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
A remotely operated vehicle (ROV) is used for underwater ocean research. When the ROV is at a depth of 26 fathoms, what is the ROV's depth in feet? (1 fathom = 6 feet)
原库参考解析
比・比例・速率与单位换算进阶
The ratio of cups of flour to cups of butter in a pie dough recipe is 2.75:1, and in a biscuit recipe is 7:1. Each recipe uses 1 cup of butter. How many more cups of flour are in the biscuit recipe than in the pie dough recipe?
原库参考解析
比・比例・速率与单位换算挑战
An object's speed, in meters per hour, is increasing at a rate of 1,530 meters per hour per second. Which of the following is closest to this rate in feet per second squared? (Use 1 meter =3.28 feet.)
原库参考解析
比・比例・速率与单位换算挑战
An object's speed, in meters per hour, is increasing at a rate of 1,490 meters per hour per second. Which of the following is closest to this rate in feet per second squared? (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 sealant costs $13 and will cover 300 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
A container has a volume of 0.84 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.)
原库参考解析
比・比例・速率与单位换算挑战
One gallon of sealant costs $29 and will cover 300 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・速率与单位换算进阶
The length of each side of triangle A is 270 millimeters. The length of each side of triangle B is double the length of each side of triangle A. What is the length, in millimeters, of each side of triangle B?
原库参考解析
比・比例・速率与单位换算挑战
The ratio 6 to 3 is equivalent to the ratio 24 to 3k, where k is a constant. What is the value of k?
原库参考解析
比・比例・速率与单位换算挑战
The ratio 10 to 2 is equivalent to the ratio 40 to 2k, where k is a constant. What is the value of k ?
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比・比例・速率与单位换算进阶
An object travels x inches in y seconds. At this rate, which expression represents the time, in seconds, it takes the object to travel a distance of 12x inches?
原库参考解析
比・比例・速率与单位换算进阶
The number of muskrat in a 134-acre area is estimated to be 2,278. What is the estimated population density, in muskrat per acre, of this area?
原库参考解析
