Keeping one checked gamma triangle shows lab time scaling with proper time. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Four proper seconds become five lab seconds
Gamma 5/4 multiplies proper time 4 s into lab time 5 s.
4⋅45=5
Eight proper seconds become ten lab seconds
Doubling the proper interval to 8 s doubles the lab interval to 10 s because gamma is unchanged.
8⋅45=10
Twelve proper seconds become fifteen lab seconds
The third row keeps the same triangle and changes only the moving-clock reading. Proper time 12 s gives lab time 15 s.