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
The ratio of k to p is constant. If \( k=7 \), then \( p=6 \). What is the value of k when \( p=336 \)?
原库参考解析
比・比例・速率与单位换算进阶
A certain town has an area of 4.29 square miles. What is the area, in square yards, of this town? (1 mile = 1,760 yards)
原库参考解析
比・比例・速率与单位换算进阶
A length of 450 meters is equal to how many decimeters? (1 meter = 10 decimeters)
原库参考解析
比・比例・速率与单位换算进阶
For a certain rectangle, the ratio of the width to the length is 1 to 2. If the width of the rectangle is 67 centimeters, what is the length, in centimeters, of the rectangle?
原库参考解析
比・比例・速率与单位换算进阶
The ratio 72 to m is equivalent to the ratio 4 to 24. What is the value of m?
原库参考解析
比・比例・速率与单位换算挑战
A figure has an area of 3,744 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
An athlete swam a distance of 6,336 yards. How far did the athlete swim, in miles? (1 mile = 1,760 yards)
原库参考解析
比・比例・速率与单位换算挑战
Before liftoff, one of a space shuttle's solid rocket boosters contained 478,000 kilograms (kg) of propellant. Exactly 17 seconds after liftoff, 392,949 kg of this propellant remained. On average, approximately how much propellant, in kg, did this solid rocket booster burn each second after liftoff?
原库参考解析
比・比例・速率与单位换算进阶
The ratio a to b is equivalent to the ratio 49 to 26. What is the value of a when \( b=182 \)?
原库参考解析
比・比例・速率与单位换算基础
During an experiment, a particle's speed was 41 feet per second. What is this speed in feet per minute?
原库参考解析
比・比例・速率与单位换算挑战
The ratio x to y is equivalent to the ratio 4 to 7. If \( x=11t \) , what is the value of y in terms of t?
原库参考解析
比・比例・速率与单位换算进阶
A truck with a mass of 2,400 kilograms (kg) was first observed to travel 1,520 meters (m) in 60 seconds (s) at a constant speed. During a second observation an hour later, the same truck was observed to travel 1,170 m in 60 s at a constant speed in the same direction. What is the positive difference, in kg·m/s, between the truck's momentum during the first observation and the truck's momentum during the second observation?
原库参考解析
