Turn a Ratio into a Proportion and Find a Missing Value

Write two ratios that compare corresponding quantities

A ratio compares two amounts; a proportion states that two ratios are equal. For example, 3:5 = 12:20 because both pairs have the same relative size. If the final value is unknown, write 3:5 = 12:X. The first entries correspond to one kind of quantity and the second entries to another. Multiplying only one side of a pair by four would break the relationship; both entries must scale together when constructing an equivalent ratio.

Solve the missing fourth term

From A/B = C/X, cross multiplication gives AX = BC when the denominators are nonzero. With A nonzero, X = BC/A. For 3:5 = 12:X, calculate X = 5×12/3 = 20. In the calculator, enter A = 3, B = 5 and C = 12. Check the answer by comparing 3/5 and 12/20, both 0.6, or by confirming the cross-products 3×20 and 5×12 are both 60.

Rearrange a missing first term before using the form

Suppose X:7 = 15:21. Dividing the right-hand pair by three shows X = 5. To use a form that always solves the fourth position, invert both ratios and swap their sides: 21:15 = 7:X. Enter A = 21, B = 15 and C = 7 to obtain X = 5. Reordering only one pair changes the equation. Write the transformed proportion on paper first so each supplied number still corresponds to its original role.

Check a rate example with the units attached

If three identical items cost 7.50 under a constant unit price, twelve items cost X. Write 3 items : 7.50 currency units = 12 items : X currency units. The answer is 30. An alternative calculation finds the unit price 7.50/3 = 2.50 and multiplies it by twelve. Agreement between the unit-rate and proportion methods checks the placement of the numbers. Bulk discounts or fixed transaction charges would require a different pricing model.

Recognize an inverse relationship

At a fixed journey distance, doubling speed halves travel time; speed and time are inversely proportional in that model. For 120 kilometres, 40 kilometres per hour takes three hours, while 60 takes two. Writing 40:3 = 60:X as a direct proportion would wrongly give 4.5 hours. The correct relationship is speed×time = constant, so 40×3 = 60×X and X = 2. Establish whether the product or the quotient is constant before entering a proportional equation. Inverse proportionality can be verified by checking the constant products for both pairs.

Keep units and the comparison order visible

A ratio compares the first named quantity with the second. The ratio of length to width differs from width to length, even though both describe the same rectangle. For quantities of the same kind, convert to matching units before simplifying: 1 metre to 25 centimetres is 100:25 = 4:1. For different kinds, the units form part of the rate, such as kilometres per hour or dollars per kilogram. Removing those labels can make a correct numerical quotient answer a different question. Write the two named quantities in the same order beside every corresponding ratio.

Check whether constant proportionality is justified

A proportional model assumes a constant multiplier between the quantities over the range being considered. Fixed fees, minimum charges, thresholds, waste and changing rates can violate that assumption. If one ticket costs 8 units plus a fixed booking fee of 3, a one-ticket total of 11 does not imply that four tickets cost 44; the stated fee rule gives 35 if the fee is charged once. The calculator solves the proportional equation entered, but cannot decide whether the real situation follows it. Confirm the relationship from the problem statement or the relevant pricing or measurement rule first.

Related guides

Calculate a Proportion with Cross-Product Checks

Solve A:B = C:X step by step, use consistent units, rearrange unknown positions, and check zero and rounding cases before interpreting the result.

Find Ratios: Counts, Measurements and Shared Totals

Simplify ratios from counts and measurements, distinguish part-to-part from part-to-whole, and divide a total into proportional shares.

Ratio Formulas: Simplification, Scaling and Shares

Use greatest common divisors, scale factors and part-to-total formulas to simplify ratios and recover quantities from a stated relationship.