Diagonal product setup.
AskSia writes a*d on one side and b*c on the other, with the diagonals colored and labeled so the move is unmistakable.
Visual
AI Solver by AskSia
Cross Multiplication Solver: solve and verify
Type any proportion or photograph it. AskSia multiplies diagonals to get ad = bc, solves the resulting equation for the unknown (linear, quadratic, or whatever it produces), substitutes back into the original to verify, and flags any extraneous solutions caused by zero denominators in the original.
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.
1
Find the points of intersection
Set the curves equal: x² = 2x → x(x - 2) = 0, so x = 0 and x = 2.
2
Identify which curve is on top
On (0, 2), 2x > x², so y = 2x is the upper curve.
3
Set up the area integral
A = ∫₀² (2x - x²) dx
4
Integrate term-by-term
A = [ x² - x³/3 ]₀²
Final Answer
A = 4/3 sq. units
Quick Answer
What is cross multiplication?
Cross multiplication is the technique for solving proportions of the form a/b = c/d. It says that two fractions are equal if and only if the product of the first numerator and the second denominator equals the product of the first denominator and the second numerator: a*d = b*c. This converts a fraction equation into a polynomial equation, which is usually easier to solve. After solving, you substitute back to check, since cross-multiplication can introduce extraneous roots when denominators contain variables.
98%
solution accuracy
50M+
problems solved
~1.5s
avg solve time
A+
study-ready explanations
Why AskSia Solver
Why students use AskSia for cross-multiplication.
Set up the diagonal product, solve, and substitute back to check.
Resulting equation solved.
Whatever the cross-product produces (linear, quadratic, polynomial), AskSia solves it with every step shown.
Step-by-step
Substitution verification.
Final answer is plugged into the original proportion. Both sides are simplified and compared.
Verified
Extraneous roots flagged.
If a candidate solution makes any original denominator zero, AskSia rejects it and reports the rejection.
Careful
Algebraic proportions.
Variables can appear in any position: numerator, denominator, both. AskSia handles them all with the same method.
Algebraic
Word problems.
Scale, similarity, rate, and unit conversion problems often reduce to proportions. AskSia parses and sets up the cross-multiply.
Applications
How It Works
Solve a proportion in three steps.
Step 01
Enter the proportion.
Type a/b = c/d, paste from homework, photograph a worksheet, or speak it. AskSia identifies numerators, denominators, and the unknown.
Input mode
Snap a Photo
Textbook, handwriting, screenshot
Paste Text
Word problem or equation
Calculator
LaTeX-ready equation editor
Step 02
Cross-multiply.
AskSia computes a*d and b*c, sets them equal, and writes the resulting equation.
1
Set curves equal
x² = 2x → x = 0, x = 2
2
Set up the integral
A = ∫₀² (2x - x²) dx
3
Evaluate
A = [x² - x³/3]₀² = 4/3
Step 03
Solve and verify.
The equation is solved with full steps. The solution is substituted back into the original proportion and confirmed.
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
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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
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Calc
98%
1.4s
Area between y=2x & y=x²
A = 4/3 sq. units ✓
Use Cases
Where cross-multiplication shows up.
Scale problems.
Map scale, model-to-real-size, blueprint conversions. AskSia sets up the proportion and solves for the unknown dimension.
Scale
Similar triangles.
Corresponding sides are proportional. Given three sides and the unknown fourth, cross-multiply.
Geometry
Unit conversion.
Convert miles to kilometers, ounces to grams, dollars to euros using known conversion ratios.
Units
Percent problems.
Part/whole = percent/100 is a proportion. Cross-multiply to find the unknown part, whole, or percent.
Percent
Rate problems.
Constant rate problems (cost per item, distance per time) reduce to proportions when you know one rate and need a corresponding quantity.
Rate
Algebraic equations.
x/(x+1) = 3/4, (x+2)/5 = (x-1)/2, and similar. Cross-multiply to clear fractions, then solve.
Algebra
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 | 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 |
FAQ
Frequently asked questions.
Why does cross multiplication work?
Multiplying both sides of a/b = c/d by b*d clears the fractions: (a/b)*(b*d) = a*d and (c/d)*(b*d) = b*c, giving a*d = b*c. So cross-multiplication is just multiplying both sides by the product of the denominators, dressed up with a visual diagonal pattern. AskSia shows the underlying algebra alongside the diagonal move.
When can cross multiplication produce extraneous solutions?
When variables appear in denominators of the original proportion. After cross-multiplying, the resulting polynomial equation may have solutions that make an original denominator zero. Those solutions are not valid because the original proportion was undefined there. AskSia checks every candidate solution against the original denominators and rejects any that produce zero.
Can I cross-multiply if there are additions in the numerator or denominator?
Yes. As long as the proportion is in the form (numerator-expression)/(denominator-expression) = (numerator-expression)/(denominator-expression), cross-multiplication multiplies the entire numerator of one side by the entire denominator of the other side. AskSia treats each numerator and denominator as a single expression and applies cross-multiplication exactly once.
What if both sides have addition outside the fractions?
Cross-multiplication does not apply directly. The expression must first be rearranged so that a single fraction equals another single fraction. AskSia detects when an equation is not in cross-multiplication-ready form and combines terms (using common denominators) until it is. Then cross-multiplication proceeds normally.
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.
Start Today
Set up the diagonal. Solve. Substitute back.
Join 2M+ students using AskSia to solve proportions by cross-multiplication step-by-step. Algebraic or numerical, with extraneous-root detection and substitution check on every solve.
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