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
In the ancient Roman measurement system, a leuga was a unit of length that was equal to 7,500 pedes. In this measurement system, how many pedes were equivalent to 3.8 leugas?
原库参考解析
比・比例・速率与单位换算挑战
A certain town has an area of 12,669,184 square yards. What is the area, in square miles, of this town? (1 mile = 1,760 yards)
原库参考解析
比・比例・速率与单位换算进阶
A dog's mass is 37 kilograms. What is the dog's mass, in grams? (1 kilogram = 1,000 grams)
原库参考解析
比・比例・速率与单位换算挑战
The area of a rectangular region is increasing at a rate of 310 square feet per hour. Which of the following is closest to this rate in square meters per minute? (Use 1 meter = 3.28 feet.)
原库参考解析
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.)
原库参考解析
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?
原库参考解析
比・比例・速率与单位换算挑战
One gallon of paint will cover 70 square feet of a surface. A room has a total wall area of w square feet. Which equation represents the total amount of paint P, in gallons, needed to paint the walls of the room twice?
原库参考解析
比・比例・速率与单位换算进阶
The ratio s to t is equivalent to the ratio 1 to 3. If the value of s is multiplied by 25, how will the value of t change to maintain this ratio?
原库参考解析
比・比例・速率与单位换算进阶
An object's speed is 60 yards per second. What is the object's speed, in feet per second? (1 yard = 3 feet)
原库参考解析
比・比例・速率与单位换算进阶
A triathlon is a multisport race consisting of three different legs. A triathlon participant completed the cycling leg with an average speed of 17.700 miles per hour. What was the average speed, in yards per hour, of the participant during the cycling leg?
(1 mile = 1,760 yards)
原库参考解析
比・比例・速率与单位换算基础
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 , when the air temperature is 29°F and the wind speed is 15 miles per hour (mph)? (Disregard the degree symbol when entering your answer.
原库参考解析
比・比例・速率与单位换算基础
Charles saves \( \frac{3}{5} \) of the $225 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?
原库参考解析
