Let’s Go the Distance
If you reviewed the previous page for standard capacity conversions, then you are smooth sailing for the rest of this section. Capacity, length, time, and weight standard conversions are all worked the same way.
Addition
Stack your problem. Work your like units. Upgrade the smaller unit to the larger one if necessary.
You have 3 feet 9 inches of plaid fabric and 2 feet 5 inches of tartan fabric. What is the total inches of fabric you have?
Subtraction
Set up the problem like you would an addition problem. “Downgrade” the larger unit to the smaller is necessary. See the subtraction problem on the standard capacity page for an example of “downgrading” a unit.
Let’s subtract the above example. Instead of adding 3 feet 9 inches and 2 feet 5 inches, we will subtract. Since 9 is larger than 5, there is no need to downgrade a foot first so we can just simply subtract like units.
Multiplication
On the previous page, we multiplied the standard unit conversion problem by converting all of the larger unit to the smaller one first. You can also multiply each like unit, then convert back to the original form, unless the problem asks for a specific unit.
Let’s multiply 40.5 yards by 3.
The first way is converting all of 40.5 yards into inches. Since there are 36 inches in 1 yard, we multiply 40 x 36 to get 1,440 inches. Don’t forget the .5 yards. To convert that, divide 36 by 2 to get 18 inches. Add 1,440 and 18 inches for a total of 1,458 inches. What we have so far is 1,458 inches = 40.5 yards. Now we are ready to multiply the total inches by 3 so 1,458 x 3 = 4,374 inches. Ok, last step: convert the 4,374 inches back to yards. Simply, divide 4,374 by 36. Your final answer will be 121.5 yards.
Same problem, just a different way. Here we are multiplying 3 by each unit separately:
Division
To divide 40.5 yards by 3, it is easier to convert the whole 40.5 to inches first. Our preference for working standard unit conversion multiplication and division problems are just to convert the larger unit to the smaller one first, but you might find working the like units better.
Just like we did in our first method of working the length multiplication problem, we convert 40.5 yards to inches. There are 36 inches in a yard; therefore, a half-yard is 18 inches. Multiply 40.5 by 36 to get 1,458 inches. Divide 1,458 by 3 to get 486 inches. Convert back to original form by dividing by 36.
You might have noticed that you could have cut some steps by just dividing 40.5 by 3 and then converting your half yard to inches. Any way you go about it will be ok as long as you understand your steps. For learning purposes, we take the longer way so that you can see how it all unfolds.