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+---- Thread: Fractions Explained — A Beginner’s Guide (/showthread.php?tid=59)
Fractions Explained — A Beginner’s Guide - Leejohnston - 11-13-2025
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.
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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
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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.
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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
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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
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5. Multiplying Fractions
Multiply straight across.
Example:
3/4 × 2/5 = 6/20 = 3/10
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6. Dividing Fractions
Flip the second fraction and multiply.
Example:
3/5 ÷ 2/3
→ 3/5 × 3/2 = 9/10
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7. Converting Between Fractions & Decimals
Divide the top by the bottom:
1/4 = 0.25
3/5 = 0.6
7/8 = 0.875
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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.