Missing term aa = (b × c) / d
Four terms. One unknown. Cross-multiplication, shown
Proportion Calculator
Use this proportion calculator to find one missing value in a / b = c / d. Enter three values and leave one blank.
Enter three known values. Leave one blank. See the answer, steps, and check.
- Any missing position
- Exact fractions
- Decimal result
- Cross-multiplication steps
- Verification check
02Start here
How to Use the Proportion Calculator
- Enter three known values in the four fields arranged as
a / b = c / d. - Leave the value you want to find blank. The missing term may be
a,b,c, ord. - Select Calculate to see the completed equation, exact result, decimal approximation, and calculation steps.
- Read the verification line. Equal cross products confirm that the solved value makes the proportion true.
The result panel completes the proportion and keeps the exact value, decimal approximation, cross-multiplication work, and verification check together in one place.
Use Clear to start over. For a problem with units, enter only the numeric values, keep corresponding quantities in the same positions, and add the correct unit back to the answer. Correct setup is as important as correct arithmetic.
03The idea
What Is a Proportion?
A proportion is an equation stating that two ratios have the same value. Its standard four-term form is:
a / b = c / d
A ratio compares two quantities; a proportion sets two ratios equal. For
example, 2 / 3 = 8 / 12 is a proportion because both fractions represent the
same value. Proportions let a relationship remain constant while the quantities
become larger or smaller.
In a / b = c / d, a and d are the extremes, while b and c are the
means. Three known terms normally determine the fourth. Zero denominators and
some zero-value combinations are undefined, impossible, or do not determine one
unique answer.
a
/
b
=
c
/
d
Extremes: a and d
Means: b and c
04Core formula
Proportion Formula and Cross Multiplication
Start with the proportion formula:
a / b = c / d
For nonzero denominators, multiplying both sides by b × d removes the
denominators and gives the cross-product rule:
The terms sit diagonally across the equal sign. Equal ratios have equal cross
products, so the rule can solve a missing value or check a completed proportion.
x into a particular box.05Worked method
How to Solve Proportions for Any Missing Value
To solve a proportion by hand, first write both ratios in the same order. Cross multiply, simplify the resulting equation, and divide by the coefficient beside the unknown. Finally, substitute the answer into the original proportion.
For 5 / 8 = x / 24, cross multiplication gives:
5 × 24 = 8 × x120 = 8xx = 120 / 8x = 15
5 / 8 = x / 24
Cross multiply
5 × 24 = 8x
Solve
x = 15
Verified
5 × 24 = 8 × 15 = 120
Checking gives 5 × 24 = 8 × 15 = 120, so the solved value is correct.
Exactly the same method works when the unknown is the first numerator, either
denominator, or the second numerator. Only the final division changes.
If the unknown is a denominator, its solved value cannot be zero. The calculator checks the completed equation instead of returning a value that would make the original ratio undefined.
06Exact values
Solve Proportions with Fractions and Mixed Numbers
Known terms do not have to be whole numbers. The solver can work with signed
values, terminating decimals, fractions such as 3/4, and mixed numbers such as
2 1/3. A mixed number is converted to an improper fraction before the
cross-product calculation; for example, 2 1/3 becomes 7/3.
1 1/2
Convert
3/2
Cross multiply
(3/2) × 8 = 3x
Exact result
x = 4
Keeping fractional values exact avoids unnecessary rounding. This matters when an answer repeats as a decimal or when the result will be used in another calculation. When an exact rational result is available, the calculator reduces it to lowest terms and displays it beside a decimal approximation. The decimal is for convenient reading; the simplified fraction remains the exact result.
For a negative mixed number, put the sign before the whole number, as in
-1 1/2; the sign applies to the entire value.
For a complex fraction, use parentheses to separate each fractional part, for
example (1/2)/(3/4). Forms such as 1/(3/4) and
(1 1/2)/(3/4) are also accepted; an ungrouped chain such as 1/2/3/4 is
rejected because its intended grouping is unclear.
07Worked examples
Proportion Calculator Examples
Solving a Proportion with Whole Numbers
Suppose 3 / 5 = 12 / x. Cross multiplication gives 3x = 5 × 12 = 60.
Dividing by 3 gives x = 20. The completed proportion is
3 / 5 = 12 / 20, and both cross products equal 60.
The missing value may remain in its original denominator position; it does not need to be moved before calculation.
Solve for x with Decimals and Negative Numbers
Solve x / 2.5 = -3 / 7.5. Cross multiplication gives
7.5x = 2.5 × -3 = -7.5. Dividing by 7.5 produces x = -1.
Substitution gives -1 / 2.5 = -3 / 7.5; both ratios equal -0.4, and both
cross products equal -7.5.
Enter the negative sign directly with the value. A finite written decimal can be kept exact during the calculation.
Fraction and Mixed-Number Proportion Example
Solve (1 1/2) / 3 = x / 8. First convert 1 1/2 to 3/2. Cross
multiplication then gives (3/2) × 8 = 3x, so 12 = 3x and x = 4.
The completed proportion is (3/2) / 3 = 4 / 8; each side equals 1/2.
Exact fraction arithmetic makes the steps auditable and prevents early rounding.
08Input guide
Supported Proportion Calculator Inputs and Results
Enter exactly three known terms and leave exactly one field blank. Supported values include the formats shown below. Accepted syntax appears beside the fields.
A result includes the missing term, exact value, decimal approximation, completed proportion, calculation steps, and cross-product check. Decimal formatting does not change the exact value used for verification.
Invalid text, the wrong number of known values, a zero denominator, or a case without one unique finite solution produces a specific error.
09Watch for
Common Proportion-Solving Mistakes
Wrong: multiply side by side
a × b = c × d
Correct: multiply diagonally
a × d = b × c
Three known terms are needed to determine one unknown.
Neither completed denominator may be zero.
Cross products are diagonal:
a × d and b × c.Corresponding units must occupy matching positions.
2 1/3 is the single value 7/3.Retain the exact fraction until the final decimal display.
Substitute the answer and compare both cross products.
10In practice
Real-World Uses for Proportions
Proportions appear whenever equivalent rates must stay in the same relationship.
Recipes compare ingredients with servings, maps compare drawn and actual
distance, and similar figures compare corresponding side lengths.
Unit conversions, price comparisons, constant-rate travel, and material mixtures
use the same equation: match the quantity order, enter three values, and solve
the missing term.
Use a specialized calculator when the task also needs conversions, several
linked ratios, percentage rules, statistical assumptions, or size presets.
11Questions
Proportion Calculator FAQ
Can the Unknown Be in Any Position?
Yes. Leave any one numerator or denominator empty. The calculator detects its position and uses the matching cross-product formula.
Can I Enter Fractions and Mixed Numbers?
Yes. Use a slash for 5/8 and a space in a mixed number such as 2 1/3.
Exact input is useful when the decimal repeats.
Can a Proportion Contain Decimals or Negative Numbers?
Yes. Decimals and signed values use the same rule as positive integers. Put the negative sign on the intended term and keep denominators nonzero.
Why Can a Denominator Not Be Zero?
Division by zero is undefined, so a valid proportion cannot have a zero denominator. Both denominator positions are checked after solving.
Why Are Both an Exact Fraction and a Decimal Shown?
The fraction preserves the exact result; the decimal is a convenient display that may be shortened. Use the fraction for further exact work.
How Can I Check That the Proportion Answer Is Correct?
Substitute the answer, then compare a × d with b × c. Equal cross
products and nonzero denominators confirm the completed proportion.
12Method note
Proportion Calculation Method and Accuracy
The calculator uses the algebraic cross-product identity. Fraction inputs are normalized, exact results are reduced, and decimals are formatted only after verification.
The method follows the standard definition and cross-product property described in OpenStax Prealgebra 2e, section 6.5. The verification recalculates both cross products. A meaningful result still depends on matching quantity order and units.