Fraction Operations (+, −, ×, ÷): Unlike Denominators & Keep-Change-Flip
Mastering fraction arithmetic unlocks higher-level middle school algebra. Unlike whole numbers, fractions require finding common denominators for addition/subtraction, multiplying straight across for multiplication, and Keep-Change-Flip for division.
🧠 Core Mental Strategies & Shortcuts
➕ Common Denominator for Addition & Subtraction
You cannot add unlike slices! Find the Least Common Denominator (LCD) first: 1/2 + 1/4 = 2/4 + 1/4 = 3/4.
✖️ Straight Across Rule for Multiplication
Multiply numerators together, and multiply denominators together: 2/3 × 4/5 = (2 × 4) / (3 × 5) = 8/15.
➗ Keep, Change, Flip (KCF) for Division
Keep the 1st fraction, Change ÷ to ×, and Flip the 2nd fraction (reciprocal): 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8.
❓ Frequently Asked Questions
Why do we flip the second fraction when dividing?
Dividing by a fraction is the exact same as multiplying by its reciprocal. For example, dividing by 1/2 is asking "how many halves fit inside?", which is the same as multiplying by 2.
Do you need a common denominator to multiply fractions?
No! Common denominators are strictly required for addition and subtraction. For multiplication, simply multiply straight across (numerator × numerator, denominator × denominator).
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