One half of two-thirds is equal to one-third. One finds this answer by multiplying the fraction two-thirds by one-half, which gives 2/6. This fraction simplifies to one-third, or 1/3.
Another method one can use to arrive at this answer is division. One can divide the dividend, two-thirds, by two, the divisor. However, one needs to use the reciprocal of two, which is one-half when performing a division of fractions. The divisor needs to be changed into its reciprocal number. One can then multiply the two fractions of one-half and two-thirds.
Fractions have numerators, the top numbers, and denominators, the bottom numbers. After performing either a division or multiplication of fractions, one may need to reduce or simplify the fraction into lowest terms.