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

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

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# 2 Answers

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

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%.

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