complete.tools

Ratio Simplifier

Simplify ratios to their lowest terms by finding the greatest common divisor.

What this tool does

Simplify ratios to their lowest terms by finding the greatest common divisor. You fill in these fields: First part (A) and Second part (B). It shows simplified ratio, simplified A, simplified B, and divided by.

Inputs

  • First part (A): A whole number. Must be at least 0. Starts at 12.
  • Second part (B): A whole number. Must be at least 0. Starts at 8.

How to use

  1. Enter the first part (A).
  2. Enter the second part (B).
  3. Read the result: simplified ratio, simplified A, simplified B, and divided by. It appears once every required field has a valid value.

Worked examples

Example 1. Inputs:

  • First part (A): 12
  • Second part (B): 8

Results:

  • Simplified ratio: 3:2 (Simplified to lowest terms)
  • Simplified A: 3
  • Simplified B: 2
  • Divided by: 4 (Number both parts were divided by)

How this is worked out: gcd(12, 8) = 4. 12 / 4 = 3 and 8 / 4 = 2, so 3:2. Divisor = 12 / 3 = 4.

Example 2. Inputs:

  • First part (A): 0
  • Second part (B): 5

Results:

  • Simplified ratio: 0:1 (Simplified to lowest terms)
  • Simplified A: 0
  • Simplified B: 1
  • Divided by: 5 (Number both parts were divided by)

How this is worked out: Zero edge case: gcd(0, 5) = 5. 0 / 5 = 0 and 5 / 5 = 1, so 0:1. Divisor = 5 / 1 = 5, taken from the first non-zero term.

Example 3. Inputs:

  • First part (A): 100
  • Second part (B): 40

Results:

  • Simplified ratio: 5:2 (Simplified to lowest terms)
  • Simplified A: 5
  • Simplified B: 2
  • Divided by: 20 (Number both parts were divided by)

How this is worked out: gcd(100, 40) = 20. 100 / 20 = 5 and 40 / 20 = 2, so 5:2. Divisor = 100 / 5 = 20.

Example 4. Inputs:

  • First part (A): 45
  • Second part (B): 30

Results:

  • Simplified ratio: 3:2 (Simplified to lowest terms)
  • Simplified A: 3
  • Simplified B: 2
  • Divided by: 15 (Number both parts were divided by)

How this is worked out: gcd(45, 30) = 15. 45 / 15 = 3 and 30 / 15 = 2, so 3:2. Divisor = 45 / 3 = 15.

Limitations

  • Works on two whole-number parts only.
  • Both parts cannot be 0, and a negative part is refused.

FAQs

Q: What does simplifying a ratio mean?
A: Both parts are divided by the same number so the ratio uses the smallest whole numbers. For example, 12:8 becomes 3:2 because both parts are divided by 4.
Q: What is the Divided by number?
A: It is the number both parts were divided by. For 12:8 it is 4, and for 45:30 it is 15.
Q: Why are only whole numbers accepted?
A: A ratio is simplified by whole-number division. Whole numbers keep the answer exact and easy to check.

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