Exchange Rate Converter

Pre-Algebra · Axiom Academy

LESSON Exchange Rates as Ratios An exchange rate is just a ratio — set up a proportion and multiply to convert one currency into another, and use the reciprocal to convert back. 1. An Exchange Rate Is a Ratio The rate says: for every 1 dollar you trade in, you receive 0.9 euros . Written as a ratio it's 1 : 0.9 — a fixed comparison between the two currencies. Watch one dollar coin trade for nine-tenths of a euro, over and over, at the same steady rate. The rate, written as a ratio of USD to EUR Same ratio, written as a unit rate (euros per dollar) 2. Convert by Setting Up a Proportion How many euros is 80 ? Set the unknown amount x in the same ratio as the rate: euros-to-dollars must match on both sides. Watch the dollar bar grow to 80 and the proportion fill in as the euro bar rises with it. Cross-multiplying, , so the " " disappears and converting comes down to a single multiplication: The shortcut: just multiply by the rate Because the dollar side of the ratio is 1 , every conversion collapses to . Below, the same rate scales to any amount — that constant multiplier is the proportion at work. 3. Convert Back Using the Reciprocal Coming home with euros? Now you're going the other way. Multiplying by 0.9 turned dollars into euros, so to undo it you divide by 0.9 — and dividing by 0.9 is the same as multiplying by its reciprocal , . Watch the euro bar feed back through the reverse arrow and land on the original dollars.

This is the written version of the interactive lesson above. See the full Pre-Algebra course.