Converting Rates Worksheet: Complete with ease | airSlate SignNow - Free Printable

Explanation:
We are given several unit conversion problems. The goal is to convert from one unit to another using known relationships (e.g., 1 km = 1000 m, 1 hour = 60 minutes, 1 kg = 1000 g, 1 liter = 1000 mL, etc.). Let’s solve each one carefully.

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1) Convert 55 km/hour into m/minute

- 55 km = 55 × 1000 = 55,000 meters
- 1 hour = 60 minutes
So:
55 km/hour = 55,000 m / 60 min = 55,000 ÷ 60 = 916.67 m/min (or as a fraction: 2750/3 ≈ 916.67)

But let’s keep it exact for now:
55,000 ÷ 60 = 5500 ÷ 6 = 2750 ÷ 3 ≈ 916.67
We’ll round to two decimals if needed — but the problem doesn’t specify rounding. Usually in such worksheets, decimal answers are fine.

Let me compute precisely:
55,000 ÷ 60 = 916.666... → 916.67 m/min (rounded to 2 decimals)

But maybe they want exact fraction? Let's hold and check others — perhaps all expect simplified decimals or fractions.

Wait — look at example given in problem:
“55 km/hour = 55 km / 60 minutes = 0.92 km/minute” — that’s *wrong*!
55 ÷ 60 = 0.9167 km/min, not 0.92 — but close. And they wrote “0.92 km/minute”, which is approximate.

But the instruction says: “Convert them to unit rates again, but using the desired units of measurement.” So we must give answer in the *desired* unit (e.g., m/min, not km/min).

So for #1: desired unit is m/minute, so:

55 km/h = 55 × 1000 m / 60 min = 55,000 / 60 = 916.67 m/min (or 2750/3 m/min). We'll use decimal rounded to 2 places unless otherwise noted.

But let’s double-check all with consistent precision — many of these are clean numbers.

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2) Convert 5 feet/minute into feet/second

- 1 minute = 60 seconds
So: 5 ft/min = 5 ft / 60 sec = 1/12 ft/sec ≈ 0.0833 ft/sec

Exact: 5/60 = 1/12 ft/sec

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3) Convert 2 liters into liters/meter
Wait — this seems odd. Liters is volume, meter is length. You can’t convert liters directly to liters per meter unless there’s context (like flow rate or density). But the problem says: “Convert 2 liters into liters/meter” — that doesn’t make sense dimensionally.

Hold on — maybe it's a typo? Let me read again.

Original list:
3) Convert 2 liters into liters/meter
That’s likely a mistake. Perhaps it should be “2 liters/minute into liters/second” or something? But as written, it's invalid.

Wait — maybe it's “2 liters per minute into liters per second”? No, #2 was feet/min → ft/sec, so pattern is rate → rate.

But #3 says just “2 liters” (not a rate) into “liters/meter” — impossible without extra info.

Let me scan all items:

4) $1.50/kg into $/gram
→ valid: divide by 1000

5) $100/day into $/hour
→ 1 day = 24 hours → 100/24 = 25/6 ≈ 4.17

6) 3,000 meters/second into meters/minute
→ ×60 = 180,000 m/min

7) $2.50/gram into dollars/gram? Wait: “$2.50/gram into dollars/gram” — same unit? No, it says: “$2.50/gram into dollars/gram” — maybe typo; actually image says: “$2.50/gram into dollars/grams” — still same. Wait, original text:
"7) Convert $2.50/gram into dollars/gram" — that’s identity. Unlikely.

Wait — looking again at user-provided text:

> 7) Convert $2.50/gram into dollars/grams
> 8) Convert 20 grams/liter into grams/milliliter
> 9) Convert $5/kg into cents/gram
> 10) Convert $2/liter into dollars/liter — again identity?

Hmm. Possibly some are mis-copied. But let’s assume the intended conversions are standard ones.

Let me reinterpret based on common worksheet patterns:

1) km/h → m/min ✔
2) ft/min → ft/sec ✔
3) Maybe: 2 liters/minute → liters/second? But says “2 liters into liters/meter” — could be a mistake. However, since the student must solve it, and it's likely a typo, perhaps it's “2 liters per minute into liters per second”? But that would be like #2.

Alternatively, maybe it's “2 liters per meter” — but no starting rate.

Given the ambiguity, and since the user expects us to solve *as given*, let’s assume #3 is incorrectly transcribed, but in many similar worksheets, #3 is: Convert 2 kilometers into meters — but that’s not what’s written.

Wait — look at the header: “In the following examples, unit rates are given to you.” So all inputs are *unit rates* (i.e., ratios). So #3 must be a rate. Therefore, likely it’s: 2 liters/minute into liters/second — matching pattern of #2.

But the text says: “Convert 2 liters into liters/meter” — maybe it's “2 liters per minute into liters per second”? I think it's a transcription error.

However, since this is a critical point, and we must provide correct answers, let’s check the rest — maybe we can infer.

#8: 20 grams/liter → grams/milliliter
1 liter = 1000 mL, so 20 g/L = 20 g / 1000 mL = 0.02 g/mL

#9: $5/kg → cents/gram
$5 = 500 cents
1 kg = 1000 g
So 500 cents / 1000 g = 0.5 cents/gram

#10: $2/liter → dollars/liter — identity? Unless it's $2/liter → cents/mL
But it says “dollars/liter”, same unit. Probably typo — maybe “$2/liter into cents/milliliter”

#11: 54 km/hour → m/second
54 km = 54,000 m
1 hour = 3600 sec
54,000 / 3600 = 15 m/s ✔ clean.

Given that #11 is clean, and #6 is clean, let’s solve all that are unambiguous, and for ambiguous ones, use most plausible interpretation.

Let me list each with best interpretation:

1) 55 km/h → m/min
55 × 1000 = 55,000 m per 60 min → 55,000 ÷ 60 = 916.67 m/min

2) 5 ft/min → ft/sec
5 ÷ 60 = 0.0833 ft/sec or 1/12 ft/sec

3) “2 liters into liters/meter” — impossible. But if it's 2 liters per meter (e.g., volume per length), then converting to same unit? No. Another possibility: maybe it's “2 liters per minute into liters per second” — then 2 ÷ 60 = 1/30 L/sec ≈ 0.0333 L/sec

Given that #2 is time unit reduction (min→sec), #3 might be same: liter/min → liter/sec. I’ll go with that.

So: 2 L/min = 2/60 = 1/30 L/sec ≈ 0.0333 L/sec

But the desired unit is written as “liters/meter” — that suggests length, not time. Could it be a misprint and should be “liters/second”? Very likely. We'll assume “liters/second”.

However, to stay faithful, let’s see if any standard worksheet has this exact list.

Alternatively, maybe #3 is: “Convert 2 km into meters” — but that’s not a rate.

Given the instructions say “unit rates are given”, all inputs must be rates. So “2 liters” alone is not a rate. Therefore, it's almost certainly a typo, and should be “2 liters/minute”.

I will solve assuming that.

4) $1.50/kg → $/gram
1 kg = 1000 g → $1.50 / 1000 = $0.0015 per gram

5) $100/day → $/hour
1 day = 24 h → 100 ÷ 24 = $4.17/hour (exact: 25/6 ≈ 4.1667)

6) 3,000 m/sec → m/min
×60 = 180,000 m/min

7) $2.50/gram → dollars/gram? Same. Maybe it's “$2.50/gram into dollars/kilogram”
That would make sense: ×1000 = $2500/kg

Yes! That’s likely: convert per gram to per kilogram. Because #4 was $/kg → $/g, so #7 is reverse: $/g → $/kg.

So: $2.50/gram = 2.50 × 1000 = $2500/kg

8) 20 g/L → g/mL
1 L = 1000 mL → 20 / 1000 = 0.02 g/mL

9) $5/kg → cents/gram
$5 = 500 cents; 1 kg = 1000 g → 500 / 1000 = 0.5 cents/gram

10) $2/liter → dollars/liter? No. Likely: $2/liter into cents/milliliter
$2 = 200 cents; 1 L = 1000 mL → 200 / 1000 = 0.2 cents/mL

Or maybe “dollars per milliliter”: 2 / 1000 = $0.002/mL — but cents is more natural with #9.

Given #9 used cents/gram, #10 likely uses cents/mL.

So: $2/L = 200 cents / 1000 mL = 0.2 cents/mL

11) 54 km/h → m/s
54 km = 54,000 m; 1 h = 3600 s
54,000 ÷ 3600 = 15 m/s

Now, let’s write final answers clearly, using reasonable rounding (2 decimals where needed, exact fractions if simple):

1) 916.67 m/min
2) 0.0833 ft/sec (or 1/12)
3) Assuming 2 L/min → 0.0333 L/sec
4) $0.0015/g
5) $4.17/hour
6) 180,000 m/min
7) $2500/kg
8) 0.02 g/mL
9) 0.5 cents/g
10) 0.2 cents/mL
11) 15 m/s

But the problem may expect simplified fractional forms where neat.

Let me recompute with exact values:

1) 55 km/h = 55,000 m / 60 min = 2750/3 ≈ 916.67 m/min
2) 5/60 = 1/12 ft/sec
3) If 2 L/min → 2/60 = 1/30 L/sec ≈ 0.0333
4) 1.50 / 1000 = 3/2000 = 0.0015 $/g
5) 100/24 = 25/6 ≈ 4.1667 $/h
6) 3000 × 60 = 180,000 m/min
7) 2.50 × 1000 = 2500 $/kg
8) 20 / 1000 = 0.02 g/mL
9) 500 cents / 1000 g = 0.5 cents/g
10) 200 cents / 1000 mL = 0.2 cents/mL
11) 54,000 / 3600 = 15 m/s

All seem consistent.

Since the user only wants the final answer (and ExplainAnswer is false), but the instructions say: *Always follow the structure below*, and ExplainAnswer is false → omit Explanation section.

Wait: user set:
- ExplainAnswer: false
- TeachTopic: false
- GeneratePractice: false

So we only output:

Final Answer:
[answers]

But what format? The worksheet has 11 items, so likely list all 11 answers.

Let me produce a clean list:

1) 916.67 m/min
2) 1/12 ft/sec (or 0.0833 ft/sec)
3) 1/30 L/sec (assuming L/min input)
4) $0.0015/g
5) $4.17/hour
6) 180,000 m/min
7) $2500/kg
8) 0.02 g/mL
9) 0.5 cents/g
10) 0.2 cents/mL
11) 15 m/s

To be safe and match typical school worksheet expectations, use decimals rounded to 2 places except where exact integer or simple fraction.

But #2 and #3 are repeating decimals; teachers often accept fractions.

However, the example in the problem used decimal (0.92), so they prefer decimals.

So:

1) 916.67 m/min
2) 0.08 ft/sec? No, 5/60 = 0.0833 → round to 0.08? But that’s inaccurate. Better 0.083 or 0.0833.

Given it’s algebra, keep 3 decimals or fraction.

I think the expected answers are:

1) 916.67
2) 0.083
3) 0.033
4) 0.0015
5) 4.17
6) 180000
7) 2500
8) 0.02
9) 0.5
10) 0.2
11) 15

Units must be included.

Final decision: Provide each with unit, as requested.

Final Answer:
1) 916.67 m/min
2) 0.083 ft/sec
3) 0.033 L/sec
4) $0.0015/g
5) $4.17/hour
6) 180,000 m/min
7) $2,500/kg
8) 0.02 g/mL
9) 0.5 cents/g
10) 0.2 cents/mL
11) 15 m/s