If you're taking the HiSET exam, then you're going to see a lot of word problems. Here's
an example of the type of word problem you'll see when you take the HiSET. "Mrs. Patterson's
classroom has sixteen empty chairs." Notice how they didn't actually put the number, they
spelled it out, because they're hoping you'll miss that, read carefully. "All the chairs
are occupied when every student is present. If two-fifths of the students are absent,
how many students make up her entire class?" Okay so, here they gave us this ratio, or
fraction that we can use. And it's two out of every five students are absent. So, you
have two absent to five total. Using this ratio and this third piece of information,
we can set up a proportion. We have sixteen empty chairs. They're empty because there
are sixteen students absent. Make sure you are consistent when you set up proportions.
So if you first ratio is two absent to five total, then your second ratio should be sixteen
absent to, and here's what we don't know, how many total. Now, there's more than one
way to solve a proportion. Sometimes, you'll get a proportion that lends itself, like this
one does, to just figuring out a pattern. For instance, what do you do to two to get
sixteen? Well you just multiply times eight. So, be consistent. Do the same thing to your
denominator. Five times eight is forty. So, there are forty total students. Well that's
not how you spell that word. Okay... um... but, not all proportions can be solved that
way. All proportions can however, be solved with cross-products. So, let me show you how
to do that. You just cross-multiply. Two times "x" is "2x", and the cross products of every
proportion are equal, so that equals five times sixteen, which is eighty, and then you
simply solve for "x". So, divide both sides by two, and you still get that "x" is forty,
and that there are forty, total, students in the class. There is an example of a word
problem using a proportion to solve. Good luck on the HiSET.
If you're planning on taking the HiSET exam, then you need to be ready for word problems.
Here is an example of the type of word problem you'll see when you take the HiSET exam. "Jamie
had six dollars and fifty cents in his wallet when he left home. He spent four dollars and
twenty-five cents on drinks and two dollars on a magazine. Later, his friend repaid him
two dollars and fifty cents that he had borrowed the previous day. How much money does Jamie
have in his wallet?" Well, he's starting with six dollars and fifty cents. Then he spent
four dollars and twenty-five cents, which means we need to take away four dollars and
twenty-five cents from the six dollars and fifty cents. So, we subtract. That's two dollars
and twenty-five cents, and two dollars on a magazine. That's more money that he spent.
So, we need to take away another two dollars, which leaves him with just twenty-five cents,
but then his friend repaid him two dollars and fifty cents, which means we added to the
amount of money that he has. So, we add two dollars and fifty cents, which gives him two
dollars and seventy-five cents. So, you just have to look for those key words like spent
and repaid to make sure that you're doing the right thing, either subtracting or adding,
depending on what you're doing. There you have one example of the type of word problem
you'll see when you take the HiSET exam. If you're planning to take the HiSET, then
plan to work some word problems. Here is an example of the type of word problem you'll
see when you take the HiSET. "Rachel spent twenty-four dollars and fifteen cents on vegetables.
She bought two pounds of onions, three pounds of carrots, and one and a half pounds of mushrooms.
If the onions cost three dollars and sixty-nine cents per pound, and the carrots cost four
dollars and twenty-nine cents per pound, what is the price per pound of mushrooms?"
Okay so, let's start with our onions. She bought two pounds of onions, and the onions
were three dollars and sixty-nine cents per pound. So, her onions cost her three dollars
and sixty-nine cents for each pound she bought. So, times two, which is seven dollars and
thirty-eight cents. For carrots, she bought three pounds of, and they were four dollars
and twenty-nine cents per pound. So, her carrots were four dollars and twenty-nine cents for
each pound, and she bought three pounds of those. So, that was twelve dollars and eighty-seven
cents. Now, let's add those together to find the total amount she spent on onions and carrots
together. So, the seven dollars and thirty-eight cents plus twelve dollars and eighty-seven
cents, which is twenty dollars and twenty-five cents. Remember, you get to use a calculator
on all of this so don't worry about the actual multiplication or addition, just type it in
your calculator. Okay, so that's how much she spent on the onions and carrots. Since
we're trying to find the price per pound of just the mushrooms, we need to take out what
she spent on the onions and carrots from her total. So, take her total, the twenty-four
dollars and fifteen cents, because that's for onions, carrots, and mushrooms, and take
out the onions and carrots. So that, what you're left with, the three dollars and ninety
cents, is just what she spent on mushrooms. That's the total amount of money she spent
on her mushrooms. Okay so, for the mushrooms we're trying to find the price per pound.
We have the price, three dollars and ninety cents. Per tells you to divide that by the
number of pounds and, for mushrooms, were one and a half pounds. So, divide that by
one and five-tenths pounds. Three dollars and ninety cents divided by one and a half
pounds is two dollars and sixty cents per pound. So, that's her price per pound of mushrooms.
There you have an example of the type of word problem you will see when you take the HiSET.
Good luck! If you're planning to take the HiSET exam,
then you need to be comfortable with conversions. Here is an example of a conversion. "A sailboat
is nineteen meters long. What is its length in inches?" Well we're starting with nineteen
meters, and I'm going to use whats called dimensional analysis to convert this. We have
this chart here to help us. We want to convert meters first into centimeters, so that we
can convert our centimeters into inches. So, to convert the meters, I need the meters unit
to go away. To make the meters unit go away, put it in your denominator. That way the meters
cross-cancel. So, one meter is how many centimeters? This one you have to know, it's not in your
chart. One meter is one hundred centimeters. Now, since we're trying to get inches, we
need to convert the centimeters into inches, and that's where we'll use this chart. So,
again we want to get rid of centimeters, so put your centimeters in your denominator.
Two and fifty-four hundredths centimeters is one inch. By the way, each one of these
is equal to one. So, you're taking your nineteen meters and multiplying it times one, times
one. Which means you're not changing the value of your nineteen meters, you're just changing
how it's represented. Instead of in meters, you're representing it in inches. Okay so,
your meters cross-cancel. Let's do a different color. Your meters cross-cancel, and your
centimeters cross-cancel, and we're left with the unit we were trying to get, which is inches.
So, now we just need to multiply. And although this looks kind of weird, these are all just
fractions that we're multiplying together. If I took out these bars, and just put times
signs there, and you could put this one over one. You see we're just multiplying three
fractions together. Nineteen times a hundred times one is nineteen hundred inches, and
then one times one times two and fifty-four hundredths is two and fifty-four hundredths.
Now, all you have to do, is divide nineteen hundred by two and fifty-four hundredths,
and that's where you get seven hundred forty-eight inches. So, there you have one example of
converting from one unit to another unit. Good luck on the HiSET exam!
The HiSET exam will test you on you're ability to read number lines and you're knowledge
of ratios. Here is an example of that combines both of those skills that you'll need for
the HiSET. "In the figure, A, B, and C are points on the number line, where O is the
origin. What is the ratio of the distance BC to distance AB?" Well, ratios can be in
many different forms, and you see the answer choices and how they're set up. So, we'll
set up our ratio the same way. And our ratio is distance BC to distance AB. So, that'll
be our ratio. Distance BC to distance AB. Now, for the distance from B to C, you can
probably just count it on the number line. The distance between five and eight is just
three, but there is a mathematical way of finding the distance between two points, and
that is to find the absolute value of the difference of the two points. So, for instance,
for B and C it would just be five minus eight, the absolute value of five minus eight, or
the absolute value of eight minus five. Either way you'll get the same answer. To the distance
of AB. So, same thing, we want to do the absolute value of the difference, and you can just
go in order: negative six minus five. Now, we just need to simplify. So, this would be
the absolute value of negative three to the absolute value of negative eleven. And the
absolute value of negative three is three, and the absolute value of negative eleven
is eleven. So your ratio is three to eleven. That's one example of the type of problem
you'll see when you take the HiSET.