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
How many centimeters are equivalent to 24 meters? (1 meter =100 centimeters)
原库参考解析
比・比例・速率与单位换算进阶
A signal from a satellite in space travels to the surface of Earth at the speed of light. The signal takes 0.1473 seconds to reach the surface of Earth. What is the approximate distance, in kilomelers, from the satellite to the surface of Earth? (Nate: Use 2.998\( \times \)108 meters/ second for the speed of light. 1,000 meters = 1 kilometer)
原库参考解析
比・比例・速率与单位换算进阶
For certain air temperatures, the table gives wind chill temperatures for two different wind speeds.
According to the table, what is the wind chill temperature, in degrees Fahrenheit (°F ), when the air temperature is 41 °F and the wind speed is 45 miles per hour (mph)? (Disregard the degree symbol when entering your answer.)
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 280 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
The ratio 12 to x is equivalent to the ratio 168 to y. Which expression represents y in terms of x?
原库参考解析
比・比例・速率与单位换算进阶
How many centimeters are equivalent to 47 meters?
(1 meter = 100 centimeters)
原库参考解析
比・比例・速率与单位换算进阶
The ratio of k to p is constant. If\( k=4 \) , then \( p=3 \) . What is the value of k when \( p=24 \)?
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 2.7 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
The total mass, in kilograms, of r identical objects is t. Which expression represents the total mass, in kilograms, of 112r of these objects?
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比・比例・速率与单位换算进阶
An object moves at a speed of \( \frac{3}{17} \) feet per second. What is this speed in yards per second? (3 feet = 1 yard)
原库参考解析
比・比例・速率与单位换算挑战
The ratio of the base to the height of a triangle is 1 to 8. The base of the triangle is 104 centimeters. What is the height, in centimeters, of the triangle?
原库参考解析
比・比例・速率与单位换算挑战
One gallon of sealant costs $23 and will cover 250 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
