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・速率与单位换算挑战
For a certain rectangular region, the ratio of its length to its width is 10 to 4.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・速率与单位换算进阶
For each of two rectangles, the ratio of the rectangle's length to its width is 10 to 5. The width of rectangle X is 16.5 times the width of rectangle Y. How does the length of rectangle x compare to the length of rectangle Y?
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 20 to 8. If the width of the rectangular region increases by 9 units, how must the length change to maintain this ratio?
原库参考解析
比・比例・速率与单位换算挑战
An object's average acceleration, in meters per second squared, is the change in the object's speed, in meters per second, divided by the time during which the change occurred, in seconds. A certain object's speed changes by 45 meters per second in 6 seconds. What is this object's average acceleration, in meters per second squared, during this time period?
原库参考解析
比・比例・速率与单位换算挑战
There is a proportional relationship between p and t. If p = 2,340 when t= 3,120, then what is the value of p when t = 2,496?
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 4. 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・速率与单位换算进阶
A sphere has a volume of 247.00 cubic yards. What is the volume of the sphere, in cubic meters? (Use 1 yard = 0.914 meter.)
原库参考解析
比・比例・速率与单位换算进阶
The ratio of the side length of square A to the side length of square B is 3 to 6. Square A has a side length of 23 inches. What is the side length, in inches, of square B?
原库参考解析
比・比例・速率与单位换算挑战
One gallon of paint will cover 310 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
How many centimeters are equivalent to 35 meters? (1 meter = 100 centimeters)
原库参考解析
比・比例・速率与单位换算进阶
A certain hybrid car uses 39 gallons of gasoline to travel 1,950 miles. At this rate, how many kilometers does the car travel using 39 gallons of gasoline? (Use 1 mile = 1.6 kilometers.)
原库参考解析
比・比例・速率与单位换算挑战
The bone mineral density of a certain person's thoracic spine was estimated to be 0.812 grams per square centimeter. What is this estimated bone mineral density in grams per square millimeter? (1 centimeter = 10 millimeters)
原库参考解析
