# I guess my answer is correct

#### dollyayesha2345

##### Junior Member
Give an example of each type of number.
a real number between $\frac59$ and $\frac69$
My approach: Two-step technique
Step 1: As one real number is asked increasing that number with 1
$1+1=2$
Step 2:Multiplying both the given fractions with$\frac22$$\frac59\times\frac22=\frac1018$(=10 upon18)
$\frac69\times\frac22=\frac1218$(=12upon18)
So one real number in between is 11/18

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#### lev888

##### Elite Member
Give an example of each type of number.
a real number between $\frac59$ and $\frac69$
My approach: Two-step technique
Step 1: As one real number is asked increasing that number with 1
$1+1=2$
Step 2:Multiplying both the given fractions with$\frac22$$\frac59\times\frac22=\frac1018$(=10 upon18)
$\frac69\times\frac22=\frac1218$(=12upon18)
So one real number in between is 11 upon 18

Sorry, don't understand your reasoning and notation. And I don't see the answer.

#### dollyayesha2345

##### Junior Member
Sorry, don't understand your reasoning and notation. And I don't see the answer.
the Latex for fractions doesn't work properly my final answer is 11/18.

#### lev888

##### Elite Member
the Latex for fractions doesn't work properly my final answer is 11/18.
11/18 works. No idea what 1+1, etc is about. Is this how you find the average of 2 numbers?

#### dollyayesha2345

##### Junior Member
11/18 works. No idea what 1+1, etc is about. Is this how you find the average of 2 numbers?
in the question "to find is 1 real number" so the Step 1 of the two-step technique is to mention x+1=y (x the number required as per the question, y the number we get after the addition) So in my case 1(x)+1=2(y)

#### lev888

##### Elite Member
in the question "to find is 1 real number" so the Step 1 of the two-step technique is to mention x+1=y (x the number required as per the question, y the number we get after the addition) So in my case 1(x)+1=2(y)
Don't understand this explanation.
Here's what I would do:
Given numbers a and b, a<b, find a real number between them.
The average of a and b is exactly in the middle of the [a,b] interval. It equals (a+b)/2.
In your case: 5/9 + 6/9 = 11/9. And (11/9)/2 = 11/18.

#### dollyayesha2345

##### Junior Member
Don't understand this explanation.
Here's what I would do:
Given numbers a and b, a<b, find a real number between them.
The average of a and b is exactly in the middle of the [a,b] interval. It equals (a+b)/2.
In your case: 5/9 + 6/9 = 11/9. And (11/9)/2 = 11/18.
what is the name of this method that you have used?

#### Harry_the_cat

##### Elite Member
This is what I'd do:

$$\displaystyle \frac{5}{9} =\frac{10}{18}$$

$$\displaystyle \frac{6}{9} =\frac{12}{18}$$

Clearly, $$\displaystyle \frac{11}{18}$$ lies between $$\displaystyle \frac{10}{18}$$ and $$\displaystyle \frac{12}{18}$$.

So, $$\displaystyle \frac{11}{18}$$ lies between $$\displaystyle \frac{5}{9}$$ and $$\displaystyle \frac{6}{9}$$.

#### dollyayesha2345

##### Junior Member
This is what I'd do:

$$\displaystyle \frac{5}{9} =\frac{10}{18}$$

$$\displaystyle \frac{6}{9} =\frac{12}{18}$$

Clearly, $$\displaystyle \frac{11}{18}$$ lies between $$\displaystyle \frac{10}{18}$$ and $$\displaystyle \frac{12}{18}$$.

So, $$\displaystyle \frac{11}{18}$$ lies between $$\displaystyle \frac{5}{9}$$ and $$\displaystyle \frac{6}{9}$$.
and the name of your method is?

#### lev888

##### Elite Member
what is the name of this method that you have used?
I described exactly what I was doing. The method is called solving math problems.

#### Subhotosh Khan

##### Super Moderator
Staff member
Give an example of each type of number.
a real number between $\frac59$ and $\frac69$
My approach: Two-step technique
Step 1: As one real number is asked increasing that number with 1
$1+1=2$
Step 2:Multiplying both the given fractions with$\frac22$$\frac59\times\frac22=\frac1018$(=10 upon18)
$\frac69\times\frac22=\frac1218$(=12upon18)
So one real number in between is 11/18

I do not know the official name of that method - but I call it "finding the middle by average".

#### Otis

##### Elite Member
\frac59\times\frac22=\frac1018
the Latex for fractions doesn't work properly
Hi Dolly. You didn't type the delimiters. The syntax for the \frac{}{} command is to place the numerator and denominator each inside a set of curly braces, like this:

\frac{10}{18}

PS: There's a LaTeX thread on the News board with examples and tutorial links.

#### Harry_the_cat

##### Elite Member
and the name of your method is?
I don't think it has a name. I'd call it "converting to a larger denominator to make room between the numerators"!