A soldier carries 45 pounds of gear. If the gear is reduced by 1/3, what is the new weight?

Method 1 (subtract the reduction): 1/3 of 45 = 15 pounds reduction; 45 - 15 = 30 pounds new weight. Method 2 (multiply by the fraction remaining): if 1/3 is removed, 2/3 remains; 2/3 × 45 = 30 pounds. Both give the same answer. Fractional reduction is similar to percent reduction. Useful shortcuts: 1/2 reduction = 1/2 remaining (cut in half); 1/3 reduction = 2/3 remaining; 1/4 reduction = 3/4 remaining; 2/3 reduction = 1/3 remaining. Real-world applications: weight reduction, scaling recipes down, reducing dosage by a fraction, lightening loads. Quick mental math: half of 45 is 22.5; one-third would be slightly less, around 15 — that's the reduction; the new total is approximately 30. The estimation supports the precise calculation.