Numbers and Operations - GED Math

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.

Set up a proportion such that this fraction is some number over 100.

Cross multiply.

Divide by 50 on both sides.

The answer is:

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 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

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:

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 .

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:

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 .

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.

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

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 .

An exponent indicates the amount of times a number (or variable) should be multiplied by itself. For example, .

In this instance, .

Write the number with a decimal point and without commas:

Counting the number of places, move the decimal point to the left until it is after the first nonzero digit:

The resulting number is 4.5; the number of places the decimal point moved to the left was 7. In scientific notation, this number is .

Write the number:

Counting the number of places, move the decimal point to the right until it is after the first nonzero digit:

The resulting number is 3.8; the number of places the decimal point moved to the right was 8. In scientific notation, this number is .

A positive number raised to any real power is positive. and are the opposites of powers of positive numbers; they are therefore the opposites of positive numbers, making both negative.

A negative number raised to an odd power, such as , is negative.

A negative number raised to an even power, such as , is positive.

is the only positive number among the choices and can be deduced as the correct choice.

For any nonzero and for any , . Equivalently, any number raised to a negative power is equal to the reciprocal of that number raised to the power of the absolute value of the exponent.

The reciprocal of a number is the quotient of 1 and the number, so the reciprocal of 0.4 is

.

Therefore,

, which is the correct response.

For any nonzero and for any , .

Also, any negative number raised to the power of an odd number is equal to the opposite of the same power of its absolute value.

Combine these concepts:

Since ,

the reciprocals are in reverse order of this:

Their opposites reverse again:

Or, equivalently,

.