Applications
jared and pedro walic i mile in about 15 minutes. they can keep op
this pace for several hours.
a. about how far can they walk in 30 minutes?
b. about how far can they walk in 5 minutes? !
swimming of a mile uses about the same number of calories as
running i mile.
a. gilda ran a 25 milo marathon. about how far would her sister
have to swim to use the same number of calories gilda used
during the marathon?
b. juan swims 5 miles a day. about how many miles would he have
to run to use the same number of calories used during his swim?
after testing many samples, an electric company determined
that approximately 2 of every 1,000 light bulbs on the market are
defective. americans buy more than 1 billion light bulbs every year.
estimate how many of these bulbs are defective.
the organizers of an environmental conference order buttons for
the participants. they pay $18 for 12 dozen buttons. write and
solve proportions to answer each question. assume that price is
proportional to the size of the order.
a. how much do 4 dozen buttons cost?
b. how much do 50 dozen buttons cost?
c. how many dozens of buttons can the organizers buy for $27?
d. how many dozens of buttons can the organizers buy for $63?

your exact question is kind of difficult to understand, so maybe an example will explain what you're supposed to do? i'll work through the first problem on the worksheet.

suppose you have a tray of 652 brownies, and you have 5 friends that you want to feed without picking favorites. how many brownies can you dole out to each of your friends in equal amounts? how many will be left over for you to eat?

what you're doing here is finding a way to arrange the number 652 as the sum of integer multiple of 5 and some remainder:

here ("q" for quotient) is the number of brownies each of your friends get, and is the remainder. that's the basic idea behind division.

we break up the number 652 into parts so that the leading digit stands on its own:

652 = 600 + 52

first we check if it's possible to hand out exactly 100 brownies to each friend. with 5 friends, this means we want to know if we can take out 500 brownies from the tray. we can do this 1 time because we have 600 brownies to take from, and when we do that we're left with 100 + 52 brownies to divvy up. so we know that

652 = 1*500 + 152

next we want to know if it's possible to hand out exactly 10 brownies per friend. if we can, we have to remove 50 brownies from the tray each time until we can't. we have 152 brownies left, and we know that 3(50) = 150, so

152 = 3*50 + 2

now we have 2 brownies left in the tray. is it possible to hand 1 out to each of your 5 friends? no, you'd need a minimum of 5 brownies to do that. so the last 2 are yours.

putting everything together, we found that

652 = 1*500 + 3*50 + 2

and we can rearrange this to write

652 = 5*100 + 5*30 + 2

652 = 5(100 + 30) + 2

652 = 5*130 + 2

so and .

you might be more accustomed to the table depicting the algorithm. that's just a compact way of organizing what we've done above. you can consult the image i've attached below.