Fraction

Definition

A fraction is a numerical quantity that represents a part of a whole. It is expressed as a ratio of two integers, where the numerator represents the part and the denominator represents the whole.

5 Must Know Facts For Your Next Test

1. Fractions can be used to represent parts of a whole, measurements, and ratios.
2. Fractions can be added, subtracted, multiplied, and divided using specific rules and operations.
3. Mixed numbers, which consist of a whole number and a fraction, can also be manipulated using the same rules as fractions.
4. Fractions can be converted to decimals, and vice versa, by dividing the numerator by the denominator.
5. Understanding fractions is essential for working with percentages, which are a special type of fraction with a denominator of 100.

Review Questions

• Explain how fractions can be used to visualize and represent parts of a whole.
  • Fractions are a way to represent parts of a whole visually. For example, a fraction like $\frac{1}{4}$ can be used to show that a whole has been divided into four equal parts, and one of those parts is being represented. This visual representation of fractions is important for understanding concepts like dividing shapes or quantities into equal parts, as well as for working with more complex fractional relationships.
• Describe the process of multiplying and dividing mixed numbers and complex fractions.
  • When multiplying or dividing mixed numbers and complex fractions, you first need to convert them to improper fractions. To multiply, you multiply the numerators together and the denominators together. To divide, you invert the second fraction and then multiply. For example, to multiply $2\frac{1}{2}$ by $3\frac{3}{4}$, you would first convert them to $\frac{5}{2}$ and $\frac{15}{4}$, respectively, and then multiply the numerators and denominators: $\frac{5}{2} \times \frac{15}{4} = \frac{75}{8}$. This process allows you to perform operations on more complex fractional expressions.
• Analyze the relationship between decimals and fractions, and explain how they can be used interchangeably.
  • Decimals and fractions are closely related, as they both represent parts of a whole. Fractions can be converted to decimals by dividing the numerator by the denominator, and decimals can be converted to fractions by writing them as a ratio with the denominator being a power of 10. Understanding this relationship is important because it allows you to move flexibly between decimal and fractional representations when solving problems, which is particularly useful when working with measurements, money, and other real-world applications involving parts of a whole.

Related terms

Numerator: The number on top of a fraction that represents the part of the whole.

Denominator: The number on the bottom of a fraction that represents the whole.

Equivalent Fractions: Fractions that represent the same quantity, even though the numerator and denominator are different.