yes, because both simplify to 2:1.
6. Example: 60 miles per hour