How to multiply by 5, 25, and 125
These three numbers have something in common that isn't obvious at first glance: each one is a clean fraction of a power of ten.
The rule
n × 25 = (n × 100) ÷ 4
n × 125 = (n × 1000) ÷ 8
Multiply by the power of ten — instant — then divide by the small number.
Why it works
5 = 10 ÷ 2, 25 = 100 ÷ 4, and 125 = 1000 ÷ 8. Since multiplying by a fraction is the same as multiplying by the numerator and dividing by the denominator, n × 5 becomes n × 10 ÷ 2 — and multiplying by a power of ten never requires actual work, just a digit shift.
Worked examples — ×5
48 × 5 — 480 ÷ 2 = 240.
73 × 5 — 730 ÷ 2 = 365.
Worked examples — ×25
24 × 25 — 2400 ÷ 4 = 600.
68 × 25 — 6800 ÷ 4 = 1700.
Worked examples — ×125
16 × 125 — 16000 ÷ 8 = 2000.
32 × 125 — 32000 ÷ 8 = 4000.
Making the division easy
Dividing by 2, 4, or 8 is itself fast if you do it in stages — dividing by 4 is just halving twice, and dividing by 8 is halving three times. That keeps every step of this shortcut at the level of "halve a number," which is usually the fastest arithmetic operation there is.
Practice it
Practice arithmetic → · See the rest of the shortcuts guide →