Giant star-forming clumps are a prominent feature of star-forming galaxies (SFGs) and contain important clues on galaxy formation and evolution. However, the basic demographics of clumps and their host galaxies remain uncertain. Using the Hubble Space Telescope/Wide Field Camera 3 F275W images from the Ultraviolet Imaging of the Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey, we detect and analyze giant star-forming clumps in galaxies at 0.5 ≤ z ≤ 1, connecting two epochs when clumps are common (at cosmic high noon, z ∼ 2) and rare (in the local Universe). We construct a clump sample whose rest-frame 1600 Å luminosity is 3 times higher than the most luminous local H ii regions (MUV ≤ −16 AB). In our sample, 35% ± 3% of low-mass galaxies (log[M∗/M⊙] < 10) are clumpy (i.e., containing at least one off-center clump). This fraction changes to 22% ± 3% and 22% ± 4% for intermediate (10 ≤ log[M∗/M⊙] ≤ 10.5) and high-mass (log[M∗/M⊙] > 10.5) galaxies, in agreement with previous studies. When compared to similar-mass nonclumpy SFGs, low- and intermediate-mass clumpy SFGs tend to have higher star formation rates (SFRs) and bluer rest-frame U − V colors, while high-mass clumpy SFGs tend to be larger than nonclumpy SFGs. However, clumpy and nonclumpy SFGs have similar Sérsic index, indicating a similar underlying density profile. Furthermore, we investigate how the UV luminosity of star-forming regions correlates with the physical properties of host galaxies. On average, more luminous star-forming regions reside in more luminous, smaller, and/or higher specific SFR galaxies and are found closer to their hosts' galactic centers.