Unit Rate & Ratio

Calculator Setup

Part a

Part b

Part c (opt.)

Enter two or three positive integers. Leave Part c blank for a 2-part ratio.

Examples

Total Amount

Units

Per how many?

Per Quantity

Per Unit

Finds the unit rate: total ÷ quantity. E.g., 180 miles in 3 hours → 60 miles/hour.

Examples

Option A

Qty A

Unit

for

Price A ($)

Option B

Qty B

Unit

for

Price B ($)

Finds price per unit for each option and highlights the better deal.

Examples

Result

Enter values above and press Calculate to see the simplified ratio, unit rate, or comparison with step-by-step work.

Simplified Ratio

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GCD Details

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Unit Rate

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Calculation

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Option A

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Better Deal

Option B

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Better Deal

Verdict

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Ratio vs Rate

ratio: a : b (same units) → simplify with GCD

Ratio compares two (or more) quantities of the same type — e.g., 2 cups of flour to 3 cups of sugar. Simplify by dividing all parts by their Greatest Common Divisor (GCD).

Rate compares quantities of different types — e.g., miles per hour, dollars per ounce.

Unit rate is a rate with a denominator of exactly 1. Divide the total by the number of units to find it: 180 miles ÷ 3 hours = 60 miles per 1 hour.

Two ratios are equivalent (proportional) if they simplify to the same ratio. Cross-multiply to check: a/b = c/d iff a·d = b·c.

Dimensional Analysis

60 mi/hr × 1 hr/60 min = 1 mi/min

Multiply by conversion fractions equal to 1 so that unwanted units cancel and desired units remain. The fraction's numerator and denominator are equivalent (just in different units), so the value doesn't change — only the unit does.

Example: convert 60 miles/hour to miles/minute:

60 mi/hr × (1 hr / 60 min) = 1 mi/min

The "hr" in the numerator and denominator cancel, leaving miles/min.

Write out all units before calculating.
Choose the conversion fraction so unwanted units cancel.
Chain multiple fractions for multi-step conversions.
Double-check: units left over should match your target.

Ratios and rates still tripping you up?