**Conversion and Units of Measure: Yards, Meters, Miles, and Furlongs!**

3,000 yards. 2,800 meters. 1.5 miles. 9 furlongs.

On first glance, one may take the easy way out and assume that they’re all equal in length. Guess what… they’re not! We’ll walk you through a couple of word problems that work with conversion and these units of measure and show you some strategies you can apply to similar types of problems at school!

*Upper Elementary:*

Arrange 3,000 yards, 2,800 meters, 1.5 miles, and 9 furlongs in order from least to greatest. (Hint: Convert into feet!)

Answer:

At Mathnasium, we have what we refer to as the *Law of SAMEness*. The Law of SAMEness states that we can only compare things that have the same name. So in order to compare 3,000 yards and 2,800 meters, for instance, we have to give both amounts the same name, which is why we express both in terms of feet.

But why feet? Simple. Yards, meters, miles, and furlongs convert more or less seamlessly into feet.

Here’s a conversion chart to get you started:

1 yard = 3 feet

1 meter = 3.28 feet

1 mile = 5280 feet

1 furlong = 660 feet

So…

3,000 yards = 3,000 x 3 = 9,000 feet

2,800 meters = 2,800 x 3.28 = 9,184 feet

1.5 miles = 1.5 x 5,280 = 7,920 feet

9 furlongs = 9 x 660 = 5,940 feet

And in order from least to greatest: **5,940 feet, 7,920 feet, 9,000 feet, 9,184 feet** ... which is: **9 furlongs, 1.5 miles, 3,000 yards, 2800 meters.**

*Middle School: *

After arranging 3,000 yards, 2,800 meters, 1.5 miles, and 9 furlongs in order from least to greatest, tell how many times bigger each number is than its predecessor.

Answer:

When we want to know “how many times bigger” a number is compared to a smaller number, we want to find out how many of the smaller number fits in the bigger number.

So, we divide.

7,920 ÷ 5,940 = **1.333… times bigger **(1.333… “5,940s” fit in 7,920.)

9,000 ÷ 7,920 = **1.13636… times bigger **(1.13636… “7,920s” fit in 9,000.)

9,184 ÷ 9,000 = **1.02 times bigger **(1.02 “9,000s” fit into 9,184.)