这部分需要会什么？
- 把比转换成份数或单位率
- 保持比例式中数量的对应关系
- 用单位抵消完成长度、面积和体积换算
核心概念与公式
若 \(A:B=m:n\)，可设 \(A=mk,B=nk\)，总量为 \((m+n)k\)。单位率表示每 1 个单位对应多少，例如千米/小时、元/件；建立比例式时每一边分子和分母的意义应一致。
换算单位可乘以数值等于 1 的换算因子，让旧单位约去。长度单位的倍率为 \(k\) 时，面积倍率为 \(k^2\)，体积倍率为 \(k^3\)。平均速度为总路程除以总时间，通常不是各段速度的简单平均。
做题时怎样使用
- 先标清数量和单位，判断是部分比部分还是部分比整体
- 用同一比例系数或单位率建式
- 换算时连同单位一起写，面积和体积需相应平方或立方
容易混淆的地方
红球与蓝球之比为 \(2:3\)，红球占总数的 \(2/5\)，不是 \(2/3\)。\(1\text{ m}^2=10{,}000\text{ cm}^2\)，不是 100。
用一个例题串起方法
知识点教学例题某溶液中成分 A 与 B 的质量比为 \(3:5\)，总质量为 640 克。求 A 的质量。
展开解题思路 ＋
共 \(3+5=8\) 份，每份 \(640/8=80\) 克，所以 A 有 \(3\times80=240\) 克。
本知识点题库
先独立作答，再查看答案与解析。
比・比例・速率与单位换算进阶
A region has a total area of 270 square feet. Within the region, there are n objects. Which expression represents the average number of objects per square foot within this region?
参考答案
比・比例・速率与单位换算挑战
An object’s speed is increasing at a rate of 6.4 meters per second squared. What is this rate, in miles per minute squared, rounded to the nearest tenth?
(Use 1 mile = 1,609 meters.)
(Use 1 mile = 1,609 meters.)
参考答案
比・比例・速率与单位换算进阶
For certain air temperatures, the table gives wind chill temperatures for two different wind speeds.
According to the table, what is the wind chill temperature, in degrees Fahrenheit (°F), when the air temperature is 27°F and the wind speed is 20 miles per hour (mph)? (Disregard the degree symbol when entering your answer.)
According to the table, what is the wind chill temperature, in degrees Fahrenheit (°F), when the air temperature is 27°F and the wind speed is 20 miles per hour (mph)? (Disregard the degree symbol when entering your answer.)
参考答案
比・比例・速率与单位换算进阶
Charles saves \( \frac{4}{5} \) of the $230 he earns each week from his summer job. If Charles continues to save at this rate, how much money, in dollars, will Charles save in 3 weeks?
参考答案
比・比例・速率与单位换算挑战
The area of a rectangular region is increasing at a rate of 80 square feet per hour.
Which of the following is closest to this rate in square meters per minute?
(Use 1 meter = 3.28 feet.)
Which of the following is closest to this rate in square meters per minute?
(Use 1 meter = 3.28 feet.)
参考答案
比・比例・速率与单位换算挑战
The area of a rectangular region is increasing at a rate of 40 square feet per hour. Which of the following is closest to this rate in square meters per minute?
(Use 1 meter = 3.28 feet.)
(Use 1 meter = 3.28 feet.)
参考答案
比・比例・速率与单位换算进阶
A triathlon is a multisport race consisting of three different consecutive events. A triathlon participant plans to complete the cycling event with an average speed of 33,264 yards per hour. What is this average speed, in miles per hour? (1 mile = 1,760 yards)
参考答案
比・比例・速率与单位换算进阶
A capillary tube is used to hold a substance while measuring its melting point. The volume of the substance in this capillary tube is 2.23 cubic millimeters. What is this volume in cubic centimeters? (1 centimeter = 10 millimeters)
参考答案
比・比例・速率与单位换算进阶
The population density of Town A is 120 people per square mile, and the population density of Town B is 80 people per square mile. Town A has a population of 14,760 people, and Town B has a population of 3,280 people. The area, in square miles, of Town A is k times the area, in square miles, of Town B. What is the value of k?
参考答案
比・比例・速率与单位换算挑战
A bicyclist rides a distance of x feet in y minutes. At this rate, which expression represents the distance, in feet, that the bicyclist rides in 119y minutes?
参考答案
比・比例・速率与单位换算基础
During a trip, Bill drove his car for 25 miles and then began driving at a constant speed of 60 miles per hour. After 2 hours of driving at this speed, what is the total distance, in miles, Bill has traveled during this trip?
参考答案
比・比例・速率与单位换算基础
A machine in a factory produces items at a constant rate of 50 items per hour. At this rate, how many items will the machine produce in 8 hours?
参考答案
