[tex] 8 \times 977 = 8 \times (1000 - 23) = 8000 - 8(23) = 8000 - 8(25-2) = 8000 - 200 + 16 = 7816[/tex]
[tex] 8 \times 977 = 8 \times (975 + 2) = 16 + 8 \times 900 + 8 \times 75 = 16 + 7200 + 24 \times 25 = 7216 + 600 = 7816 [/tex]
Why does it work? Mostly the distributive law.
