Understanding fractions · half of 1/2
Half of 1/2 is 1/4. You can see it by cutting one half into two equal pieces, or by multiplying 1/2 × 1/2 — taking half of an amount means multiplying by one half.
Explore the main fraction lessonQuick answer
Half of 1/2 = 1/2 × 1/2 = 1/4. Cutting the half into two equal shares makes each share one quarter of the whole.
Draw one bar and shade half of it. That shaded half is the amount being shared. To take half of it, cut the shaded region into two equal pieces — each piece is now one of four equal pieces of the whole bar, which is 1/4.
The pieces shrink because sharing divides the size of each piece, not the number of wholes. One half shared between two people gives each person a quarter: smaller than the start, exactly as sharing should be.
Taking half of an amount means multiplying by 1/2. So half of 1/2 is 1/2 × 1/2: multiply the numerators (1 × 1 = 1) and the denominators (2 × 2 = 4) for 1/4. No common denominators — multiplication never needs them.
The same rule answers nearby questions without new work: half of 1/3 is 1/6, half of 3/4 is 3/8, and half of 1/4 is 1/8. In every case the denominator doubles because each piece is cut in two.
Students sometimes expect halving a fraction to double it. Check the direction: half of a pizza slice is a smaller slice. Multiplying by 1/2 — a number less than 1 — always shrinks the amount, so 1/4 must be smaller than 1/2.
A quick sanity check: 1/4 is half the size of 1/2 on the number line, sitting exactly midway between 0 and 1/2. If a halving answer lands larger than the amount you started with, the multiplication went to the wrong operation.
Step by step
One half of a whole is the amount being shared.
Splitting the half into two equal pieces makes quarters of the whole.
1/2 × 1/2 = 1/4 — taking half means multiplying by one half.
1/4 sits midway between 0 and 1/2: smaller than the start, as sharing requires.
Example
1/2 × 1/2 = 1/4. Each of two equal shares of the half is one quarter of the whole.
Example
1/3 × 1/2 = 1/6. The same pattern: the denominator doubles, the numerator stays.
Common questions
