🗺️ Chapter Roadmap
1 What is a Fraction?
A fraction simply represents a part of a whole. When you divide something into equal pieces, a fraction tells you how many of those pieces you have.
2 Types of Fractions
Proper Fraction
The top number (Numerator) is smaller than the bottom number.
Improper Fraction
The top number is larger than or equal to the bottom number. (Top-heavy)
Mixed Fraction
A whole number mixed with a proper fraction. (Read as "One and three-fourths")
3 Adding & Subtracting (The Butterfly Method)
If the bottom numbers (denominators) are the same, just add the top numbers. But if they are different, finding the LCM can be confusing. Use the Butterfly Method instead!
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1
Cross Multiply (The Wings):
Multiply top-left with bottom-right: 2 × 4 = 8
Multiply top-right with bottom-left: 1 × 3 = 3 -
2
Add the Wings (New Top):
Add the two answers you just got: 8 + 3 = 11. This is your new Numerator. -
3
Multiply Bottoms (The Body):
Multiply the two original bottom numbers: 3 × 4 = 12. This is your new Denominator.
4 Multiplying & Dividing Fractions
Multiplying and dividing is actually much easier than adding or subtracting because you do not need to make the bottoms the same!
Multiplication (Straight Across)
Simply multiply top with top, and bottom with bottom.
Division (Keep, Change, Flip)
Keep the first fraction, Change ÷ to ×, and Flip the second fraction upside down.
5 Decimals & Conversions
Decimals and Fractions are just two different languages for expressing the exact same thing (parts of a whole).
➡️ Decimal to Fraction
Remove the decimal point. Put a 1 at the bottom. Then, count how many numbers were after the point, and add that many zeros at the bottom.
⬅️ Fraction to Decimal
If the bottom is 10, 100, or 1000, just count the zeros and move the decimal point that many spaces to the left on the top number.