Is 8/5 proportional to 24/15 ?
1 answer:
Hey there!
The answer to your question is, yes, it is
Given:
To see if they are equal, we can use cross products (see below for information about this, if you don't know what it is). Let us assume they are equal. This would mean that:
Let's solve it and see if it is true:
Therefore, they <em>are </em>proportional.
<u>Cross products</u>
WORD DEFINITION:
Given two fractions, you can take the numerator of the first fraction multiplied by the denominator of the second fraction and it should equal the denominator of the first fraction multiplied by the numerator of the second fraction.
ALGEBRAIC DEFINITION:
Given two fractions,
,
<em>should </em>equal to
Hope it helps, and have a terrificly amazing day!
You might be interested in
The system is
i)
ii)
In the second equation, the bases are equal, so we make the exponents equal to set the equation:
5y-4=10x-4. This means that 5y=10x, that is y=2x.
So, we can substitute y with 2x in the first equation:
.
Multiplying the second fraction by 2/2 and -1 by 2x/2x, we have:
.
Since the denominators are all equal, we can only work with the numerators, setting the equation:
-12+8x-10x+12=-2x,
simplifying we get 0-2x=-2x, that is -2x=-2x, which is always true. (Here remember that x cannot be 0 since x was in the denominator).
This means that for any (x, y) such that y=2x, the system is satisfied.
We can check that the correct statements are:
3) The point (1, 2) is a solution. (Since we have y=2x).
6) The system has infinitely many solutions. (Since any pair (x, 2x) is a solution, except when x=0)
i)
ii)
In the second equation, the bases are equal, so we make the exponents equal to set the equation:
5y-4=10x-4. This means that 5y=10x, that is y=2x.
So, we can substitute y with 2x in the first equation:
Multiplying the second fraction by 2/2 and -1 by 2x/2x, we have:
Since the denominators are all equal, we can only work with the numerators, setting the equation:
-12+8x-10x+12=-2x,
simplifying we get 0-2x=-2x, that is -2x=-2x, which is always true. (Here remember that x cannot be 0 since x was in the denominator).
This means that for any (x, y) such that y=2x, the system is satisfied.
We can check that the correct statements are:
3) The point (1, 2) is a solution. (Since we have y=2x).
6) The system has infinitely many solutions. (Since any pair (x, 2x) is a solution, except when x=0)