Multi-step unit conversion examples

Brooklyn purchased three pounds of pasta and 12 ounces of cheese to make macaroni and cheese. What is the total weight in ounces of the pasta and cheese combined?

So they give us the weight of the pasta in pounds and they give us the weight of the cheese in ounces, and we want to add the total weight, but they have to all be in ounces.

So let's first convert these three pounds of pasta into a certain amount of ounces of pasta. We already know that one pound is equal to 16 ounces; they tell us that. So what would three pounds be? If I had three pounds, how many ounces would that be? I encourage you to pause the video and think about it.

Well, let's see. If you're having three times the pounds, you're also going to have three times the ounces. So, if 1 pound is 16 ounces, if you have three times as many pounds, you're going to have three times as many ounces.

So, 16 times 3 is 48. 48 ounces. So, Brooklyn, the 3 pounds of pasta that she purchased can also be viewed as 48 ounces of pasta. She has 48 ounces of pasta and 12 ounces of cheese.

So what is the total weight in ounces of them combined? Well, it's going to be 48 ounces plus the 12 ounces of cheese. 48 ounces of pasta plus 12 ounces of cheese gives us a total of 60 ounces of pasta and cheese combined.

Let's do another example with other units. We are told David is making a wall out of bricks. Each brick is 2/3 of a foot long. There are 20 bricks lined up end to end to make the wall. What is the total length of the wall in inches?

We got to pay attention to the units. They give us the length of each brick in feet. We know that each brick, here, let me draw a brick, the length here is 2/3 of a foot. 2/3 of a foot. So what would this length be in inches?

Well, once again, we can look at the conversion between foot and inch. If I go from 1 foot to 2/3 of a foot, well, I've multiplied by 2/3. So, if one foot is 12 inches and if I want to know how many inches 2/3 of a foot is in inches, well, I would multiply by 2/3 again.

In either case, you could view this as multiplying both sides of this conversion by 2/3. So, 2/3 of a foot is going to be 2/3 times 12 inches. So, 12 times 2 over 3 would be 24 over 3.

So this is going to be equal to 24 over 3, and I'll just write "in" for short right over here, 24 over 3, which is equal to 8 inches. So, each brick is either viewed as 2/3 of a foot long or you could view it as 8 inches long.

And there are 20 bricks lined up end to end to make the wall. So what is the total length of the wall in inches? Well, it's going to be 8 inches for each brick times 20.

8 times 20 is 160 inches.

Let's do one more of these, and this time let's deal with some volume. This says Blanca buys two gallons of green paint. She uses five quarts to paint her front porch and 0.5 quarts to paint the front porch swing. How many quarts of paint does Blanca have left?

So we're given the original amount in gallons, but we want to know how many quarts she has left. So let's convert the amount she originally has into quarts. They tell us one gallon is equal to four quarts.

So, two gallons is going to be equal to two gallons. It's going to be eight quarts. So that's what she starts with. One way to think about this is that I just took this conversion.

Well, if I'm going to have twice as many gallons, then I'm going to have twice as many quarts if I want to express that volume in quarts. So, she starts with eight quarts.

She uses five quarts to paint her front porch, so minus 5 quarts for the front porch is what she used. And she used 0.5 quarts to paint the porch swing, so minus 0.5 quarts.

That looks like 0.5 quarts. Well, what is that going to be? Well, 8 minus 5 is 3, minus 0.5 is 2.5. So, she is going to be left with 2.5 quarts.

And we have answered the question in terms of the units they care about—in terms of quarts.