# Two Simple Rules for Conquering Conversion Problems

*This tip for improving your GMAT score was provided by David Newland at Veritas Prep.*

One of the easiest tools the GMAT has to convert an easy problem into a more challenging one involves making you do a conversion of units. While the process of multiplying or dividing may come natural to you, the process of deciding what to do in which cases is often a challenge: when feet are converted to miles and hours to minutes it is difficult to know what to multiply and what to divide. Two simple rules will help to keep everything straight.

Rule 1

When going from larger units to smaller units simply multiply on the same side of the fraction line.

For example, if you have the current rate of 10 miles per hour and you wanted to state this is terms of feet per minute then you would multiply the numerator by 5280 (the number of feet in a mile ) and multiply the denominator by 60 (the number of minutes in an hour).

10 miles/1 hour = 10 * 5280 feet/ 1 * 60 minutes = 52,800 feet/60 minutes, or 880 feet/minute.

The reason that we multiplied each number on the same side of the fraction line is because we INCREASED each of the units. There are more feet than miles so the numerator should certainly be larger. You would expect to go farther in terms of feet than in terms of miles! This is why you want to multiply when going from miles to feet.

And when you convert from an hour to a minute you would expect to go a SHORTER distance and therefore you would have a larger denominator to divide the numerator by. There are more minutes than hours so you want to multiply the denominator when going from hours to minutes or from minutes to seconds.

Rule 2

But what about converting from smaller to larger units? What do you do then? This is where people are more likely to get confused, but the rule is simple. It is just the reverse of the first rule.

When going from smaller units to larger units just cross the fraction line and then multiply.

Let’s start with the result of the above equation and apply rule 2. If everything works correctly we should be back to 10 miles per hour when finished.

At a rate of 880 feet/ minute how many miles can a car travel in one hour?

Let’s do this in two stages. We will go from feet to miles and then from minutes to hours.

When converting from feet to miles it is clear that we should have many fewer miles than feet. So we want to divide by 5280. This is accomplished by crossing the fraction line and multiplying the denominator by 5280. So our rate now becomes: 880/5280 = miles per minute.

Rather than do the division go ahead and convert from minutes to hours and then simplify the fraction all at once, taking advantage of a common theme on the GMAT: the GMAT rewards you for factoring out numerators and denominators. When converting from minutes to miles, clearly the car should drive much further, so you want to increase the numerator of the fraction. Rule 2, tells us that when we are going from a smaller unit (minutes) to a larger one (hours) that we simply cross the fraction line and multiply. So you can multiply the numerator by 60.

The converted rate is now ready to be simplified. 880 * 60/5280 = miles per hour becomes 52,800 / 5280 which equals 10 miles/ hour.

The final step is the one that is most difficult for many test takers. It is easier to understand that dividing the numerator means to multiply the denominator, so that going from feet to miles requires that you divide by 5280…10,560 feet = two miles.

However, knowing how to divide the denominator is more conceptually challenging. That is where rule 2 helps. In order to move from a smaller unit in the denominator (such as minutes) to a larger unit (such as hours) you need to multiply the numerator. Multiplying the numerator is effectively dividing the denominator. So that if a bug can crawl 2 feet in a minute it can crawl 2*60 feet in an hour.

That is why it works, but on test day you do not need to worry about that. Simply apply these two rules and you will easily keep track of conversion problems!

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