Math Problem Statement

Find an equivalent ratio in simplest terms: 36, colon, 99 36:99

Solution

To simplify the ratio 36:9936:99, we need to find the greatest common divisor (GCD) of 36 and 99, and divide both numbers by this GCD.

  1. Find the GCD of 36 and 99:

    • The factors of 36 are: 1,2,3,4,6,9,12,18,361, 2, 3, 4, 6, 9, 12, 18, 36
    • The factors of 99 are: 1,3,9,11,33,991, 3, 9, 11, 33, 99
    • The greatest common divisor is 99.
  2. Divide both numbers by 9: 369=4,999=11\frac{36}{9} = 4, \quad \frac{99}{9} = 11

Thus, the simplified ratio is: 4:114:11

Would you like further details on how to find the GCD or any other clarifications?

Here are 5 related questions:

  1. What is the process for finding the GCD of two numbers?
  2. Can you simplify the ratio 48:6448:64?
  3. How do you express a ratio as a fraction?
  4. What are some real-life applications of ratios?
  5. How do you convert a ratio into a percentage?

Tip: Always divide a ratio by the GCD to ensure it is in its simplest form.

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Math Problem Analysis

Mathematical Concepts

Ratios
Simplification
Greatest Common Divisor (GCD)

Formulas

Simplified Ratio = (a / GCD) : (b / GCD)

Theorems

Euclidean algorithm for finding GCD

Suitable Grade Level

Grades 6-8