Live a:b = c:d board that solves any missing term or checks four known values, with a cross-product twin, means/extremes peel, and scale ladder.
Educational proportion literacy only. Not a computer-algebra system or exam oracle. Confirm methods with your course when grades are on the line.
By Ahmet C. Toplutaş·Site owner & editor · Math tools
Last updated May 21, 2026 · Reviewed May 21, 2026 · Planning estimates only - not tax, medical, or investment advice
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A proportion says two ratios are equal: a : b = c : d. Cross-multiplication turns that into a × d = b × c. Know any three terms and the fourth is determined; know all four and you can check.
This page’s framing is a cross-product twin, with a means/extremes peel, a scale ladder, and solve vs check modes. It is not the percentage job switcher, not P vs C combinatorics, and not fraction simplify work.
Decision framing: “Which term is missing, and do both cross products agree once the board is closed?”
Educational proportion literacy only. Not a computer-algebra system or exam oracle. Confirm methods with your course when grades are on the line. See our disclaimers.
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In a:b = c:d, a and d are the extremes and b and c are the means. Their products match in a true proportion. The peel also shows a/b and c/d so ratio form stays visible beside the products.
Load Check equal. Both products are 36. Flip a number and watch the unequal narrative fire.
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Multiply a:b by 0.5, 1, 2, and 3. Equivalent ratios keep the same relationship. That ladder is the product beat: scaling both parts together preserves the proportion.
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Solve blanks one letter and computes it. Check asks whether four entered values already satisfy a×d = b×c. Use check for homework verification without overwriting a written guess.
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Cross-multiplication identities.
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After a proportion closes, hand off for ratio simplify, percent jobs, fractions, or the three-known rule-of-three shortcut.
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Scenario A: Recipe scale. 2:3 = 8:d → d = 12. Cross products both equal 24.
Flip solve-for to c with a=2, b=3, d=12. You should recover c = 8.
Scenario B: Map scale. 1:4 = c:20 → c = 5. Means/extremes products match.
Scenario C: Votes. 3:5 = 12:d → d = 20. Scale ladder shows 6:10 and 9:15 as equivalents of 3:5.
Scenario D: Check equal. 4:6 =? 6:9 is true (both products 36). Change 9 to 10 in check mode to see unequal.
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Stop here for four-term proportions. Hand off for ratio simplify, percent jobs, fractions, or rule-of-three story problems. Nonlinear relationships are not proportions.
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It solves a:b = c:d for any missing term using cross-multiplication, or checks whether four known values form a true proportion. A cross-product twin compares a×d with b×c, a means/extremes peel shows the same products by name, and a scale ladder lists equivalent left ratios.
If a/b = c/d, then a×d = b×c. Solving for one unknown rearranges that identity. The twin board prints both products so equality is visible, not just a single answer.
In a:b = c:d, a and d are the extremes and b and c are the means. In a true proportion the product of the extremes equals the product of the means.
It multiplies the closed left ratio a:b by 0.5, 1, 2, and 3 to show equivalent ratios. Scaling both parts the same way preserves the proportion.
Solve finds the missing letter. Check asks whether four entered values already satisfy a×d = b×c, which is useful for homework verification.
Percentage jobs are % of / what % / % change. Ratio tools often simplify a:b. Rule of three is a common three-known special case. This page is the full a:b = c:d board with cross-product literacy.
No. It is educational proportion literacy for homework and quick checks. Confirm methods with your course when grades are on the line.
LIVE a:b = c:d BOARD
Cross products →Scene preset
Mode
Solve for
a : b = c : d
CLOSED PROPORTION
2 : 3 = 8 : 12
Solved d = 12
CROSS-PRODUCT TWIN
a × d
24
b × c
24
MEANS / EXTREMES PEEL
SCALE LADDER · LEFT RATIO
Updates as you type. Share writes the URL; typing does not. True proportions keep a×d = b×c.
Solved d
12
2:3 = 8:12 · a×d 24 · b×c 24
Read the closed a:b = c:d line, then confirm both cross products. The scale ladder shows equivalent left ratios.
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