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Proportion Calculator
Solve a/b = c/d for one missing term by cross multiplying, and compare unit prices to find the better buy.
a/b = c/d. Leave exactly one box blank.
Formula
a × d = b × c
Enter three numbers and leave one box blank. The blank is the term to solve for.
This proportion calculator solves a/b = c/d when you leave exactly one of the four terms blank. It writes the cross-multiplication step with your numbers, then gives the missing value as a whole number or a simplified fraction. Decimals and negative numbers are allowed, and a zero denominator is explained in words instead of an infinite result. A second mode divides price by quantity to show a unit price and, with two purchases, which one is the better buy.
How to solve a proportion
A proportion means two ratios are equal, written a/b = c/d. Leave exactly one box blank and fill in the other three. The page cross multiplies, a times d equals b times c, then divides to find the blank. In 2/3 = x/12, 2 times 12 equals 3 times x, so x = 8. If the value is not a whole number, it is reduced to lowest terms.
The other mode is a unit rate, the price of one unit. Divide the price by the quantity. At $3 for 12 oz the rate is $0.25 per ounce. Add a second purchase, such as $4 for 20 oz at $0.20 per ounce, and the lower rate is the better buy. A quantity must be greater than zero, because a unit rate cannot divide by zero.
Frequently Asked Questions
How do you solve a proportion?
Write the proportion as a/b = c/d and leave the unknown term blank. Cross multiply so that a times d equals b times c, then divide to isolate the blank. For 2/3 = x/12, 2 times 12 equals 3 times x, so x = 24/3 = 8.
What does cross multiply mean?
Cross multiply means multiply the numerator of each ratio by the denominator of the other ratio. In a/b = c/d, the products are a times d and b times c. The proportion is true when those products are equal, and that equation is what you solve for a missing term.
What is a unit rate?
A unit rate is a ratio with 1 as the quantity, such as dollars per 1 ounce. Divide the price by the quantity. $3 for 12 oz is 3 divided by 12, which is $0.25 per ounce, or 1/4 of a dollar per ounce.
How do you tell which is the better buy?
Compute the unit price of each purchase by dividing price by quantity. The lower price per unit is the better buy. $3 for 12 oz is $0.25 per ounce, and $4 for 20 oz is $0.20 per ounce, so $4 for 20 oz is the better buy.