Complex Operations - GED Math
Card 0 of 1125
Simplify:
Simplify:
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Simplify:
Simplify:
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Which number has 5.25 as its reciprocal?
Do not use a calculator.
Which number has 5.25 as its reciprocal?
Do not use a calculator.
The number that has 5.25 as its reciprocal is, in return, the reciprocal of 5.25.
Convert 5.25 to a fraction:
Switch the numerator and the denominator to obtain the reciprocal - this number is 
.
The number that has 5.25 as its reciprocal is, in return, the reciprocal of 5.25.
Convert 5.25 to a fraction:
Switch the numerator and the denominator to obtain the reciprocal - this number is
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Rewrite 0.24 as a fraction in simplest form.
Rewrite 0.24 as a fraction in simplest form.
The last nonzero digit of 0.24 - namely, the "4" - is in the hundredths place, so the fractional representation is
Reduce this to simplest form by dividing both halves by their greatest common factor, which is 4:
The last nonzero digit of 0.24 - namely, the "4" - is in the hundredths place, so the fractional representation is
Reduce this to simplest form by dividing both halves by their greatest common factor, which is 4:
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Rewrite 
as a decimal expression.
Rewrite
Divide 7 by 5, adding a decimal point and zeroes to the former as needed. The division looks like this:
The quotient, 1.4, is the decimal equivalent of 
.
Divide 7 by 5, adding a decimal point and zeroes to the former as needed. The division looks like this:
The quotient, 1.4, is the decimal equivalent of
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Express as a decimal: 
Express as a decimal:
Divide 11 by 12:
The "6" repeats forever, so
.
Divide 11 by 12:
The "6" repeats forever, so
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Express as a fraction:
Express as a fraction:
Let 
Then
and
We can subtract:
Let
Then
and
We can subtract:
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Express as a decimal: 
Express as a decimal:
Divide 15 by 16:
Divide 15 by 16:
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Express as a fraction: 
Express as a fraction:
Let 
Then 
Subtract:
Let
Then
Subtract:
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Express as a decimal: 
Express as a decimal:
Divide 16 by 15:
The "6" repeats forever, so
.
Divide 16 by 15:
The "6" repeats forever, so
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Express as a decimal: 
Express as a decimal:
Divide 12 by 11:
The "09" repeasts forever, so
.
Divide 12 by 11:
The "09" repeasts forever, so
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Which of the following numbers has 
as its reciprocal?
Do not use a calculator.
Which of the following numbers has
Do not use a calculator.
The number that has 
as its reciprocal is, in return, the reciprocal of 
. This number is the result of switching the numerator and denominator - 
. Since we are looking for the decimal equivalent, we divide 29 by 8:
, the correct choice.
The number that has
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What is the decimal represented by the fraction 
?
What is the decimal represented by the fraction
Set up a proportion such that this fraction is some number over 100.
Cross multiply.
Divide by 50 on both sides.
The answer is: 
Set up a proportion such that this fraction is some number over 100.
Cross multiply.
Divide by 50 on both sides.
The answer is:
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Which of the following represents the equivalent of 
?
Which of the following represents the equivalent of
You can convert 
to the fraction:
After you do this, you then need to simplify. You can divide out of numerator and denominator the value 
, giving you:
You can convert
After you do this, you then need to simplify. You can divide out of numerator and denominator the value
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Which of the following is equivalent to 
?
Which of the following is equivalent to
You can begin by converting 
into the fraction:
Now, you can begin canceling from the numerator and the denominator. You are looking for factors of 
. The denominator is only made up of 
and 
factors (because it is a power of 
). The denominator is really merely: 
. This means that it has a total of four 
s. That is the same as 
. Does the numerator have this many twos? You can try to figure that out by dividing it by 
. It does! This gets you the value 
. Therefore, you will have:
, or 
You can begin by converting
Now, you can begin canceling from the numerator and the denominator. You are looking for factors of 
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Convert the following decimal to a fraction:
Convert the following decimal to a fraction:
Convert the following decimal to a fraction:
To convert this to a fraction, let's begin by changing the decimal to a percent and putting it over 100.
Now, we just need to simplify our fraction. We can do so by dividing out two two's from the top and bottom.
So, our answer is:
Convert the following decimal to a fraction:
To convert this to a fraction, let's begin by changing the decimal to a percent and putting it over 100.
Now, we just need to simplify our fraction. We can do so by dividing out two two's from the top and bottom.
So, our answer is:
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A painting that originally costs 
goes on sale for 
off. After a week, the painting did not sell, so the price was decreased by a further 
. The painting finally sold. In dollars, what was the final sale price of the painting?
A painting that originally costs
Start by finding how much the painting cost after it was put on sale at 
off.
Now, we will need to take 
off this already reduced price to find the final sale price of the painting.
Make sure to round to the nearest cent.
The final sale price for the painting is 
.
Start by finding how much the painting cost after it was put on sale at
Now, we will need to take
Make sure to round to the nearest cent.
The final sale price for the painting is
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James deposits 
into a savings account. After 
years, his savings account has 
in it. What is the interest rate, to the nearest hundredths place, for his account?
James deposits
Recall the equation to find the amount of simple interest generated:
, where 
is the initial investment, 
is the rate, and 
is time in years.
Start by subtracting his balance after six years by his initial investment to get the amount of interest that was generated.
Now, we know the initial investment and the amount of time for this account, so we can now solve for the rate.
Because rate is always expressed in a percentage, multiply by 
to get the rate.
Recall the equation to find the amount of simple interest generated:
Start by subtracting his balance after six years by his initial investment to get the amount of interest that was generated.
Now, we know the initial investment and the amount of time for this account, so we can now solve for the rate.
Because rate is always expressed in a percentage, multiply by
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Which of the following decimals is equivalent to the fraction 
?
Which of the following decimals is equivalent to the fraction
Which of the following decimals is equivalent to the fraction 
?
To solve this problem efficiently, first eliminate any unreasonable answers. We are given an improper fraction, so we know that our answer must be grater than one. With this in mind we can eliminate one of our answers.
Next, let's make this fraction a mixed number. To do so, subtract the denominator from the numerator. This will become our new numerator. Because 6 only goes into 9 once, we will put a 1 out in front.
Now, can we simplify 3 6ths? Yes we can.
Now, the fraction one-half is equivalent to 0.5 If you weren't sure on this, you can find this out by dividing 1 by 2:
So, our answer is 
Which of the following decimals is equivalent to the fraction
To solve this problem efficiently, first eliminate any unreasonable answers. We are given an improper fraction, so we know that our answer must be grater than one. With this in mind we can eliminate one of our answers.
Next, let's make this fraction a mixed number. To do so, subtract the denominator from the numerator. This will become our new numerator. Because 6 only goes into 9 once, we will put a 1 out in front.
Now, can we simplify 3 6ths? Yes we can.
Now, the fraction one-half is equivalent to 0.5 If you weren't sure on this, you can find this out by dividing 1 by 2:
So, our answer is
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Convert this decimal into a fraction: 
Convert this decimal into a fraction:
There are two ways you can go about solving this. If you have a calculator, you can simply take the fraction answers and figure out which one matches the decimal we need to convert.
If you don't have a calculator, then we will work with the decimal and convert it into a fraction.
There are many different fractions 
can be, but for this problem we will use the easiest one.
We can assume that this is 
out of 
, with our 
on the top and our 
on the bottom.
It doesn't look exactly right though, and none of our answers are like that. So let's make 
become 
by moving its decimal place two back. We need to do the same for 
, whose decimal place would be right behind the number.
We now moved our decimal place two back to create 
. This is our right answer as if you put this fraction into your calculator you will get 
, but also that 
out of 
is the same as saying 
out of 
.
Our answer is 
.
There are two ways you can go about solving this. If you have a calculator, you can simply take the fraction answers and figure out which one matches the decimal we need to convert.
If you don't have a calculator, then we will work with the decimal and convert it into a fraction.
There are many different fractions
We can assume that this is
It doesn't look exactly right though, and none of our answers are like that. So let's make
We now moved our decimal place two back to create
Our answer is
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