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Math · Fractions & Decimals
Adding & Subtracting Fractions
You can only add or subtract fractions when the slices are the same size — so first give them a common denominator!
🍎The Slices Must Match!
🚫Different sizes — NO!
It's like 3 apples + 2 oranges. The pieces aren't the same size, so you can't just add them yet.
✅Same sizes — YES!
Turn ½ into 2⁄4. Now every slice is a fourth — same size! — so they're ready to add.
🧮Worked Example: ½ + ¼
1Unlike denominators? The 2 and the 4 are different. Find a common denominator — 4 works (it's the LCM of 2 and 4).
2Make equivalent fractions. Multiply 12 top & bottom by 2 → 24. (¼ already has a 4.)
3Add the numerators, keep the denominator: 24 + 14 = 2+14 = 34.
4Simplify if you can. Here 34 is already in lowest terms — done!
½ + ¼ = 2⁄4 + ¼ = 3⁄4 ✏️
📋The 4-Step Recipe
🔍Look at the bottoms. Like denominators? Add or subtract straight away. Unlike? Keep going.
🤝Find a common denominator — a number both bottoms divide into (the LCM is the easiest one).
🔁Build equivalent fractions so both have that same bottom. Whatever you do to the bottom, do to the top.
➕Add or subtract the tops only, keep the bottom the same — then simplify if you can.
📏See It on a Number Line
🔑Key Terms
🤝Common Denominator A shared bottom number two fractions can both use, so the slices match.
🪜Least Common Multiple (LCM) The smallest number that is a multiple of both denominators.
🔁Equivalent Fraction A fraction with the same value, written a different way (½ = 2⁄4).
🔝Numerator The top number — the part you actually add or subtract.
🔢Denominator The bottom number — it names the size of each part.
✂️Simplify Shrink a fraction by dividing top & bottom by their greatest common factor.
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Remember: match the denominators first, then add or subtract only the tops — the bottom number stays exactly the same!