Multiplying fractions is simpler than it looks. Just multiply the numerators together and the denominators together, and you're done: 2/3 × 3/4 = (2×3)/(3×4) = 6/12 = 1/2 (simplified). You can see why this works at a glance with a grid. Draw a rectangle that's 3 columns wide and 4 rows tall, then shade 2 of the columns and 3 of the rows. The overlapping squares number 6, and the whole grid has 3×4 = 12 squares, so the shaded part is exactly 6/12 (= 1/2).
Dividing fractions can feel a little unfamiliar at first. The rule is to "flip the fraction you're dividing by (take its reciprocal) and multiply" — but why flip it? Think about 6/8 ÷ 2/8. This is really asking, "How many times does 2/8 fit inside 6/8?" Since the denominators match, you only need to compare the numerators — 2 fits into 6 three times, so the answer is 3. Now try 6/8 × 8/2 (the reciprocal): (6×8)/(8×2) = 48/16 = 3 — the exact same answer. This shows that matching denominators and dividing the numerators, and multiplying by the reciprocal, always give you the same result.
More generally, for a/b ÷ c/d, first give both fractions the common denominator bd, turning it into (ad)/(bd) ÷ (bc)/(bd). With matching denominators, you just divide the numerators: ad ÷ bc = ad/bc. And that result is exactly the same as a/b × d/c (the reciprocal). So the rule "dividing means multiplying by the reciprocal" isn't magic — it falls naturally out of finding a common denominator and then dividing the numerators.
Multiplying and dividing fractions comes up all the time in real life. "If you eat 2/3 of the 3/4 of a cake that's left, how much of the whole cake did you eat?" is a multiplication problem (3/4 × 2/3), while "How many pieces do you get if you cut a 5/6 m ribbon into 1/3 m lengths?" is a division problem (5/6 ÷ 1/3). On our activity page, you can change both fractions with sliders and watch multiplication play out on a grid, while division shows up as a bar model and the step-by-step process of "turning into multiplication by the reciprocal."