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 \(\displaystyle \frac{7}{5}\).

Convert the following decimal to a fraction:

\(\displaystyle 0.68\)

To convert this to a fraction, let's begin by changing the decimal to a percent and putting it over 100.

\(\displaystyle 0.68\rightarrow 68 \% \rightarrow \frac{68}{100}\)

Now, we just need to simplify our fraction. We can do so by dividing out two two's from the top and bottom.

\(\displaystyle \frac{68}{100}=\frac{34}{50}=\frac{17}{25}\)

So, our answer is:

\(\displaystyle \frac{17}{25}\)

Start by finding how much the painting cost after it was put on sale at \(\displaystyle 17\%\) off.

\(\displaystyle \text{First Price}=5512-5512(0.17)=4574.96\)

Now, we will need to take \(\displaystyle 19\%\) off this already reduced price to find the final sale price of the painting.

\(\displaystyle \text{Final Sale Price}=4574.96-4574.96(0.19)=3705.7176\)

Make sure to round to the nearest cent.

The final sale price for the painting is \(\displaystyle 3705.72\).

Recall the equation to find the amount of simple interest generated:

\(\displaystyle \text{Interest}=prt\), where \(\displaystyle p\) is the initial investment, \(\displaystyle r\) is the rate, and \(\displaystyle t\) 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.

\(\displaystyle \text{Interest generated}=687.39-555.15=132.24\)

Now, we know the initial investment and the amount of time for this account, so we can now solve for the rate.

\(\displaystyle 132.24=(555.15)(6)r\)

\(\displaystyle r=0.0397\)

Because rate is always expressed in a percentage, multiply by \(\displaystyle 100\) to get the rate.

\(\displaystyle r=3.97\%\)

Which of the following decimals is equivalent to the fraction \(\displaystyle \frac{9}{6}\)?

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.

\(\displaystyle \frac{9}{6} \rightarrow 9-6=3\rightarrow 1\frac{3}{6}\)

Now, can we simplify 3 6ths? Yes we can.

\(\displaystyle 1 \frac{3}{6}=1\frac{1}{2}\)

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:

\(\displaystyle 1 \div2=0.5\)

So, our answer is \(\displaystyle 1.5\)

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 \(\displaystyle .75\) can be, but for this problem we will use the easiest one. 

We can assume that this is \(\displaystyle .75\) out of \(\displaystyle 1\), with our \(\displaystyle .75\) on the top and our \(\displaystyle 1\) on the bottom.

\(\displaystyle \frac{.75}{1}\)

It doesn't look exactly right though, and none of our answers are like that. So let's make \(\displaystyle .75\) become \(\displaystyle 75\) by moving its decimal place two back. We need to do the same for \(\displaystyle 1\), whose decimal place would be right behind the number.

\(\displaystyle \frac{75}{100}\)

We now moved our decimal place two back to create \(\displaystyle \frac{75}{100}\). This is our right answer as if you put this fraction into your calculator you will get \(\displaystyle .75\), but also that \(\displaystyle 75\) out of \(\displaystyle 100\) is the same as saying \(\displaystyle .75\) out of \(\displaystyle 1\).

Our answer is \(\displaystyle \frac{75}{100}\).

You can convert \(\displaystyle 0.35\) to the fraction:

\(\displaystyle \frac{35}{100}\)

After you do this, you then need to simplify. You can divide out of numerator and denominator the value \(\displaystyle 5\), giving you:

\(\displaystyle \frac{35\div5}{100\div5}=\frac{7}{20}\)

You can begin by converting \(\displaystyle 0.3024\) into the fraction:

\(\displaystyle \frac{3024}{10000}\)

Now, you can begin canceling from the numerator and the denominator. You are looking for factors of \(\displaystyle 2\). The denominator is only made up of \(\displaystyle 2\) and \(\displaystyle 5\) factors (because it is a power of \(\displaystyle 10\)). The denominator is really merely: \(\displaystyle 10\cdot10\cdot10\cdot10\). This means that it has a total of four \(\displaystyle 2\)s. That is the same as \(\displaystyle 2\cdot2\cdot2\cdot2=16\).  Does the numerator have this many twos?  You can try to figure that out by dividing it by \(\displaystyle 16\). It does! This gets you the value \(\displaystyle 189\). Therefore, you will have:

\(\displaystyle \frac{189}{5\cdot5\cdot5\cdot5}\), or \(\displaystyle \frac{189}{625}\)

\(\displaystyle \small 8^4=8\times8\times8\times8=4,096\)

An exponent indicates the amount of times a number (or variable) should be multiplied by itself. For example, \(\displaystyle \small 2^3=2\times2\times2=8\).

In this instance, \(\displaystyle \small n^4=n\times n\times n\times n\).