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・速率与单位换算挑战
An object's speed is increasing at a rate of 5.70 meters per second squared. What is this rate, in miles per minute squared, rounded to the nearest tenth?
(Use 1 mile = 1,609 meters.)
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 270 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・速率与单位换算挑战
On average, a certain tree grows 87 centimeters every m months. At this rate, which expression represents the number of centimeters, on average, the tree grows every k years?
原库参考解析
比・比例・速率与单位换算进阶
A certain pigeon species can fly at an average speed of 16 meters per second when in continuous flight. At this rate, how many meters would this pigeon species fly in 4 seconds?
原库参考解析
比・比例・速率与单位换算挑战
An object moves at a speed of \( \frac{3}{50} \) feet per second. What is this speed, in yards per second? (3 feet = 1 yard)
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 consecutive events. A triathlon participant plans to complete the cycling event with an average speed of 19,008 yards per hour. What is this average speed, in miles per hour? (1 mile =1,760 yards)
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 3.51 square miles. What is the area, in square yards, of this town?(1 mile = 1,760 yards)
原库参考解析
比・比例・速率与单位换算挑战
An object's speed is increasing at a rate of 10.7 meters per second squared. What is this rate, in miles per minute squared, rounded to the nearest tenth? (Use 1 mile = 1,609 meters.)
原库参考解析
比・比例・速率与单位换算进阶
A remotely operated vehicle (ROV) is used for underwater ocean research. When the ROV is at a depth of 31 fathoms, what is the ROV's depth in feet? (l fathom = 6 feet)
原库参考解析
比・比例・速率与单位换算挑战
Carl, Ryan, and Jodie can make pancakes in the ratio of 2: 3: 5. If Jodie can make a pancake in 4 minutes, how many minutes will it take Carl and Ryan to make 5 pancakes if the two of them work together?
原库参考解析
比・比例・速率与单位换算挑战
Ruben can finish painting a wall in 2 hours. Jake can finish painting the same wall in 3 hours. If the two of them help paint the same wall together, how long will it take them to finish the job?
原库参考解析
比・比例・速率与单位换算挑战
A rectangle has an area of 21 square yards. What is the area, in square feet, of the rectangle? ( 3 feet = 1 yard)
原库参考解析
