What is the basic ratio of 120:150 in simplest foem

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What is the basic ratio of 120:150 in simplest foem

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What is the basic ratio of 120:150 in simplest form?

Answer: To find the simplest form of the ratio 120:150, follow these steps:

  1. Find the Greatest Common Divisor (GCD): First, determine the Greatest Common Divisor (GCD) of the two numbers. The GCD is the largest number that can evenly divide both numbers.

  2. Prime Factorization Method:

    • Perform the prime factorization for 120:

      120 = 2^3 \times 3 \times 5

    • Perform the prime factorization for 150:

      150 = 2 \times 3 \times 5^2

    • The common prime factors are 2, 3, and 5.

  3. Determine the GCD:

    • The GCD is obtained by taking the lowest power of each common prime factor that appears in the factorizations.
      • For 2: The lowest power is 2^1.
      • For 3: The lowest power is 3^1.
      • For 5: The lowest power is 5^1.
    \text{GCD} = 2^1 \times 3^1 \times 5^1 = 2 \times 3 \times 5 = 30

  4. Divide Both Numbers by the GCD:

    • Divide 120 by 30:

      \frac{120}{30} = 4

    • Divide 150 by 30:

      \frac{150}{30} = 5

  5. Write the Ratio in Simplest Form:

    • The simplified ratio of 120:150 is 4:5.

Therefore, the basic ratio of 120:150 in simplest form is 4:5.