Adding and Subtracting Fractions

🧱 See It

Try to add 1/2 and 1/3 directly and there's an immediate problem: a half-piece and a third-piece are not the same size.

1/2 — one piece out of 2

1/3 — one piece out of 3

The shaded piece on the left is bigger than the shaded piece on the right. You can't just push two different-sized pieces together and call the result "2 pieces out of 5" — the pieces have to be the same size first.

✏️ Draw It

Redraw both bars using the same size of piece — sixths — so they finally line up:

1/2 redrawn as 3/6

1/3 redrawn as 2/6

Now that every piece is the same size, the shaded pieces can actually be combined:

3 sixths + 2 sixths = 5 sixths

🔢 Write It

Step 1 — find the LCM of the denominators:

LCM(2, 3) = 6

Step 2 — convert both fractions to that common denominator:

1/2 = 3/6 and 1/3 = 2/6

Step 3 — add (or subtract) just the numerators; the denominator stays put:

1/2 + 1/3 = 3/6 + 2/6 = 5/6

The denominator never gets added or subtracted — it just names the piece size, and that size has to already match.

💡 Worked Examples

Example 1: 1/4 + 1/6

Find the LCM of the denominators: LCM(4, 6) = 12
Convert both fractions: 1/4 = 3/12 and 1/6 = 2/12
Add the numerators, keep the denominator: 3/12 + 2/12 = 5/12
Answer: 5/12

Example 2: 3/4 − 1/6

Find the LCM of the denominators: LCM(4, 6) = 12
Convert both fractions: 3/4 = 9/12 and 1/6 = 2/12
Subtract the numerators, keep the denominator: 9/12 − 2/12 = 7/12
Answer: 7/12

🧠 Quick Reference

Find the LCM of the denominators first. Convert BOTH fractions to that common denominator. THEN add or subtract just the top numbers — the bottom number never changes once it's common.