proportion

A proportion is a statement that two ratios are equal, such as 3 pens / $4.50 = 7 pens / x dollars. To solve one, write the two ratios so that like units sit opposite each other — items over items, money over money — and then cross-multiply: multiply the two knowns diagonally and divide by the remaining number. Here 4.50 × 7 ÷ 3 = $10.50. The same answer comes from finding the unit rate first: $4.50 ÷ 3 = $1.50 per pen, then × 7 = $10.50. The error that costs points is writing the ratios upside-down, so that like units no longer face each other; the arithmetic still produces a number, and it is the wrong one. Checking that the units cancel, and that one pen is cheaper than seven, catches it. A proportion is the general form of three common questions: scaling a recipe, a map scale, and a unit conversion.