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
In a box of pens, the ratio of black pens to red pens is 8 to 1. There are 40 black pens in the box. How many red pens are in the box?
原库参考解析
比・比例・速率与单位换算基础
The population density of Worthington is 290 people per square mile. Worthington has a population of 92,800 people. What is the area, in square miles, of Worthington?
原库参考解析
比・比例・速率与单位换算基础
For the values j and k, the ratio of j to k is 11 to 12. If j is multiplied by 17, what is k multiplied by in order to maintain the same ratio?
原库参考解析
比・比例・速率与单位换算基础
How many feet are equivalent to 34 yards? (1 yard = 3 feet)
原库参考解析
比・比例・速率与单位换算挑战
A triathlon is a multisport race consisting of three different legs. A triathlon participant completed the cycling leg with an average speed of 19.700 miles per hour. What was the average speed, in yards per hour, of the participant during the cycling leg? (1 mile = 1,760 yards)
原库参考解析
比・比例・速率与单位换算进阶
The ratio 140 to m is equivalent to the ratio 4 to 28. What is the value of m?
原库参考解析
比・比例・速率与单位换算基础
A participant in a bicycle race completes the race with an average speed of 24,816 yards per hour. What is this average speed, in miles per hour? 1 mile=1,760 yards
原库参考解析
比・比例・速率与单位换算基础
A product costs 11.00 dollars per pound. What is the cost, in dollars, for 6 pounds of the product?
原库参考解析
比・比例・速率与单位换算挑战
An object travels at a constant speed of 6 centimeters per second. At this speed, what is the time, in seconds, that it would take for the object to travel 24 centimeters?
原库参考解析
比・比例・速率与单位换算挑战
An insect moves at a speed of \( \frac{3}{20} \) feet per second. What is this speed, in yards per second? 3 feet = 1 yard
原库参考解析
比・比例・速率与单位换算进阶
The ratio x to y is equivalent to the ratio 12 to t. When x =156, 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 cherry pitting machine pits 12 pounds of cherries in 3 minutes. At this rate, how many minutes does it take the machine to pit 96 pounds of cherries?
原库参考解析
