主題 結合律 分配律 結合律與分配律的差異 Community: Channel 9, MVP program, ISV Buddy program 1033 Microsoft employees signed up for the program 1098 ISVs have a buddy assigned to them Revenue growth of $1.3bn last year – bigger than a BEA Systems (approx. $1.1bn) or a Novell ($1.1bn). We basically created a top 20 software company in revenue growth alone. 分配律

結合律定義 例如: 1. 20+30+40=20+(30+40)=90 2. 5 ×10 ×20=5 ×(10 ×20)=1000 在連加或連乘的算式中，不論先算哪個部分，結果都是一樣，但位置不可移動。 例如: 1. 20+30+40=20+(30+40)=90 2. 5 ×10 ×20=5 ×(10 ×20)=1000 Community: Channel 9, MVP program, ISV Buddy program 1033 Microsoft employees signed up for the program 1098 ISVs have a buddy assigned to them Revenue growth of $1.3bn last year – bigger than a BEA Systems (approx. $1.1bn) or a Novell ($1.1bn). We basically created a top 20 software company in revenue growth alone.

分配律定義 1.乘法對加法的分配律。 2.乘法對減法的分配律。 我們可以把合在一起的兩個數分開處理,也可以先處理分開的兩個數,再合起來。這叫做乘法分配律。可再細分為兩種: 1.乘法對加法的分配律。 2.乘法對減法的分配律。 Community: Channel 9, MVP program, ISV Buddy program 1033 Microsoft employees signed up for the program 1098 ISVs have a buddy assigned to them Revenue growth of $1.3bn last year – bigger than a BEA Systems (approx. $1.1bn) or a Novell ($1.1bn). We basically created a top 20 software company in revenue growth alone.

分配律的意義 例如: (10+8) ×5=10×5+8×5 12×6+15×6=(12+15) × 6 1.乘法對加法的分配律。 (a + b) × c = a × c + b × c 例如: (10+8) ×5=10×5+8×5 12×6+15×6=(12+15) × 6 Community: Channel 9, MVP program, ISV Buddy program 1033 Microsoft employees signed up for the program 1098 ISVs have a buddy assigned to them Revenue growth of $1.3bn last year – bigger than a BEA Systems (approx. $1.1bn) or a Novell ($1.1bn). We basically created a top 20 software company in revenue growth alone.

分配律的意義 例如: (10-5) × 3=10× 3-10× 5 15× 20-10× 20=(15-10) × 20 2.乘法對減法的分配律。 (a - b) × c = a × c - b × c 例如: (10-5) × 3=10× 3-10× 5 15× 20-10× 20=(15-10) × 20 Community: Channel 9, MVP program, ISV Buddy program 1033 Microsoft employees signed up for the program 1098 ISVs have a buddy assigned to them Revenue growth of $1.3bn last year – bigger than a BEA Systems (approx. $1.1bn) or a Novell ($1.1bn). We basically created a top 20 software company in revenue growth alone.

除法是否有分配律呢? 可簡單說除法沒有分配律! 例如: (12+8) ÷ 4=12÷ 4+8 ÷4 雖然 (a + b) ÷ c = a ÷ c + b ÷ c 但是d÷ (e + f) ≠d÷ e +d÷ f 因此… 可簡單說除法沒有分配律! 例如: (12+8) ÷ 4=12÷ 4+8 ÷4 18 ÷(6+3) ≠ 18÷6+18÷3 Community: Channel 9, MVP program, ISV Buddy program 1033 Microsoft employees signed up for the program 1098 ISVs have a buddy assigned to them Revenue growth of $1.3bn last year – bigger than a BEA Systems (approx. $1.1bn) or a Novell ($1.1bn). We basically created a top 20 software company in revenue growth alone.

為什麼? 例如: (12+8) ÷ 4=12×1/4+8 ×1/4 為什麼(a + b) ÷ c = a ÷ c + b ÷ c可以成立 可以簡單把(a + b) ÷ c看成(a + b) ×1/c，那麼也是乘法對加法的分配律。 例如: (12+8) ÷ 4=12×1/4+8 ×1/4 Community: Channel 9, MVP program, ISV Buddy program 1033 Microsoft employees signed up for the program 1098 ISVs have a buddy assigned to them Revenue growth of $1.3bn last year – bigger than a BEA Systems (approx. $1.1bn) or a Novell ($1.1bn). We basically created a top 20 software company in revenue growth alone.

結合律與分配律混淆之處 常常會把分配律a × c + b × c=(a+b) ×c，其中(a+b)先合起來算 (結合)，就誤把分配律當作結合律。 Community: Channel 9, MVP program, ISV Buddy program 1033 Microsoft employees signed up for the program 1098 ISVs have a buddy assigned to them Revenue growth of $1.3bn last year – bigger than a BEA Systems (approx. $1.1bn) or a Novell ($1.1bn). We basically created a top 20 software company in revenue growth alone. 接下來讓我們來練習一下結合律:

下列何者為結合律的應用，是的打，不是的打× 40+88+12=40+(88+12) × 68+50+32=68+32+50  38×125×8= 38×(125×8) 答對了嗎?

下列何者為分配律的應用，是的打，不是的打× 7×15+13×15=(7+13) ×15  97 × 28 － 97 × 18=97 ×(28 －18) × 48 ÷(4+8)=48 ÷4+48 ÷8 答對了嗎?

下列是分配律應用的打，是結合律的打○  92×99＝92×(100-1) 85×48 ×93＝ 85×(48 ×93) ○  175×633＋25×633＝(172+25) ×633

分配律延伸題: 答對了嗎? 題目 說明 計算20052006×20062005 －20052005×20062006之值。 ＝（20052005＋1）×20062005－20052005×（20062005＋1） ＝（20052005×20062005＋20062005）－ （20052005×20062005＋20052005） ＝20062005－20052005 ＝10000 說明 答對了嗎?

應用問題練習: 小明去商店買了7盒糖果，每盒有25包，一包賣4元，小明一共要花多少元? 題目 7×25×4 ＝ 7×(25×4) 1 2 ＝7×100 3 ＝700 使用結合律技巧把(25×4)先算 ，可簡化計算。 說明

應用問題練習: 題目 1 2 3 ＝59503 說明 商店老闆買進197件T恤，每件T恤賣299元，如果全部賣完，老闆可以賣得多少元? 299×197 ＝(300-1) ×197 1 2 ＝300×197－1×197 ＝59700－197 ＝59503 3 將299使用分配律技巧化為(300-1) ，可簡化計算。 說明

The End Community: Channel 9, MVP program, ISV Buddy program 1033 Microsoft employees signed up for the program 1098 ISVs have a buddy assigned to them Revenue growth of $1.3bn last year – bigger than a BEA Systems (approx. $1.1bn) or a Novell ($1.1bn). We basically created a top 20 software company in revenue growth alone.