Algebra
write a mixed number for p so that
3 1/4 x p is more than 3 1/4=
I was not sure I was thinking 2 2/3?
I bet p has to be greater than 1
it does
To find a mixed number that makes the equation 3 1/4 x p > 3 1/4 true, we need to find a value for p that is greater than 1.
Let's first convert the mixed numbers into improper fractions:
3 1/4 = (4 * 3 + 1) / 4 = 13 / 4
To find p, we need to divide the right side of the equation by 3 1/4:
13 / 4 x p > 13 / 4
To cancel out the fraction on the left side, we can multiply both sides of the inequality by the reciprocal of 13/4, which is 4/13:
(4/13)(13 / 4 x p) > (4/13)(13 / 4)
This simplifies to:
p > 1
So, any value of p that is greater than 1 would make the equation 3 1/4 x p > 3 1/4 true.
Therefore, a possible mixed number for p could be 2 1/2 or any other mixed number greater than 1.
To find the mixed number for p so that 3 1/4 x p is more than 3 1/4, we can start by setting up the inequality:
3 1/4 x p > 3 1/4
To simplify, let's convert both numbers to improper fractions:
3 1/4 can be written as (3*4 + 1)/4 = 13/4
3 1/4 x p > 13/4
Now divide both sides of the inequality by 13/4:
(3 1/4 x p) / (13/4) > (13/4) / (13/4)
Simplifying the right side, we have:
(3 1/4 x p) / (13/4) > 1
To eliminate the fraction on the left side, we can multiply both sides by the reciprocal of (13/4), which is (4/13):
[(3 1/4 x p) / (13/4)] * (4/13) > 1 * (4/13)
Simplifying both sides, we get:
(3 1/4 x p) / 1 > 4/13
Now, let's simplify the left side by multiplying the whole number and the fraction:
(13/4 x p) / 1 > 4/13
To remove the fractions, we can multiply both sides by 4:
[(13/4 x p) / 1] * 4 > (4/13) * 4
Simplifying, we have:
13p > 16/13
Finally, divide both sides of the inequality by 13 to solve for p:
(13p) / 13 > (16/13) / 13
This gives us:
p > 16/169
So, any mixed number greater than 16/169, such as 1 1/2 or 2 2/3, would satisfy the inequality 3 1/4 x p > 3 1/4. Therefore, your answer of 2 2/3 as a mixed number for p is correct.