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Math Smart
How to Estimate
E
stimating is an important skill on the math test. If you can
solve a problem through estimating and then compare your
answer to the answer choices, you can do many problems more
quickly and easily. Be careful. Some problems require you to have
precise information, so you’ll need to judge when you can or can’t
estimate to get to the correct answer.
Estimating helps you work through problems in your head,
and it’s a great tool for checking your answers because it’s quick and
easy. When you estimate, you trade off accuracy of your answer for
ease of doing the problem. So, it’s important to ask yourself: how
accurate does my answer have to be? How much can I estimate and
still be close enough to know the answer?
To estimate, you need to round off the numbers that you’re
using. You’ll need to decide what numbers to round off and what
to round them off to. The trick is to choose numbers that will be
easy for you to work with, while keeping in mind how accurate you
need to be. Let’s take this problem we’ve already solved, and try to
solve it using estimation:
Gregor manages a machining shop which makes specialized
bolts. One worker can generate 112 bolts per hour and
works 8 hours per day. Gregor’s biggest customer needs
him to fill an order for 15,000 bolts in the next 5-day work
week. How many workers does Gregor have to schedule to
fill the order?
T
he first thing you need to do is multiply 112 times 8 to get
the number of bolts one worker can make in a day. So, what’s
the most accurate, easiest way to round the numbers and get an
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accurate count? You could round 112 to 100 and 8 to 10, and get
1,000, but that’s not going to be very accurate. A better way is to
round 112 to 110 and multiply it by 8 to get 880. It’s easy to do
in your head, because 1’s and 0’s are both easy to work with. You
could even round it to 111 × 8 = 888, and you’d be really close
to the answer. But let’s say the answer is a little more than 880.
Because we rounded 112 down to 110, the accurate answer will be
a little more than our rounded answer, 880.
In general, round down when a digit is 4 or less:
14 rounds down to 10, but you might want to estimate it
at 15 (more accurate)
1,402 rounds down to 1,400 (more accurate) or 1,000
(less accurate), but you might want to estimate it at 1,500
(middle accuracy).
In general, round up when a digit is 5 or more:
15 rounds up to 20
1,592 rounds up to 1,600 (more accurate) or to
2,000 (less accurate)
The bigger the difference is between the original number
and the rounded number, the less accurate the rounded
number will be. Try to get the most accurate number
that’s easiest to work with.
©2008 by The GED Academy. You are licensed one copy of this document for personal use only. Any other
reproduction or redistribution is prohibited. All rights reserved. w w w . p a s s G E D . c o m
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Math Smart
T
he next step is to multiply by 5, the number of workdays in
a week, to find out how many bolts a worker can make in a
week. Besides rounding, one thing you can do is break apart your
numbers to make them easier to estimate. That way, your answer
stays pretty accurate, but it’s still easy to do. For example, if you
know that 8 × 5 = 40, than 800 × 5 will be 4,000. And, 80 × 5 will
be 400. And it’s easy to put them together: 4,400. One worker can
make a little more than 4,400 bolts in a week.
Here are some examples of breaking apart a number for easier
multiplication:
756 × 2 = (750 × 2) + (6 × 2) = 1,500 + 12 = 1,512
898 × 4 = (900 × 4) − (2 × 4) = 3,600 − 8 = 3,592
555 × 11 = (555 × 10) + (555 × 1) = 5,550 + 555 =
6,105
This is a great skill to practice to improve your mental math. It
gives accurate results.
T
he next step is to divide 15,000 by 4,400. This one is a little
trickier because the numbers aren’t very easy to work with.
One thing you can do right away to a division problem to make it
a little more manageable is to drop the same number of zeros off
the end of each number. You can take two zeros off each number
without changing the division problem. That gives you 150 divided
by 44. That’s easier to get your head around. Since 44 is less than
50, you know that 44 will go into 150 at least 3 times. Would it go 4
times? No, because 40 times 4 is 160, and 44 is more than 40. So, 44
©2008 by The GED Academy. You are licensed one copy of this document for personal use only. Any other
reproduction or redistribution is prohibited. All rights reserved. w w w . p a s s G E D . c o m
Math Smart
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goes into 150 between 3 and 4 times. The answer will be between 3
and 4. Since the problem is asking how many workers you’ll need,
all you need to know is that the answer is between 3 and 4. If the
answer is higher than 3 but less than 4, you’ll need 4 workers to
complete the job. The answer is 4.
Practice Problems
Use estimation and mental math to find the answers. When you
estimate, will the answer be a little higher or a little lower than your
estimate? Compare your answers with the results from a calculator.
8940 × 22 =
5699 × 5 =
9340 × 112 =
3558 × 33 =
333 × 51 =
506 × 10 =
209 × 90 =
201 × 23 =
89 + 896 =
233 + 2359 =
11 + 452 =
342+ 96 =
40 + 2394 =
6874 + 234 =
475 + 232 =
3204 + 33 =
9401 ÷ 23 =
576 ÷ 7 =
457 ÷ 12 =
4050 ÷ 5 =
3944 ÷ 9 =
4o52 ÷ 66 =
485 ÷ 5 =
1000 ÷ 21 =
0394 – 44 =
4587 – 333 =
2931 – 223 =
567 – 34 =
998 – 200 =
935 – 495 =
6542 – 922 =
4938 – 344 =
©2008 by The GED Academy. You are licensed one copy of this document for personal use only. Any other
reproduction or redistribution is prohibited. All rights reserved. w w w . p a s s G E D . c o m