11-13-2025, 12:34 PM
Fractions Explained — A Beginner’s Guide
Fractions appear everywhere in mathematics and science.
This guide explains what they are, how they work, and how to use them confidently.
-----------------------------------------------------------------------
1. What Is a Fraction?
A fraction represents a part of a whole.
Examples:
• 1/2 → one half
• 3/4 → three quarters
• 7/10 → seven out of ten equal parts
Top number = numerator
Bottom number = denominator
-----------------------------------------------------------------------
2. Equivalent Fractions
Two fractions can represent the same amount.
Examples:
• 1/2 = 2/4 = 3/6
• 3/5 = 6/10
To create an equivalent fraction:
Multiply or divide the numerator and denominator by the same number.
-----------------------------------------------------------------------
3. Simplifying Fractions
We reduce a fraction to its simplest form.
Examples:
• 8/12 → divide both by 4 → 2/3
• 15/25 → divide both by 5 → 3/5
-----------------------------------------------------------------------
4. Adding Fractions
Case 1: Same denominators
Add the numerators.
Example:
3/8 + 2/8 = 5/8
Case 2: Different denominators
Find a common denominator.
Example:
1/3 + 1/6
Common denominator = 6
→ 2/6 + 1/6 = 3/6 = 1/2
-----------------------------------------------------------------------
5. Multiplying Fractions
Multiply straight across.
Example:
3/4 × 2/5 = 6/20 = 3/10
-----------------------------------------------------------------------
6. Dividing Fractions
Flip the second fraction and multiply.
Example:
3/5 ÷ 2/3
→ 3/5 × 3/2 = 9/10
-----------------------------------------------------------------------
7. Converting Between Fractions & Decimals
Divide the top by the bottom:
1/4 = 0.25
3/5 = 0.6
7/8 = 0.875
-----------------------------------------------------------------------
Summary
Fractions become easy once you remember:
• Same denominators → add/subtract normally
• Multiply straight across
• Flip the second fraction to divide
• Simplify when you can
If you understand these rules, you're ready for algebra, ratios, and higher maths.
Fractions appear everywhere in mathematics and science.
This guide explains what they are, how they work, and how to use them confidently.
-----------------------------------------------------------------------
1. What Is a Fraction?
A fraction represents a part of a whole.
Examples:
• 1/2 → one half
• 3/4 → three quarters
• 7/10 → seven out of ten equal parts
Top number = numerator
Bottom number = denominator
-----------------------------------------------------------------------
2. Equivalent Fractions
Two fractions can represent the same amount.
Examples:
• 1/2 = 2/4 = 3/6
• 3/5 = 6/10
To create an equivalent fraction:
Multiply or divide the numerator and denominator by the same number.
-----------------------------------------------------------------------
3. Simplifying Fractions
We reduce a fraction to its simplest form.
Examples:
• 8/12 → divide both by 4 → 2/3
• 15/25 → divide both by 5 → 3/5
-----------------------------------------------------------------------
4. Adding Fractions
Case 1: Same denominators
Add the numerators.
Example:
3/8 + 2/8 = 5/8
Case 2: Different denominators
Find a common denominator.
Example:
1/3 + 1/6
Common denominator = 6
→ 2/6 + 1/6 = 3/6 = 1/2
-----------------------------------------------------------------------
5. Multiplying Fractions
Multiply straight across.
Example:
3/4 × 2/5 = 6/20 = 3/10
-----------------------------------------------------------------------
6. Dividing Fractions
Flip the second fraction and multiply.
Example:
3/5 ÷ 2/3
→ 3/5 × 3/2 = 9/10
-----------------------------------------------------------------------
7. Converting Between Fractions & Decimals
Divide the top by the bottom:
1/4 = 0.25
3/5 = 0.6
7/8 = 0.875
-----------------------------------------------------------------------
Summary
Fractions become easy once you remember:
• Same denominators → add/subtract normally
• Multiply straight across
• Flip the second fraction to divide
• Simplify when you can
If you understand these rules, you're ready for algebra, ratios, and higher maths.