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 April 8th, 2016, 10:00 AM #1 Newbie   Joined: Feb 2016 From: Phoenix, Arizona Posts: 20 Thanks: 0 Math Focus: Multiplication I need to know how to figure out the answer to this problem A fraction whose value is the same as 3/4 is? Please show me how to get the answer, do not tell me the answer please.
 April 8th, 2016, 10:02 AM #2 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,675 Thanks: 2655 Math Focus: Mainly analysis and algebra What is the value of $2 \over 2$? What happens if we multiply a number by 1?
 April 8th, 2016, 11:50 AM #3 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 First, do you understand that there are an infinite number of correct answers to this? You are just asked for one. The other thing you need to know is that $\displaystyle \frac{ab}{ac}= \frac{b}{c}$. Multiplying both numerator and denominator by the same thing gives you a new fraction with the same value s the original. That was V8Archie's point.
April 8th, 2016, 02:26 PM   #4
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Quote:
 Originally Posted by Country Boy First, do you understand that there are an infinite number of correct answers to this? You are just asked for one. The other thing you need to know is that $\displaystyle \frac{ab}{ac}= \frac{b}{c}$. Multiplying both numerator and denominator by the same thing gives you a new fraction with the same value s the original. That was V8Archie's point.
How do you know what number to multiply it by?

 April 8th, 2016, 03:18 PM #5 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,675 Thanks: 2655 Math Focus: Mainly analysis and algebra Any number will do. $\frac22=\frac33=\frac44=\ldots=1$
 April 11th, 2016, 12:14 AM #6 Senior Member   Joined: Apr 2014 From: UK Posts: 955 Thanks: 342 A fraction whose value is the same as 3/4 is Equal
April 11th, 2016, 01:59 AM   #7
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Quote:
 Originally Posted by Angelwngs26 A fraction whose value is the same as 3/4 is? Please show me how to get the answer, do not tell me the answer please.
This question is about equivalent fractions. Equivalent fractions are fractions that have the same value, but they describe that value in different ways.

Remember this rule... multiplying or dividing the top and bottom numbers of a fraction by the same number doesn't change the fraction's value.

So if you want an equivalent fraction to $\displaystyle \frac{3}{4}$, you just have to multiply or divide the top and bottom numbers of that fraction by some other number (which you can make up ) to get a new fraction.

-----

One way to explain equivalent fractions is to think of pizza. A pizza is cut into slices and everyone at your party wants the same amount of pizza.

Let's say you cut a pizza into 4 slices (quarters) and you take one slice for yourself. The fraction can be represented by numbers using:

fraction = $\displaystyle \frac{number \, of \, slices \, taken}{total \, number \, of \, slices}$

so in our case we have $\displaystyle \frac{1}{4}$.

Now... let's say a second pizza arrives and we instead cut the pizza into 8 slices and you take two of them. The new fraction is

$\displaystyle \frac{2}{8}$

Since one eighth of a pizza is just a quarter chopped in half again, taking two of those eighths would give us the same amount of pizza we had before, which was one quarter.

Using maths-speak, $\displaystyle \frac{2}{8}$ is not in its simplest form. It is not in its simplest form because we can divide the top and bottom numbers by 2:

2 divided by 2 = 1
8 divided by 2 = 4

So...

$\displaystyle \frac{2}{8} = \frac{1}{4}$

Last edited by Benit13; April 11th, 2016 at 02:04 AM.

April 11th, 2016, 03:43 AM   #8
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Quote:
 Originally Posted by Angelwngs26 How do you know what number to multiply it by?
You don't! I said, in what you quoted, "there are an infinite number of correct answers". choose whatever (non-zero) number you want.

 April 11th, 2016, 08:55 AM #9 Newbie   Joined: Mar 2016 From: Paris, France Posts: 6 Thanks: 0 Math Focus: Arithmetics, Numeical Analysis, Probabilty and Statistics The answer is "equivalent" to 3/4. A fraction a/b is equivalent to 3/4 if a/b=3/4 or, multiplying both sides by 4b: 4a=3b. Thus 4a is a multiple of 3 and, as 4 and 3 are relatively prime (no common factor), a is a multiple of 3: a=3k. The consequence of that, if we substitute 3k to a in the equation, is that we have 12k=4b. Let's divade both sides by 4: we get b=3k. So we have ^rooved that a fraction a/b is equivalent to 3/4 if and only ik it is on the form 3k/4k for any non zero integer k.

,

### vrcat25

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