Conversions
Proportions are commonly used to complete conversions from one unit to another, like in measurements. Here are some common relationships that are used in conversions.
- 12 inches = 1 foot
- 3 feet = 1 yard
- 16 ounces = 1 pound
- 5280 feet = 1 mile
Metric Conversions
Metric conversions are a little easier to make, because they are all made off of a base unit. If a larger or smaller unit is more appropriate for the measurements, a prefix is added to the base unit to create a larger or smaller equivalent.
To covert between metric units, look at the table to recognize the prefix on the starting unit and find the prefix for the target unit. Note the number of places and direction you move from the starting unit to the target unit. Then, move the decimal the same number of places in the same direction.
Example #2
Simplify the ratios.
Solution: In order to simplify the ratio, both numbers must be in the same unit. Which relationship can we use to simplify the ratio?
- 12 inches = 1 foot
- 3 feet = 1 yard
- 16 ounces = 1 pound
- 5280 feet = 1 mile
Answer: 12 inches = 1 foot ; The ratio has units of feet and inches, so 12 inches = 1 foot is correct.
That's correct! We have feet and inches in our ratio, so that's the relationship we can use.
If 12 inches = 1 foot, how many inches = 3 feet?
___ inches = 3 feet
Answer: 36
Yes! 36 inches = 3 feet. Now we can substitute 36 inches into the ratio to solve.
Answer: 36
Great! To finish and simplify, find a common factor to reduce the numerator and denominator.
Answer: 1, 4
Your Turn #3
Solution: Let's start by identifying the numerator and denominator units.
Numerator: ___
Answer: kilo
Denominator: ___
Answer: centi
Great! You can convert either unit to the other to solve this problem, but it will be easier to change the kilometers to centimeters? Why? If you change smaller units to larger units, you sometimes end up with decimals. This will not affect your answer, but if you don't like working with decimals, always change larger units to smaller ones.
To change kilo to centi on the scale below, move ___ spaces to the ___.
Answer: 5, right
That's correct! You'll need to move the decimal place on 2km five spaces to the right.
Enter the appropriate number in so we can continue.
Answer: 200,000
Great! Now, all we need to do is reduce the fraction.
Answer: 2,000 , 1
