Fractions

Definition

Fractions are numerical expressions representing the division of one quantity by another, typically written in the form of 'a/b', where 'a' is the numerator and 'b' is the denominator. They are fundamental in expressing parts of a whole, allowing for the comparison and manipulation of quantities in various mathematical contexts.

5 Must Know Facts For Your Next Test

1. Fractions can be simplified by dividing both the numerator and denominator by their greatest common factor (GCF).
2. When adding or subtracting fractions, they must have a common denominator; otherwise, you need to find one before performing the operation.
3. Multiplying fractions involves multiplying the numerators together and multiplying the denominators together.
4. Dividing by a fraction is equivalent to multiplying by its reciprocal, which is obtained by flipping the numerator and denominator.
5. Fractions can be converted into decimals by performing division on the numerator by the denominator.

Review Questions

• How do you add fractions with different denominators, and what steps must you take to ensure accuracy?
  • To add fractions with different denominators, first find a common denominator, which is often the least common multiple (LCM) of both denominators. Then, convert each fraction into an equivalent fraction that has this common denominator. After adjusting the numerators accordingly, you can add the numerators together while keeping the common denominator, and finally simplify if needed.
• Explain how to multiply fractions and how this process differs from adding them.
  • When multiplying fractions, you simply multiply the numerators together to get a new numerator and multiply the denominators together for a new denominator. This process differs from adding fractions because when adding, you need a common denominator first. In multiplication, there's no need to adjust or find a common base; you work directly with the original fractions.
• Evaluate how understanding fractions is essential for solving real-world problems, especially in contexts such as cooking or construction.
  • Understanding fractions is crucial for solving real-world problems because they often arise in everyday activities like cooking or construction. For example, recipes frequently require fractional amounts of ingredients, so knowing how to add or convert fractions ensures accurate measurements. In construction, measurements often involve fractional lengths and areas, making it important to perform operations on fractions correctly to achieve precise results and maintain safety standards.

Related terms

Numerator: The top part of a fraction that indicates how many parts of the whole are being considered.

Denominator: The bottom part of a fraction that indicates the total number of equal parts in the whole.

Improper Fraction: A fraction where the numerator is greater than or equal to the denominator, indicating a value equal to or greater than one.