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Chapter 0: Problem 20

For exercises 13-22, rewrite the improper fraction as a mixed number. $$ \frac{100}{51} $$

Short Answer

Expert verified
1 \(\frac{49}{51}\)

Step by step solution

01

- Divide the Numerator by the Denominator

Divide 100 by 51 to find the whole number part of the mixed number. 100 divided by 51 is 1 with a remainder.
02

- Find the Remainder

The remainder when 100 is divided by 51 is 49. This means 100 can be expressed as 51 * 1 + 49.
03

- Rewrite as a Mixed Number

Use the whole number part (1) and the remainder (49) to rewrite the improper fraction. The mixed number is 1 with a fractional part of \(\frac{49}{51}\). Therefore, \(\frac{100}{51}\) as a mixed number is \(1 \frac{49}{51}\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Division
Understanding division is crucial when converting improper fractions to mixed numbers. Division helps to determine how many whole units fit into the numerator. For the improper fraction \(\frac{100}{51}\), you start by dividing the numerator (100) by the denominator (51). This division results in a quotient of 1, which represents the whole number part of the mixed number. We then pay attention to the remainder, which is what鈥檚 left over after dividing.
Remainder
The remainder is an essential component when converting improper fractions. After dividing 100 by 51, the quotient is 1 and we have a remainder. In this case, the remainder is 49. This can be written as 100 = 51 * 1 + 49. The remainder tells us the part of the fraction that doesn't fit into a whole unit. This remainder becomes the new numerator of the fractional part in the mixed number.
Mixed Number Conversion
To convert an improper fraction \(\frac{100}{51}\) to a mixed number, follow these steps:
  • Divide the numerator by the denominator. Here, 100 divided by 51 equals 1.
  • Find the remainder, which is 49 in this example.
  • Rewrite the improper fraction using the whole number and the remainder. Thus, \(\frac{100}{51}\) becomes 1 \(\frac{49}{51}\).
The mixed number is expressed as a combination of a whole number and a proper fraction, making it easier to understand and visualize.
Fractions
A fraction represents a part of a whole. An improper fraction like \(\frac{100}{51}\) has a numerator larger than its denominator. Mixed numbers combine a whole number with a proper fraction, where the numerator is smaller than the denominator. Converting improper fractions to mixed numbers involves division and recalculating parts, making them more intuitive. Understanding fractions helps us perform daily measurements and portions with ease.

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