Three-halves of a number exceeds five-sixths of the number by four-thirds.Find the number.
3/2 N -5/6 N=4/3
get a common denominator of 30
3*15 N -25N=40
20N=40
N=2
Ah, numbers and fractions, the perfect recipe for my clown brain! Let's break it down in a funny way:
So, we're dealing with a number, let's call it "X". Now, the problem says that three-halves of X exceeds five-sixths of X by four-thirds.
Well, if three-halves (which is the same as one and a half) of a number exceeds five-sixths of that number by four-thirds, then we can write it like this:
1.5X - (5/6)X = 4/3
Simplify that equation and solve for X, and you'll have your answer! Happy number crunching!
Let's assume the number is represented by "x".
According to the problem, three-halves of the number (3/2 * x) exceeds five-sixths of the number (5/6 * x) by four-thirds (4/3).
Putting this into an equation, we have:
(3/2) * x = (5/6) * x + (4/3)
To simplify the equation, let's get rid of the fractions by multiplying every term by the least common multiple (LCM) of the denominators of the fractions, which is 6:
6 * [(3/2) * x] = 6 * [(5/6) * x + (4/3)]
Expanding and simplifying, we get:
9x = 5x + 8
Subtracting 5x from both sides:
9x - 5x = 5x - 5x + 8
4x = 8
Solving for x by dividing both sides by 4:
4x/4 = 8/4
x = 2
Therefore, the number is 2.
To find the number, let's assume that the number is represented by "x".
According to the problem statement:
"Three-halves of a number exceeds five-sixths of the number by four-thirds."
We can translate this into an equation as follows:
(3/2)x - (5/6)x = 4/3
To solve this equation, we need to combine like terms on the left side:
(9/6)x - (5/6)x = 4/3
Simplifying further:
(4/6)x = 4/3
Now, let's solve for x by multiplying both sides of the equation by the reciprocal of (4/6):
x = (4/3) * (6/4)
Multiplying the numerators gives:
x = 24/12
Simplifying further, we have:
x = 2
Therefore, the number is 2.