速算計Maths Questions

Q1.
246 x 321963/123369
=(6 x 41) x (3 X 17 X 59 X 107) / (3 X 17 X 41 X 59)
=6 X 107
=642

Q2.
1/2＋（1/3＋2/3）＋（1/4＋2/4＋3/4）＋（1/5＋2/5＋3/5＋ 4/5）＋...＋（1/10＋2/10＋...＋9/10）
=(1/2 X 1) + (1/2 X 2) + (1/2 X 3) + ......+ (1/2 X 10)
=1/2 X (1+2+3+4+5+6+7+8+9+10)
=1/2 X 45
=22又1/2

1) 抽 common factors?

2)
1/2 = 0.5
1/3 + 2/3 = 1
1/4 +2/4 +3/4 = 1.5
....

From the above, you can see that
1/3 + 2/3 = 1
1/4 + 3/4 = 1
1/5 + 4/5 = 2/5 + 3/5 = 1

你會發現 number of terms x 0.5 = answer.
Therefore answer is 45 terms x 0.5 = 22.5

Q2.) （1/3＋2/3）=1;
（1/4＋2/4＋3/4）=1;
（1/5＋2/5＋3/5＋4/5）=1;
（1/10＋2/10＋...＋9/10）=1
therefore,
（1/3＋2/3）＋（1/4＋2/4＋3/4）＋（1/5＋2/5＋3/5＋4/5）＋...＋（1/10＋2/10＋...＋9/10）=8
8+1/2=8又1/2