國一數學分數問題

1.
4/(2×6) = (6-2)/(2×6) = (1/2) - (1/6)
4/(6×10) = (10-6)/(6×10) = (1/6) - (1/10)
4/(10×14) = (14-10)/(10×14) = (1/10) - (1/14)
4/(14×18) = (18-14)/(14×18) = (1/14) - (1/18)
4/(18×22) = (22-18)/(18×22) = (1/18) - (1/22)

[4/(2×6)] + [4/(6×10)] + [4/(10×14)] + [4/(14×18)] + [4/(18×22)]
= [(1/2) - (1/6)] + [(1/6) - (1/10)] + [(1/10) - (1/14)] + [(1/14) - (1/18)] +[(1/18) - (1/22)]
= (1/2) - (1/22)
= (11/22) - (1/22)
= 10/22
= 5/11


====
2.
答案： B. 11

(323⁴ / 143⁴) - (221⁴ / 209⁴)
= [(323⁴ × 209⁴) /(143⁴ × 209⁴)] - [(221⁴ × 143⁴) /(209⁴ × 143⁴)]
= [67507⁴ / (143⁴×209⁴)] -[31603⁴ / (143⁴×209⁴)]
= (67507⁴ - 31603⁴) / (143⁴ × 209⁴)
= [(67507² + 31603²)(67507² - 31603²)] /(143⁴ × 209⁴)
= [(67507² + 31603²)(67507 + 31603)(67507 - 31603)]/ (143⁴ × 209⁴)
= [(67507² + 31603²) × 99110 × 35904] / (143⁴ × 209⁴)
= 11 × [(67507² + 31603²) × 9010 × 35904] / (143⁴ × 209⁴)

2015-03-08 21:54:14 補充：
2. 另解
(323⁴ / 143⁴) - (221⁴ / 209⁴)
= [(17⁴ × 19⁴) / (11⁴ × 13⁴)] - [(13⁴ × 17⁴) / (11⁴ × 19⁴)
= [(17⁴ × 19⁸) / (11⁴ × 13⁴ × 19⁴)] - [(13⁸ × 17⁴) / (11⁴ × 13⁴ × 19⁴)
= [(17⁴ × 19⁸) - (13⁸ × 17⁴)] / (11⁴ × 13⁴ × 19⁴)

2015-03-08 21:54:41 補充：
分子
= 17⁴ × 19⁸ - 13⁸ × 17⁴
= 17⁴ × (19⁸ - 13⁸)
= 17⁴ × (19⁴ + 13⁴)(19⁴ - 13⁴)
= 17⁴ × (19⁴ + 13⁴)(19² + 13²)(19² - 13²)
= 17⁴ × (19⁴ + 13⁴)(19² + 13²)(19 + 13)(19 - 13)
= 17⁴ × (19⁴ + 13⁴) × (19² + 13²) × 22 × 6
= 17⁴ × (19⁴ + 13⁴) × (19² + 13²) × 2 × 11 × 6 ...... 答案選B

數學一和數學二、三、四的要求不一樣,數學一考查的內容比較多,但有一些東西也是必考的,比如偏導數,比如數學一要考線面積分,這是肯定要考的大題,







之前有人問過,
建議你去看看~
應該可以幫到你！

參考資料：
http://www.okonlineshop.com

(網址為: okonline shop.com(不要空格) )

　

[(17⁴ × 19⁸) - (13⁸ × 17⁴)] / (11⁴ × 13⁴ × 19⁴)
= 17⁴ × (19⁴ + 13⁴) × (19² + 13²) × 2 × 11 × 6 / (11⁴ × 13⁴ × 19⁴)
= 17⁴ × (19⁴ + 13⁴) × (19² + 13²) × 2 × 6 / (11³ × 13⁴ × 19⁴)

化為最簡分數,下列何數為分子之因數

答案 :D 17

原式
=(323^4×209^4−221^4×143^4)/(143^4×209^4)
=[(323×209)^4−(221×143)^4]/(143×209)^4
=[(11×17×19^2)^4−(11×13^2×17)^4]/(11^2×13×19)^4
=(11^4×17^4)(19^8−13^8)/(11^8×13^4×19^4)
=17^4(19^8−13^8)/(11^4×13^4×19^4)

題目怎打的

直接按計算機不就好了

連一點點題目都打得亂七八糟
你是起制般的嗎~