A mixed number combines a whole number and a fraction. To convert a decimal to a mixed number, we first identify the whole number part. In the case of 3.75, the whole number is 3. The decimal part, 0.75, represents the fraction. To express it as a fraction, we place it over the denominator 100 (since 0.75 can be written as 75/100).

Therefore, 3.75 can be written as the mixed number 3 3/4. The 3 represents the whole number part, and the 3/4 represents the fractional part. This mixed number form is more commonly used in everyday life and measurements, as it provides a clear and concise way of expressing non-integer quantities.

In various real-world applications, mixed numbers play a crucial role. For instance, in carpentry, measurements often involve mixed numbers to represent the dimensions of lumber or the lengths of cuts. Similarly, in cooking, recipes may specify ingredient quantities using mixed numbers, ensuring precise measurements for accurate results.

Understanding the Conversion Process

Converting 3.75 to a mixed number involves understanding the relationship between decimals and fractions. Here’s a step-by-step breakdown of the conversion process:

  1. Identify the whole number part: In 3.75, the whole number is 3.
  2. Convert the decimal part to a fraction: 0.75 can be written as 75/100.
  3. Simplify the fraction (if possible): 75/100 can be simplified to 3/4.
  4. Combine the whole number and fraction: Therefore, 3.75 can be written as the mixed number 3 3/4.

Applications of Mixed Numbers

Mixed numbers find practical applications in various fields, including:

  • Measurements: Carpentry, architecture, and engineering often use mixed numbers to express measurements accurately.
  • Cooking: Recipes may specify ingredient quantities using mixed numbers to ensure precise measurements.
  • Timekeeping: Mixed numbers are commonly used to represent time durations, such as 2 hours and 30 minutes (2 1/2 hours).

Comparison with Decimal Form

While both 3.75 and 3 3/4 represent the same quantity, the mixed number form offers certain advantages over the decimal form:

  • Clarity: Mixed numbers are often easier to read and understand, especially for individuals who are not familiar with decimal notation.
  • Precision: Mixed numbers can provide more precise measurements in certain scenarios, particularly when representing fractional parts with small denominators.

Fractions vs. Mixed Numbers

It’s important to distinguish between fractions and mixed numbers. A fraction represents a part of a whole, while a mixed number represents a whole number and a fraction. The key difference between the two is the presence of a whole number part in a mixed number.

Converting Mixed Numbers to Decimals

Converting a mixed number to a decimal is also straightforward:

  1. Multiply the whole number by the denominator of the fraction: 3 x 4 = 12.
  2. Add the numerator of the fraction: 12 + 3 = 15.
  3. Divide by the denominator: 15 ÷ 4 = 3.75.

Simplifying Mixed Numbers

In some cases, mixed numbers can be simplified to reduce the fraction part:

  • If the numerator is greater than the denominator: Convert the fraction to a whole number and add it to the whole number part.
  • If the numerator is less than the denominator: Leave the fraction part as it is.

Equivalent Mixed Numbers

A given mixed number can have multiple equivalent mixed numbers. For example, 3 3/4 is equivalent to 4 1/4, 5 5/4, and so on. To find equivalent mixed numbers, multiply both the whole number and the fraction by the same number.

Conclusion

Converting 3.75 to a mixed number involves understanding the relationship between decimals and fractions. The mixed number form, 3 3/4, offers advantages in terms of clarity and precision in certain applications. By mastering the conversion process and understanding the practical applications of mixed numbers, individuals can effectively utilize this mathematical concept in various real-world scenarios.

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