How does AskSia solve a proportion a/b = c/d?

AskSia uses cross-multiplication: multiply both sides by the product bd, which cancels the denominators on each side and gives ad = bc. The cross-multiplication step is shown explicitly with the cancellation, so you can see why it works, not just that it works. Once you have ad = bc, AskSia solves the resulting linear equation for the unknown variable, then checks the answer by substituting back into the original proportion and confirming both fractions are equal. The check appears at the end of every solve.

What is direct proportion and how does AskSia handle it?

Two quantities are directly proportional if they're related by y = kx, where k is the constant of variation. When y increases, x increases by the same factor; when y doubles, x doubles. AskSia finds k by using a given (x, y) pair: divide y by x. Once k is known, AskSia can find y for any new x, or x for any new y. Examples include earnings as a function of hours worked (k is the hourly rate) and the length of a spring as a function of force (Hooke's law).

What is inverse proportion and how is it different from direct?

Two quantities are inversely proportional if they're related by y = k/x (or equivalently xy = k). When x doubles, y halves; the product is constant. AskSia finds k by multiplying a given (x, y) pair, then uses y = k/x to find any missing value. The classic example is pressure and volume of a gas at constant temperature (Boyle's law), or speed and time for a fixed distance. AskSia distinguishes direct from inverse based on the word problem phrasing and confirms which case applies.

Can AskSia solve proportion word problems?

Yes. Word problems with explicit phrasing like 'y is directly proportional to x' or 'y varies inversely with x' are translated directly into y = kx or y = k/x. Word problems with implicit proportions (recipe scaling, currency conversion, map distances, similar figures) are also handled: AskSia identifies the two ratios that should be equal, sets up the proportion a/b = c/d, cross-multiplies, and interprets the numerical answer back in the original context.

How accurate is AskSia?

AskSia is engineered for accuracy on standard high school and college coursework. Accuracy comes from subject-specialized models, a symbolic verification pass that catches arithmetic errors, and a self-check step that re-derives the answer before showing it to you.

Can I get practice problems and flashcards?

Yes. After any solve, ask Sia to generate similar practice problems at SAT, ACT, AP, IB, or college difficulty, or build a flashcard set on the underlying concept in one tap. Useful for exam prep and spaced repetition before a quiz, midterm, or final.

How much does AskSia cost?

AskSia has a free plan that includes daily solves across all subjects. AskSia Pro and Super include unlimited solves, advanced subjects, the full AI tutor companion, exports, and priority response speed. See pricing for details.

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AskSia AI 求解器

比例求解器：交叉相乘、求解、检查

Name: AskSia Proportion Solver
Author: AskSia

使用交叉相乘逐步求解任何比例 a/b = c/d 中的未知数。AskSia 可处理直接、反向和联合变异，以及具有比例推理的应用题，并在每次求解时包含代入检查。

Works with word problems, equations, code, and science prompts.

∫ 3x² · sin(x) dx

SubjectsCalculusAlgebraPhysicsChemistryBiologyCSStatisticsEcon

4.9 / 5 · trusted by 2M+ students · 50M+ problems solved

asksia.ai/solver

98% · Verified

Problem

Find the area enclosed between y = x² and y = 2x in the first quadrant.

Find the points of intersection

Set the curves equal: x² = 2x → x(x - 2) = 0, so x = 0 and x = 2.

Identify which curve is on top

On (0, 2), 2x > x², so y = 2x is the upper curve.

Set up the area integral

A = ∫₀² (2x - x²) dx

Integrate term-by-term

A = [ x² - x³/3 ]₀²

Final Answer

A = 4/3 sq. units

快速解答

AskSia 比例求解器是什么？

AskSia 比例求解器是一款人工智能工具，可为未知变量求解任何比例 a/b = c/d。AskSia 进行交叉相乘 (ad = bc)，求解所得方程，并通过将答案代回原始比例进行检查。AskSia 还可处理直接比例 (y = kx)、反向比例 (y = k/x) 和联合变异 (y = kxz)，找到变异常数并用它来求解任何缺失值。具有比例推理的应用题会自动翻译。

98%

solution accuracy

50M+

problems solved

~1.5s

avg solve time

A+

study-ready explanations

为什么选择 AskSia 求解器

所有比例类型，正确交叉相乘。

大多数比例错误来自设置错误的交叉相乘。AskSia 首先正确设置，然后逐步展示代数运算。

清晰展示交叉相乘

对于 a/b = c/d，AskSia 将两边乘以 bd 得到 ad = bc。交叉相乘步骤会明确标出，以便您了解其工作原理（乘以 bd 可消去两个分母），而不仅仅是知道它有效。

交叉相乘

直接比例：y = kx

给定 y 与 x 直接成比例且有一个 (x, y) 对，AskSia 找到变异常数 k，然后使用 y = kx 来查找任何缺失值。适用于比例缩放问题和胡克定律类型的设置。

直接变异

反向比例：y = k/x

给定 y 与 x 成反比，AskSia 从已知对中找到 k 并使用 y = k/x 来查找缺失值。适用于两个量相乘得到常数的玻意耳定律类型问题。

反向变异

联合和复合变异

对于 y = kxz（联合）或 y = kx/z（复合），AskSia 从一个完整的数据行中找到 k 并将其应用于其他数据行。变异常数会被命名，并显示代入过程。

联合和复合

应用题翻译

具有“直接成比例”、“反向成比例”或隐含比例（食谱缩放、比例模型、地图距离）的应用题会自动翻译成正确的比例或变异方程。

应用题

最后进行代入检查

求解后，AskSia 将答案代回原始比例并验证两边是否匹配。检查可在您提交前发现算术错误。

代入验证

工作原理

三个步骤即可求解比例。

步骤 01

捕获比例

拍摄照片、粘贴或键入比例或应用题。AskSia 可识别 a/b = c/d 符号、分数线以及诸如“y 与 x 直接成比例”之类的表述。

Input mode

Snap a Photo

Textbook, handwriting, screenshot

Paste Text

Word problem or equation

Calculator

LaTeX-ready equation editor

步骤 02

观看 Sia 进行交叉相乘和求解

AskSia 进行交叉相乘 (ad = bc) 并求解所得方程以得到未知数。每个步骤都有名称，以便您可以在下一个问题中应用该方法。

Calculus · Step 4 of 4

1.4s

Set curves equal

x² = 2x → x = 0, x = 2

Set up the integral

A = ∫₀² (2x - x²) dx

Evaluate

A = [x² - x³/3]₀² = 4/3

步骤 03

查看检查

AskSia 将答案代回原始比例并确认两边相等。生成练习题或提出后续问题。

Auto-generated diagram

Region between y = 2x and y = x² — area = 4/3

Available On

Solve anywhere
you study.

Every solve syncs across Web, iOS, and Android — start it at your desk, finish on your phone.

Web App

Full study studio

Split-panel interface with the worked solution on the left, the auto-generated diagram and AI tutor chat on the right.

Drag & drop image upload + LaTeX equation editor

Auto-generated diagrams render alongside steps

Side-panel AI tutor chat for hints and alt methods

Export to PDF, DOCX, Notion, or Google Docs

app.asksia.ai/solver

Hi! What are we studying today?

Ask about your homework, lecture, or readings...↑

Calculus

98% verified

1.4s

Step 4 of 4 · Evaluate

A = [x² - x³/3]₀² = 4/3

Mobile App

Snap & solve, anywhere

Open the camera, frame the problem, and the worked solution plus diagram appear in seconds.

One-tap snap-and-solve on iOS and Android

Pinch-to-zoom diagrams, swipe between steps

Auto-sync solves with your Web library

Offline review of saved solutions and flashcards

☰

AskSia

What can I do for you?

✦

Homework solver

✦

Live transcribe

✦

File summary

✦

Snap

✦

YouTube

✦

Flashcard

Calc

98%

1.4s

Area between y=2x & y=x²

A = 4/3 sq. units ✓

用例

所有比例用例。

📐

中学比例

首次遇到的比例问题，包含小的整数值。AskSia 使用与中学课本相符的语言解释交叉相乘，并明确显示检查过程。

中学

⚛️

代数 1 和 2 变异问题

直接和反向变异问题，通过给定的 (x, y) 对找到常数 k。然后 AskSia 使用该方程来查找任何缺失值。

代数 1 和 2

🧪

比例应用题

食谱缩放、地图距离、货币换算、相似三角形和单位换算。AskSia 可识别文本中的比例并设置交叉相乘。

应用题

🧬

联合和复合变异

y 依赖于两个或多个变量的问题 (y = kxz, y = kx²/z)。AskSia 处理多变量情况并从完整的数据点中找到 k。

联合变异

💻

SAT、ACT、GRE 比例

比例问题是 SAT、ACT 和 GRE 的常客。在任何求解后，都可以生成适合目标考试难度的练习题。

SAT、ACT、GRE

🎯

比例缩放和相似图形

相似三角形、比例模型和地图问题都归结为比例。AskSia 一起处理几何设置和代数运算。

相似图形

Compare

AskSia vs. ChatGPT,
Photomath & Symbolab.

General chatbots hallucinate. Photo solvers stop at math. AskSia is built for actual coursework with verified accuracy, visual learning, and every subject.

Feature comparison between AskSia Solver and alternatives
Feature	AskSia Solver	ChatGPT	Photo Solvers
Solution accuracy	✓ 98%	~70-85%, hallucinations	~90%, math only
Auto-generated diagrams	✓ Every solve	Inconsistent / broken	Graphs only, math-only
Step-by-step explanations	✓ Numbered + plain English	Inconsistent depth	✓ Math steps
Subject coverage	✓ Math, Physics, Chem, Bio, CS, Econ	✓ Wide but unverified	Math only
Photo input	✓ Handwriting + diagrams + code	Photos OK, weak on handwriting	✓ Math photos only
Answer verification	✓ Self-checked before display	No verification	Math engine only
Tutor follow-ups	✓ Hints, alt methods, ELI5	✓ General chat	Not available
Practice and flashcards	✓ One-tap from any solve	Manual prompting	Not available
Code debugging	✓ Python, Java, C++, SQL...	✓ Yes	Not available
Free to start	✓ Daily solves, no card	Limited model access	Steps locked behind paywall

常见问题解答

常见问题。

AskSia 如何求解比例 a/b = c/d？

AskSia 使用交叉相乘：将两边乘以乘积 bd，这会消去两边的分母并得到 ad = bc。交叉相乘步骤会明确显示消去过程，以便您了解其工作原理，而不仅仅是知道它有效。一旦得到 ad = bc，AskSia 会求解所得的线性方程以得到未知变量，然后通过将答案代回原始比例并确认两个分数相等来检查答案。检查会出现在每次求解的末尾。

什么是直接比例以及 AskSia 如何处理它？

如果两个量之间的关系是 y = kx，其中 k 是变异常数，则这两个量是直接成比例的。当 y 增加时，x 增加相同的倍数；当 y 加倍时，x 也加倍。AskSia 通过使用给定的 (x, y) 对来找到 k：将 y 除以 x。一旦知道 k，AskSia 就可以为任何新的 x 找到 y，或为任何新的 y 找到 x。例如，收入与工作小时数的关系（k 是每小时费率）以及弹簧长度与力的关系（胡克定律）。

什么是反向比例以及它与直接比例有何不同？

如果两个量之间的关系是 y = k/x（或等效地 xy = k），则这两个量是反向成比例的。当 x 加倍时，y 减半；乘积是恒定的。AskSia 通过将给定的 (x, y) 对相乘来找到 k，然后使用 y = k/x 来查找任何缺失值。经典示例是在恒定温度下气体的压力和体积（玻意耳定律），或固定距离的速度和时间。AskSia 根据应用题的措辞区分直接比例和反向比例，并确认适用的情况。

AskSia 能解决比例应用题吗？

是的。具有明确表述的应用题，如“y 直接与 x 成比例”或“y 与 x 成反比”，会直接翻译成 y = kx 或 y = k/x。具有隐含比例的应用题（食谱缩放、货币换算、地图距离、相似图形）也能处理：AskSia 识别应相等的两个比率，设置比例 a/b = c/d，进行交叉相乘，并将数值答案解释回原始上下文。

AskSia 的准确性如何？

AskSia 旨在在标准高中和大学课程中实现准确性。准确性来自于专业化的模型、能够捕获算术错误的符号验证过程以及在显示答案之前重新推导答案的自我检查步骤。

我可以获得练习题和抽认卡吗？

是的。在任何求解后，都可以要求 Sia 生成类似练习题，难度级别为 SAT、ACT、AP、IB 或大学水平，或一键构建关于基本概念的抽认卡集。在测验、期中或期末考试前进行考试准备和间隔重复非常有用。

AskSia 的费用是多少？

AskSia 提供免费套餐，包括所有科目的每日求解次数。AskSia Pro 和 Super 套餐包括无限次求解、高级科目、完整的 AI 辅导伴侣、导出和优先响应速度。有关详细信息，请参阅定价。

立即开始

任何比例。求解、检查、解释。

加入 200 万+ 使用 AskSia 的学生，通过交叉相乘、清晰找到变异常数以及每次求解都进行代入检查来解决比例和变异问题。

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