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Chapter 2: Problem 22

Write the improper fraction as a mixed number or a whole number. $$\frac{27}{9}$$

Short Answer

Expert verified
The improper fraction \(\frac{27}{9}\) can be written as the whole number 3.

Step by step solution

01

Identify the Improper Fraction

The given number is an improper fraction \(\frac{27}{9}\). In an improper fraction, the numerator is greater than the denominator.
02

Perform Division

Perform the division \(\frac{27}{9}\) to convert the fraction to a whole number or a mixed number. Divide 27 by 9, and the result is 3.
03

Write as Whole Number

As there is no remainder from the division in step 2, the result 3 is a whole number. So, \(\frac{27}{9}\) can be written as the whole number 3.

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Key Concepts

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

Understanding Mixed Numbers
A mixed number is a number that combines a whole number and a proper fraction. This occurs when an improper fraction鈥攁 fraction with a numerator larger than its denominator鈥攊s converted into a form that includes both parts. For example, if you have the improper fraction \(\frac{11}{4}\), it can be rewritten as 2\(\frac{3}{4}\).

  • The whole number 2 signifies how many times 4 can completely divide 11.
  • The fraction \(\frac{3}{4}\) represents the leftover part, since 11 divided by 4 leaves a remainder of 3.
To convert from an improper fraction to a mixed number, divide the numerator by the denominator. The quotient becomes the whole number, and the remainder over the original denominator becomes the fraction. Mixed numbers can make it easier to understand quantities in everyday scenarios, such as when measuring ingredients or distances.
Identifying Whole Numbers
Whole numbers are numbers without fractions or decimals. They include zero and all positive integers like 1, 2, 3, and so on. They are used in situations where you count whole, complete objects.
In the exercise, the improper fraction \(\frac{27}{9}\) was successfully converted directly into the whole number 3.
  • When an improper fraction has a numerator that is a multiple of its denominator, the result of division is a whole number.
Since doing the division results in a whole quotient, there鈥檚 no fractional part remaining, making it a straightforward conversion. Recognizing when an improper fraction converts to a whole number is essential in simplifying fractions without unnecessary calculations.
The Basics of Division of Fractions
Division of fractions isn't as complex as it might seem. To divide fractions, one typically multiplies by the reciprocal of the divisor. However, when transforming an improper fraction to a mixed number or whole number, understanding how division operates is key.
For the improper fraction \(\frac{27}{9}\), you simplify this by performing the division directly. Here's how it works:
  • Divide the numerator by the denominator: 27 divided by 9 equals 3.
  • In situations where there is no remainder, you have a whole number as a result.
This division process reduces the improper fraction to a simpler form, which is often easier to understand and work with in mathematical operations or real-life contexts. Understanding this concept helps in effortlessly converting complex fractions into simpler representations.

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