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・速率与单位换算基础
How many meters are equivalent to 2,300 centimeters? (100 centimeters = 1 meter)
原库参考解析
比・比例・速率与单位换算进阶
The ratio x to y is equivalent to the ratio 9 to 5. lf the value of x is 162, what is the value of y?
原库参考解析
比・比例・速率与单位换算基础
The number of raccoons in a 131-square-mile area is estimated to be 2,358. What is the estimated population density, in raccoons per square mile, of this area?
原库参考解析
比・比例・速率与单位换算挑战
The speed of a vehicle is increasing at a rate of 7.3 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 distance of 354 furlongs is equivalent to how many feet? (1 furlong = 220 yards and 1 yard = 3 feet)
原库参考解析
比・比例・速率与单位换算基础
An object's speed is 64 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 landscaper uses a hose that puts 88x ounces of water in a bucket in 5y minutes. Which expression represents the number of ounces of water the hose puts in the bucket in 9y minutes at this rate?
原库参考解析
比・比例・速率与单位换算基础
What length, in centimeters, is equivalent to a length of 51 meters? (1 meter = 100 centimeters)
原库参考解析
比・比例・速率与单位换算挑战
One gallon of stain will cover 170 square feet of a surface. A yard has a total fence area of \( w \) square feet. Which equation represents the total amount of stain \( S \), in gallons, needed to stain the fence in this yard twice?
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 250 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
One gallon of paint will cover 220 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
A distance of 112 furlongs is equivalent to how many feet? (1 furlong = 220 yards and 1 yard = 3 feet)
原库参考解析
