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
A figure has an area of 7,344 square inches. What is the area, in square feet, of this figure? (1 foot = 12 inches)
原库参考解析
比・比例・速率与单位换算进阶
One gallon of sealant costs $17 and will cover 450 square feet of a surface. A deck has a total surface area of d square feet. Which equation represents the cost c, in dollars, of the sealant needed to cover the deck twice?
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 12.60 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 150 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
What length, in meters, is equivalent to a length of 230 decimeters?
(1 meter = 10 decimeters)
原库参考解析
比・比例・速率与单位换算挑战
One gallon of paint will cover 280 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・速率与单位换算挑战
The area of a rectangular region is increasing at a rate of 330 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
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 33,792 yards per hour. What is this average speed, in miles per hour? (1 mile = 1,760 yards)
参考答案
比・比例・速率与单位换算挑战
There is a proportional relationship between p and t. If \( p=2,310 \) when \( t=3,080 \), then what is the value of t when \( p=1,848 \)?
参考答案
比・比例・速率与单位换算进阶
There is a proportional relationship between p and t. If \( p=5,610 \) when \( t=7,480 \), then what is the value of t when \( p=4,488 \)?
参考答案
比・比例・速率与单位换算挑战
A container has a volume of 0.83 cubic meters. Which of the following is closest to this volume, in quarts?
(Note: 100.00 centimeters = 1 meter. Use 946.35 cubic centimeters = 1.00 quart.)
参考答案
比・比例・速率与单位换算进阶
During a physics experiment, the speed of an object was determined to be 177.0 inches per second. What is this speed in feet per second? (12 inches=1 foot)
参考答案
