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
An object travels at a constant speed of 12 centimeters per second.At this speed, what is the time, in seconds, that it would take for the object to travel 108 centimeters?
原库参考解析
比・比例・速率与单位换算挑战
For a certain rectangular region, the ratio of its length to its width is 35 to 10.If the width of the rectangular region increases by 7 units, how must the length change to maintain this ratio?
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
A certain park has an area of 11,863,808 square yards. What is the area, in square miles, of this park? (1 mile = 1,760 yards)
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 rocket contained 467 ,000 kilograms (kg) of propellant before launch. Exactly 21 seconds after launch, 362,105 kg of this propellant remained. On average, approximately how much propellant, in kg, did the rocket burn each second after launch?
原库参考解析
比・比例・速率与单位换算基础
A printer produces posters at a constant rate of 42 posters per minute. At what rate, in posters per hour, does the printer produce the posters?
原库参考解析
比・比例・速率与单位换算挑战
A sample of oak has a density of 807 kilograms per cubic meter. The sample is in the shape of a cube, where each edge has a length of 0.90 meters. To the nearest whole number, what is the mass, in kilograms, of this sample?
原库参考解析
比・比例・速率与单位换算进阶
A special camera is used for underwater ocean research. The camera is at a depth of 39 fathoms. What is the camera's depth in feet? (1 fathom = 6 feet)
原库参考解析
比・比例・速率与单位换算基础
At a particular track meet, the ratio of coaches to athletes is 1 to 26. If there are x coaches at the track meet, which of the following expressions represents the number of athletes at the track meet?
原库参考解析
比・比例・速率与单位换算进阶
A certain bird species can fly at an average speed of 16 meters per second when in continuous flight. At this rate, how many meters would this bird species fly in 4 seconds?
原库参考解析
比・比例・速率与单位换算基础
Brian saves \( \frac{2}{5} \) of the $215 he earns each week from his iob. If Brian continues to save at this rate, how much money, in dollars, will Brian save in 9 weeks?
原库参考解析
