Half of an amount that is already a fraction
To multiply fractions, multiply their top numbers and multiply their bottom numbers. Half of three quarters is three eighths: 1/2 × 3/4 = 3/8.
Imagine a recipe that uses three quarters of a litre of stock. You want to make half the recipe. Half of that stock is three eighths of a litre. The measuring jug has not changed size; you are taking part of the amount in it.
Keep the original whole in view
Picture one litre divided into four equal quarters. The recipe uses three of them. Now split each quarter in half: the whole litre has eight equal eighths.
The three quarters contain six eighths. Half of those six eighths is three eighths. That is why the answer is 3/8 of the original litre, not three eighths of some newly chosen whole.
The calculation records the same idea
The top number is the numerator; the bottom number is the denominator. For 1/2 × 3/4, the top calculation is 1 × 3 = 3. The bottom calculation is 2 × 4 = 8.
OpenStax gives this multiplication rule and explains how to simplify the result. You do not need a common denominator to multiply fractions.
Try 2/3 × 3/4. Multiplication gives 6/12. Divide both numbers by six and you get 1/2. Changing 6/12 into 1/2 changes the notation, not the amount.
Why did multiplication make it smaller?
Multiplying a positive amount by a positive fraction below one takes only part of that amount. Half of three quarters is therefore smaller than three quarters. That is a useful check on the recipe answer.
Multiplication does not always make a number bigger. Here, the multiplier tells you what share to keep.
This is different from adding fractions, where you first need matching-sized pieces. If simplifying still feels unfamiliar, revisit equivalent fractions.
Another recipe, without changing the rule
A full recipe needs 2/3 of a cup of oats. You make three quarters of the recipe. How much oats will you use?
Show the calculation
3/4 × 2/3 = 6/12 = 1/2 cup. Three quarters of the original two-thirds amount is half of the original cup.