Fraction (Basics)

What is a Fraction?

A fraction is a way of representing a part of a whole. It is written as two numbers separated by a slash or line, like this: numerator/denominator.

• Numerator: The number on the top of the fraction. It tells you how many parts you have.
• Denominator: The number on the bottom of the fraction. It tells you into how many equal parts the whole is divided.

Example:

In the fraction ¾:

• Numerator (3): You have 3 parts.
• Denominator (4): The whole is divided into 4 equal parts.

Types of Fractions

1. Proper Fraction:
   • The numerator is less than the denominator.
   • Example: ⅓, ¾, ½
2. Improper Fraction:
   • The numerator is greater than or equal to the denominator.
   • Example: 5/4, 7/6, 9/9
3. Mixed Number:
   • A whole number combined with a fraction.
   • Example: 1 ½ (one and a half), 2 ¾ (two and three-fourths)
4. Equivalent Fractions:
   • Fractions that represent the same value but look different.
   • Example: ½ is the same as 2/4, 4/8, 8/16.

Simplifying Fractions

To simplify a fraction means to reduce it to its simplest form, where the numerator and denominator have no common factors other than 1.

Example:

• Simplify 4/8:
  • Both 4 and 8 can be divided by 4.
  • 4 ÷ 4 = 1, 8 ÷ 4 = 2
  • So, 4/8 simplifies to 1/2.

Converting Improper Fractions to Mixed Numbers

To convert an improper fraction (where the numerator is greater than the denominator) into a mixed number, you divide the numerator by the denominator:

Example:

• 7/4:
  • 7 ÷ 4 = 1 with a remainder of 3.
  • So, 7/4 is 1 ¾ (1 whole and ¾ left over).

Adding and Subtracting Fractions

To add or subtract fractions, you need to have the same denominator (called like fractions).

Example:

• 1/4 + 2/4 = 3/4 (same denominator)
• If the fractions have different denominators, you need to find a common denominator before adding or subtracting.

Multiplying Fractions

When multiplying fractions, multiply the numerators and the denominators separately:

Example:

• 2/3 × 3/4 = (2 × 3) / (3 × 4) = 6/12
• Simplify the result: 6/12 = 1/2

Dividing Fractions

To divide fractions, flip the second fraction (the divisor) and then multiply:

Example:

• 2/3 ÷ 3/4:
  • Flip the second fraction: 3/4 becomes 4/3.
  • Multiply: 2/3 × 4/3 = 8/9

Fraction Terms Review

• Numerator: The number on top, shows how many parts you have.
• Denominator: The number on the bottom, shows how many equal parts the whole is divided into.
• Simplify: Reduce the fraction to its lowest terms.
• Equivalent Fractions: Fractions that represent the same value but look different.
• Mixed Number: A whole number and a fraction combined.
• Improper Fraction: The numerator is greater than or equal to the denominator.

Summary

Fractions are a way of expressing parts of a whole. They can be proper, improper, or mixed numbers, and you can perform basic operations like addition, subtraction, multiplication, and division. Understanding how to simplify and convert between improper fractions and mixed numbers is also important!