Improper Fraction

Definition

An improper fraction is a fraction where the numerator is greater than the denominator. It represents a value greater than 1 and can be expressed as a mixed number or a decimal.

5 Must Know Facts For Your Next Test

1. Improper fractions can be converted to mixed numbers by dividing the numerator by the denominator and using the remainder as the new numerator.
2. Multiplying and dividing improper fractions involves the same process as multiplying and dividing proper fractions, with the result potentially being an improper fraction.
3. When adding or subtracting fractions with different denominators, the fractions must first be converted to equivalent fractions with a common denominator, which may result in improper fractions.
4. Improper fractions can be represented on a number line or in a visual model, showing that the value is greater than 1.
5. Decimals can be converted to improper fractions by writing the decimal as a fraction with the denominator being a power of 10 based on the number of decimal places.

Review Questions

• Explain how to convert an improper fraction to a mixed number and provide an example.
  • To convert an improper fraction to a mixed number, you divide the numerator by the denominator. The whole number part of the result becomes the whole number component of the mixed number, and the remainder becomes the new numerator, with the original denominator. For example, to convert the improper fraction 7/4 to a mixed number, you would divide 7 by 4, which gives you 1 with a remainder of 3. Therefore, the mixed number representation would be 1 3/4.
• Describe the process of multiplying and dividing improper fractions, and how the result may be an improper fraction.
  • When multiplying or dividing improper fractions, you follow the same steps as with proper fractions. To multiply, you multiply the numerators together and the denominators together. To divide, you invert the second fraction and multiply. The result of these operations may be an improper fraction, which would need to be converted to a mixed number or decimal if necessary. For example, multiplying the improper fractions 5/3 and 7/2 would give you 35/6, which is an improper fraction.
• Analyze how improper fractions are used in the context of adding and subtracting fractions with different denominators.
  • When adding or subtracting fractions with different denominators, the fractions must first be converted to equivalent fractions with a common denominator. This process may result in improper fractions, either in the intermediate steps or in the final answer. The ability to work with improper fractions is crucial in these situations, as the fractions must be manipulated and simplified correctly to arrive at the final solution. Understanding how improper fractions are represented and transformed is essential for successfully adding and subtracting fractions with different denominators.

Related terms

Proper Fraction: A proper fraction is a fraction where the numerator is less than the denominator, representing a value less than 1.

Mixed Number: A mixed number is a combination of a whole number and a proper fraction, representing a value greater than 1.

Equivalent Fraction: An equivalent fraction is a fraction that represents the same value as another fraction, with a different numerator and denominator.