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
The number of muskrat in a 131-acre area is estimated to be 2,096.what is the estimated population density, in muskrat per acre, of this area?
原库参考解析
比・比例・速率与单位换算进阶
The density of a certain type of wood is 553 kilograms per cubic meter. A sample of this type of wood is in the shape of a cube, where each edge has a length of 0.60 meter. To the nearest whole number, what is the mass, in kilograms, of this sample?
原库参考解析
比・比例・速率与单位换算挑战
How many square meters per minute is equivalent to a rate of 1800 square centimeters per hour? (Note: 1 meter = 100 centimeter)
原库参考解析
比・比例・速率与单位换算进阶
The ratio of green tiles to blue tiles in a piece of artwork is 5 to 2. If there are 16 blue tiles in the piece of artwork, how many green tiles are there?
原库参考解析
比・比例・速率与单位换算挑战
The speed of a white-throated needletail, a type of bird, in flight was measured to be 49 miles per hour. What was the white-throated needletail's measured speed, in kilometers per hour? (Use 1 mile = 1.6 kilometers.)
原库参考解析
比・比例・速率与单位换算进阶
During a trip, Bill drove his car for 16.0 miles and then began driving at a constant speed of 60.0 miles per hour. After 2 hours of driving at this speed, what is the total distance, in miles, Bill has traveled during this trip?
原库参考解析
比・比例・速率与单位换算挑战
A certain park has an area of 4,860,000 square meters. What is the area, in square kilometers, of this park ? (1 kilometer = 1,000 meters)
原库参考解析
比・比例・速率与单位换算挑战
An object has a mass of 308 grams and a volume of 28 cubic centimeters. What is the density, in grams per cubic centimeter, of the object?
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 1,560 square centimeters per hour. What is this rate, in square meters per minute? (1 meter =100 centimeters)
原库参考解析
比・比例・速率与单位换算进阶
On average, a certain tree grows 39 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・速率与单位换算挑战
An object's speed is increasing at a rate of 4.9 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 certain dove species can fly at an average speed of 16 meters per second when in continuous flight. At this rate, how many meters would this dove species fly in 3 seconds?
原库参考解析
