商务数学
合集下载
相关主题
- 1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
- 2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
- 3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。
Contemporary Business Mathematics 商务数学
主讲教师：张亚卿
课程简介
商务数学是财务、金融及商业管理的入门数 学。旨在介绍一些对于商业运作比较重要的 数学概念，这些概念将被应用到诸如会计、 经济及财务方面课程上面。
Part I Mathematics Fundamentals and Business Applications
4.Linear Systems线性系统
1 Review of Arithห้องสมุดไป่ตู้etic 算数回顾
Objectives学习目的
1.用基本的操作指令简化数学表达式。
2.确定等分数，把分数转化成小数。
3.把百分数转化成分数和小数，把小数和分数转化成百 分数。
4.通过解决问题，估算简单数学和加权平均数。 5.确定职工酬劳总收益，例如薪水，计时工资，佣金。 6.通过解决问题，估算GST，销售税和财产税。
■ A. Basic problems
■ B. Problems involving Simple Arithmetic
Average (简单算术平均数问题)
Arithmetic Average /mean(算术平均数) A = [A1 + A2 + . . . + An ] / n
Example 1.4D P14 Monthly sales of Sheridan Service for
Chapter 1
1.4 Applications------Averages（平均数，P12） 1.5 Applications------Payroll （工资表，P19） 1.6 Applications------Taxes（税收，P26）
1.4 Applications------Averages
Chapter 1
1.1 Basics of Arithmetic（算数基础, P2） 1.2 Fractions （分数, P3） 1.3 Percent （百分数, P8 ）
1.1 Basics of Arithmetic
B --- Bracket括号
E --- Exponent 指数，幂
D --- Division除法
（1）What are Javier’s net sales for August? → 25 540.00 – 360.00 = $ 25,180.00 （2） How much is his commission for August? → 25 180 x 0.115 = $ 2895.70 （3） If Javier drew $ 900.00 in August, what is the amount due to him? → 2895.70 – 900.00 = $ 1995.70
Javier receives a commission of 11.5% on his net sales and is entitled to drawings of up to $ 1000.00 per month. During August, Javier’s gross sales amounted to $25,540.00 and sales returns and allowances were $ 360.00
Example 1.5A, P20 An employee with an annual salary of $23,296.00 is paid every 2 weeks. The regular work week is 40 hours. （1） What is the gross pay per pay period? → 23,296/26=$896.00 （2） What is the hourly rate of pay? → 896/80 = $11.20 （3）What is the gross earning for a pay period in which the employee worked 6 hours of overtime and is paid 1.5 times the regular hourly rate of pay? → Regular gross earning per 2-week period = $896.00 → Overtime pay = $11.20 x 1.5 x 6 = $100.80, → Total earning = $996.80
Grade-point average （GPA）/Average per credit hour 平均成绩点数：一般是将每门课程的学分乘以学时，加 起来以后除以总的学时，得出平均分。 GPA =Total Weighted Points (学时乘学分的总和)/ total Credit Hours (学时总和) → GPA = 69 / 23 = 3.0 → Average course grade = 19 / 7 = 2.71
August September October November December
12,800 13,800 15,300 14,400 13,900
Average monthly sales = total sales / number of months = ＄ 164,100 / 12 = ＄13,675
● Graduated commission 渐进佣金: Higher ( )% for higher sale level 销售额越大, 佣金率越高
● Salary plus Commission (底薪+佣金): lower ( )% / quota (定额)
Example 1.5D, P22
■ C. Weighted arithmetic Average （加权平均） Aw = （W1A1 + W2A2 + . . . +WnAn） /（W1+ W2+ . . . +Wn） Example 1.4G , P16 The credit hours and grades for Dana’s first-term courses are listed here. Courses Credit Hour Grades Weighted Points Accounting 5 A=4 20 Economics 3 B=3 9 English 4 C=2 8 Law 2 D=1 2 Marketing 4 A=4 16 Mathematics 3 A=4 12 Elective 2 D=1 2 Total 23 19 69
last year were listed below. What were Sheridan’s average monthly sales for the year?
January $13,200 July $13,700
February March April May June
11,400 14,600 13,100 13,600 14,300
We can place a dot above a decimal places to show that it repeats.
Change percents to fractions (把百分数变为分数) 30%=30/100=3/10 Change percents to decimals(把百分数变为小数) 18%=0.18 Change decimals to percents (把小数变为百分数) 0.32=32% Change fractions to percents(把分数变为百分数) 9/6=1.5=150%
■ B. Commission (佣金), P21 ● Straight commission 纯佣金制，指无底薪工资 = Net sales 净销售额 x Rate of commission 佣金率 Net sales 净销售额 = Gross sales 毛销售额 (Sales returns and Allowances) (销售退回与折让)
1.5 Applications------Payroll
■ A. Salaries （工资）, P19 ★on a monthly or a yearly basis 工资以月或年为基础 计算
★Employees may be paid monthly, semi-monthly, every two weeks or weekly.在国外，经常以月、半月、每两周、 每周形式发放月工资。
The year is assumed to consist of exactly 52 weeks. Gross Earnings 总收益； Overtime 加班
★ Regular pay (规定工作时间的薪水) Methods of computation (计算方法): 1. If salary is on monthly basis, yearly pay = monthly salary x12 2. Weekly pay = yearly pay / 52 3. Hourly rate of pay = weekly pay / regular workweek hours (Normally 40 or 37.5) ★ Overtime pay (加班费) = 1.5 x Regular rate of pay (Monday-Saturday) = 2 x Regular rate of pay (Sunday & holidays)
1 Review of Arithmetic 算数回顾
重点词汇 Important Words
Fraction 分数 a/b
Decimal 小数0.a
Percent百分数a%
Weighted average 加权平均数
Bracket括号；Exponent 指数，幂；Division除法； Multiplication乘法； Addition加法； Subtraction减法
% means /100 用100替换分数的分母
Reduce fractions to lowest terms (把分数简化为低阶形式) 约分：21/35 →3/5, 210/255 → 14/17 Convert fractions to higher terms（把分数转化为高阶形 式） 通分： 2/3 →12/18, 5/7 → 20/28 Round … to two decimal places (四舍五入到小数位后两 位) 8.451 → 8.45, 1.235 →1.24 Convert fractions into decimal form (把分数变为小数) 9/8 → 1.125, 1/3 →0.3333…
数学基本原理及商业应用
Includes Chapters 1, 2, 3, 4（包括第1,2,3,4章） 1 Review of Arithmetic 算数回顾
2 Review of Basic Algebra 基本代数回顾
3 Ratio, Proportion, and Percent 比率，比例与百分比
M --- Multiplication乘法
A --- Addition加法
S --- Subtraction减法
Do you know the “BEDMAS” rule?
1.2 Fractions
2 ------------numerator分子 ------- -------------dividing line 3 ------------denominator分母 2 and 3 are called the terms of the fraction （分数项）.
proper fraction 真分数 3/8
Fraction improper fraction假分数6/5 complex fraction 繁分数420/（1600×315/360）
1.3 Percent
Percent means “per hundred”, and the symbol % is used to show “parts of one hundred”.
主讲教师：张亚卿
课程简介
商务数学是财务、金融及商业管理的入门数 学。旨在介绍一些对于商业运作比较重要的 数学概念，这些概念将被应用到诸如会计、 经济及财务方面课程上面。
Part I Mathematics Fundamentals and Business Applications
4.Linear Systems线性系统
1 Review of Arithห้องสมุดไป่ตู้etic 算数回顾
Objectives学习目的
1.用基本的操作指令简化数学表达式。
2.确定等分数，把分数转化成小数。
3.把百分数转化成分数和小数，把小数和分数转化成百 分数。
4.通过解决问题，估算简单数学和加权平均数。 5.确定职工酬劳总收益，例如薪水，计时工资，佣金。 6.通过解决问题，估算GST，销售税和财产税。
■ A. Basic problems
■ B. Problems involving Simple Arithmetic
Average (简单算术平均数问题)
Arithmetic Average /mean(算术平均数) A = [A1 + A2 + . . . + An ] / n
Example 1.4D P14 Monthly sales of Sheridan Service for
Chapter 1
1.4 Applications------Averages（平均数，P12） 1.5 Applications------Payroll （工资表，P19） 1.6 Applications------Taxes（税收，P26）
1.4 Applications------Averages
Chapter 1
1.1 Basics of Arithmetic（算数基础, P2） 1.2 Fractions （分数, P3） 1.3 Percent （百分数, P8 ）
1.1 Basics of Arithmetic
B --- Bracket括号
E --- Exponent 指数，幂
D --- Division除法
（1）What are Javier’s net sales for August? → 25 540.00 – 360.00 = $ 25,180.00 （2） How much is his commission for August? → 25 180 x 0.115 = $ 2895.70 （3） If Javier drew $ 900.00 in August, what is the amount due to him? → 2895.70 – 900.00 = $ 1995.70
Javier receives a commission of 11.5% on his net sales and is entitled to drawings of up to $ 1000.00 per month. During August, Javier’s gross sales amounted to $25,540.00 and sales returns and allowances were $ 360.00
Example 1.5A, P20 An employee with an annual salary of $23,296.00 is paid every 2 weeks. The regular work week is 40 hours. （1） What is the gross pay per pay period? → 23,296/26=$896.00 （2） What is the hourly rate of pay? → 896/80 = $11.20 （3）What is the gross earning for a pay period in which the employee worked 6 hours of overtime and is paid 1.5 times the regular hourly rate of pay? → Regular gross earning per 2-week period = $896.00 → Overtime pay = $11.20 x 1.5 x 6 = $100.80, → Total earning = $996.80
Grade-point average （GPA）/Average per credit hour 平均成绩点数：一般是将每门课程的学分乘以学时，加 起来以后除以总的学时，得出平均分。 GPA =Total Weighted Points (学时乘学分的总和)/ total Credit Hours (学时总和) → GPA = 69 / 23 = 3.0 → Average course grade = 19 / 7 = 2.71
August September October November December
12,800 13,800 15,300 14,400 13,900
Average monthly sales = total sales / number of months = ＄ 164,100 / 12 = ＄13,675
● Graduated commission 渐进佣金: Higher ( )% for higher sale level 销售额越大, 佣金率越高
● Salary plus Commission (底薪+佣金): lower ( )% / quota (定额)
Example 1.5D, P22
■ C. Weighted arithmetic Average （加权平均） Aw = （W1A1 + W2A2 + . . . +WnAn） /（W1+ W2+ . . . +Wn） Example 1.4G , P16 The credit hours and grades for Dana’s first-term courses are listed here. Courses Credit Hour Grades Weighted Points Accounting 5 A=4 20 Economics 3 B=3 9 English 4 C=2 8 Law 2 D=1 2 Marketing 4 A=4 16 Mathematics 3 A=4 12 Elective 2 D=1 2 Total 23 19 69
last year were listed below. What were Sheridan’s average monthly sales for the year?
January $13,200 July $13,700
February March April May June
11,400 14,600 13,100 13,600 14,300
We can place a dot above a decimal places to show that it repeats.
Change percents to fractions (把百分数变为分数) 30%=30/100=3/10 Change percents to decimals(把百分数变为小数) 18%=0.18 Change decimals to percents (把小数变为百分数) 0.32=32% Change fractions to percents(把分数变为百分数) 9/6=1.5=150%
■ B. Commission (佣金), P21 ● Straight commission 纯佣金制，指无底薪工资 = Net sales 净销售额 x Rate of commission 佣金率 Net sales 净销售额 = Gross sales 毛销售额 (Sales returns and Allowances) (销售退回与折让)
1.5 Applications------Payroll
■ A. Salaries （工资）, P19 ★on a monthly or a yearly basis 工资以月或年为基础 计算
★Employees may be paid monthly, semi-monthly, every two weeks or weekly.在国外，经常以月、半月、每两周、 每周形式发放月工资。
The year is assumed to consist of exactly 52 weeks. Gross Earnings 总收益； Overtime 加班
★ Regular pay (规定工作时间的薪水) Methods of computation (计算方法): 1. If salary is on monthly basis, yearly pay = monthly salary x12 2. Weekly pay = yearly pay / 52 3. Hourly rate of pay = weekly pay / regular workweek hours (Normally 40 or 37.5) ★ Overtime pay (加班费) = 1.5 x Regular rate of pay (Monday-Saturday) = 2 x Regular rate of pay (Sunday & holidays)
1 Review of Arithmetic 算数回顾
重点词汇 Important Words
Fraction 分数 a/b
Decimal 小数0.a
Percent百分数a%
Weighted average 加权平均数
Bracket括号；Exponent 指数，幂；Division除法； Multiplication乘法； Addition加法； Subtraction减法
% means /100 用100替换分数的分母
Reduce fractions to lowest terms (把分数简化为低阶形式) 约分：21/35 →3/5, 210/255 → 14/17 Convert fractions to higher terms（把分数转化为高阶形 式） 通分： 2/3 →12/18, 5/7 → 20/28 Round … to two decimal places (四舍五入到小数位后两 位) 8.451 → 8.45, 1.235 →1.24 Convert fractions into decimal form (把分数变为小数) 9/8 → 1.125, 1/3 →0.3333…
数学基本原理及商业应用
Includes Chapters 1, 2, 3, 4（包括第1,2,3,4章） 1 Review of Arithmetic 算数回顾
2 Review of Basic Algebra 基本代数回顾
3 Ratio, Proportion, and Percent 比率，比例与百分比
M --- Multiplication乘法
A --- Addition加法
S --- Subtraction减法
Do you know the “BEDMAS” rule?
1.2 Fractions
2 ------------numerator分子 ------- -------------dividing line 3 ------------denominator分母 2 and 3 are called the terms of the fraction （分数项）.
proper fraction 真分数 3/8
Fraction improper fraction假分数6/5 complex fraction 繁分数420/（1600×315/360）
1.3 Percent
Percent means “per hundred”, and the symbol % is used to show “parts of one hundred”.