A fraction represents a part of a whole. When we divide something into equal parts, each part is a fraction of the whole.
Key Concepts
Numerator and Denominator: In the fraction a/b, a is the numerator (how many parts we have) and b is the denominator (total equal parts the whole is divided into).
- Types of Fractions:
- Proper fraction: Numerator < Denominator. Example: 3/5
- Improper fraction: Numerator > Denominator. Example: 7/4
- Mixed number: A whole number + a proper fraction. Example: 1 and 3/4
Equivalent Fractions: Fractions that represent the same value. Multiply or divide both numerator and denominator by the same number. Example: 1/2 = 2/4 = 3/6.
Comparing Fractions: With the same denominator, the fraction with the larger numerator is bigger. With different denominators, convert to a common denominator first.
- Adding and Subtracting Fractions:
- Same denominator: Add/subtract numerators, keep denominator.
- Different denominators: Find the LCM, convert fractions, then add/subtract.
---
Find two equivalent fractions for 2/3.
- 2/3 = (2x2)/(3x2) = 4/6
- 2/3 = (2x3)/(3x3) = 6/9
- Equivalent fractions: 4/6 and 6/9
---
Add 1/4 + 2/4.
- Same denominator (4), so add numerators: 1 + 2 = 3
- Answer: 3/4
---
Add 1/3 + 1/4.
Key formulas
---
Subtract 3/8 from 7/8.
- Same denominator: 7/8 - 3/8 = 4/8 = 1/2
---
Convert 11/4 to a mixed number.
- 11 / 4 = 2 remainder 3
- Mixed number: 2 and 3/4
---
Key Formulas
Key formulas
Common mistakes
- Adding denominators along with numerators. Never add the denominators; only add the numerators when denominators are equal.
- Forgetting to simplify the final answer.
Summary
Fractions show parts of a whole. Find equivalent fractions by multiplying/dividing. To add or subtract, always use the same denominator first.