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# 4/5 10/15 0.8 ..are the numbers same value?

Do these numbers have the same volume? Why or why not?

### 2 Answers by Expert Tutors

Ralph L. | Algebra I, II, Visual Basic, Beginning C++ tutorAlgebra I, II, Visual Basic, Beginning C...
4.0 4.0 (1 lesson ratings) (1)
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4/5 and .8 are the same value.

4/5 is the same as 8/10. 8/10 in decimal has a value of .8

LeighAnne D. | Highly Effective Educator available for Tutoring in Multiple SubjectsHighly Effective Educator available for ...
4.9 4.9 (131 lesson ratings) (131)
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Hi Chris,

Here are the steps I recommend you use to solve this problem:

Change all the terms to either fractions OR decimals or  percents. I personally like percents because they are "easier" for me to understand.

1. We can change 4/5 to a percent. Remember that percent means "out of 100". That means I need to find an equivalent fraction that will have a denominator of 100.
So, let's write 4/5 = ?/100.
I can see that I multiplied the 5 by 20 to get my new denominator of 100. So I have to also multiply the numerator by 20. 4 x 20 = 80.  My new fraction is 80/100.
I know that ANY fraction written over 100 can be changed into a percent.... in this case, it is 80 out of 100, or 80%

2. 10/15 will can be simplified. If we divide BOTH the numerator (top number) and denominator (bottom number) by 5, then my new fraction is 2/3.   Well, 2/3 is one of those fractions that we have to think about to understand the percent.

Think 100 cut into 3 nearly equal parts. Each part will be 33.3

2/3 is equivalent to about 67%.

3. Now, we are left with .8    Decimals convert to percents somewhat "easily".   .8 means the same as 8/10. If we multiply our numerator and denominator by 10, we get a fraction equivalent to 80/100.

Do you remember what to do with this fraction now to get it to be a percent? It means, 80 out of 100, or 80%.

Now, lets look at our numbers again- we have:

4/5 = 80%
10/15= 67
.8=80%

So- these numbers do NOT have the same value! 4/5 and .8 both equal 80%, but 10/16 equals 67%.