What values could the missing denominator have?

[Guest]

3/?>3/8, what values could the missing denominator have if the fractions are parts of the same whole?

[Guest]

[tex]\frac{3}{x}> \frac{3}{8}[/tex]
[tex]\frac{1}{x}> \frac{1}{8}[/tex]
[tex]x< 8[/tex]

Therefore x must be less than 8
so ( - infinity, 8 )

[Guest]

3/5 > 3/8 find decimal for both fractions 1 divided by 5 = .2 times 3 = .6 of the whole
1 divided by 8 = .125 times 3 = .375 of the whole
.6
+.375
+ .975 parts of the whole
Answer to the ? is 5

[Guest]

3/5 > 3/8 find decimal for both fractions 1 divided by 5 = .2 times 3 = .6 of the whole
1 divided by 8 = .125 times 3 = .375 of the whole
.6
+.375
+ .975 parts of the whole
Answer to the ? is 5

https://www.math10.com/forum/posting.php?mode=quote&f=24&p=18384#
The original question was
"3/?>3/8, what values could the missing denominator have if the fractions are parts of the same whole
"Values" is plural and the previous answer, that the denominator must be less than 8, is correct. Assuming that the number must be an integer, it must be 1, 2, 3, 4, 5, 6, or 7.

[Guest]

In addition to [tex]\frac{3}{x}> \frac{3}{8}[/tex] the OP required that the two fractions be "parts of the same whole" which I take to mean that [tex]\frac{3}{x}+ \frac{3}{8}< 1[/tex].

The fact that [tex]\frac{3}{x}> \frac{3}{8}[/tex] simply means that x< 8 and I an also going to assume that "3/x" is a "regular fraction" so x is a positive integer, 1, 2, 3, 4, 5, 6, or 7.

[tex]\frac{
3}{x}+ \frac{3}{8}= \frac{24+ 3x}{8x}< 1[/tex]
Since, again, x is positive 24+ 3x< 8x, 24< 5x, x> 24/5= 4 4/5 so x can be 5, 6, or 7.

Check: If x= 5, 3/x= 3/5= 0.60 which is indeed greater than 3/8= 0.375.
Further 0.60+ 0.375= 0.675< 1.

If x= 6, 3/x= 3/6= 1/2= 0.50 which is indeed greater than 3/8= 0.375.
Further 0.50+ 0.375= 0.87< 1.

If x= 7, 3/x= 3/7= 0.428... which is indeed greater than 3/8= 0.375.'
Further 0.428...+ 0.375= 0.803...< 1.

x= 9 or higher does not work because 3/x= 3/9= 1/3 which is less than 3/8.

x= 4 or less does not work because 3/4+ 3/8= 9/8+ 3/8= 12/8= 3/2 which is larger than 1.

[Angus53]

To compare the fractions 3/? and 3/8, where both fractions represent parts of the same whole, we can set up the inequality:

3/? > 3/8

Now, to solve for the missing denominator, let's cross multiply:

3 * 8 > 3 * ?

24 > 3 * ?

Divide both sides by 3:

24 / 3 > ?

8 > ?

So, any denominator greater than 8 would satisfy the inequality, such as 9, 10, 11, and so on.

[RobertMills]

To compare fractions with different denominators, we need to make sure they have the same denominator. In this case, we want to find a denominator that makes both fractions parts of the same whole.
Given 3/?>3/8, we need to find a denominator for the left fraction such that it's greater than 3/8.
Let's denote the missing denominator as d.
So, we have:
3/d>3/8
To make the comparison easier, let's find a common denominator for both fractions. The least common multiple (LCM) of d and 8 is 8d.
Now, we'll rewrite both fractions with the common denominator 8d:
3/d*8/8>3/8*d/d
24/8d >3d/8d
Now, we can simplify and solve the inequality:
24>3d
Dividing both sides by 33:
8>d
So, for the inequality 3/?>3/8, the missing denominator (d) could take any value less than 8 for the fractions to represent parts of the same whole. Therefore, the possible values for the missing denominator are d<8.

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