What is 16:64 ratio simplified

General
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what is 16:64 ratio simplified

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What is the simplified ratio of 16:64?

Answer:

Introduction to Ratios:

  • A ratio is a way to compare two quantities by using division. It expresses how much of one thing there is compared to another. The ratio 16:64 compares the numbers 16 and 64.

Understanding Ratio Simplification:

  • Simplifying a ratio involves reducing it to its smallest integer terms while keeping the relationship between the numbers constant. This is similar to simplifying a fraction.

Step 1: Identify the Greatest Common Divisor (GCD)

  • To simplify the ratio 16:64, begin by determining the greatest common divisor of both numbers. The GCD is the largest number that divides both terms without leaving a remainder.

  • For 16 and 64, the factors are:

    • Factors of 16: 1, 2, 4, 8, 16
    • Factors of 64: 1, 2, 4, 8, 16, 32, 64

  • The greatest common factor in both lists is 16.

Step 2: Simplify the Ratio Using the GCD

  • Divide both terms of the ratio by their GCD.

    \frac{16}{16} : \frac{64}{16}

  • Simplification:

    • Dividing 16 by 16 gives 1.
    • Dividing 64 by 16 gives 4.

Step 3: Write the Simplified Ratio

  • After performing the division, the simplified form of the ratio 16:64 is 1:4.

Final Answer:

The simplified ratio of 16:64 is 1:4.