eval. 5(-1/x)^2 (-3x)^3 div. by((-7)^2 -3^2 + x(-5)) for x=2

[tiff]

over the summer i did no math word at all, and now in one the first day of algebra 2 class i cant remember that much.

im haing a hard time with problems with fractions in them, i really need help
(^2 or ^3 are supposed to be exponents)
(and 1/2 is a fraction.)

1. evaluate the following expression if x=2
5(-1/x)^2 (-3x)^3 divided by((-7)^2 -3^2 + x(-5))

2. evaluate the following expressions if r=3
(-2/r)^2 divided by (-1/2)^3 divided by (4/5r)^2

 

[Loren]

Re: help!

1. evaluate the following expression if x=2
5(-1/x)^2 (-3x)^3 divided by((-7)^2 -3^2 + x(-5))

becomes \(\displaystyle \frac{5(-\frac{1}{2})^2(-3\cdot 2)^3}{(-7)^2 -3^2 + 2(-5)}\)

Now, just do the arithmetic following the order of operations convention.

 

[tiff]

Re: help!

1. evaluate the following expression if x=2
5(-1/x)^2 (-3x)^3 divided by((-7)^2 -3^2 + x(-5))

becomes \(\displaystyle \frac{5(-\frac{1}{2})^2(-3\cdot 2)^3}{(-7)^2 -3^2 + 2(-5)}\)

Now, just do the arithmetic following the order of operations convention.

Thats the part i need help with.

 

[Loren]

Re: help!

Try googling "order of operations".

 

[mmm4444bot]

Re: help!

Thats the part i need help with.

What part? The arithmetic, or the order in which to do it? :wink:

You mentioned that you have trouble with fractions. Are you trying to ask for help simplifying something like (-1/2)^2 ?

If so, that's (-1/2) * (-1/2)

Numerator times numerator (-1 * -1) over denominator times denominator (2 * 2)

(-1/2)^2 = 1/4

If this is not what you mean, then perhaps you're thinking about canceling numbers above and below the large fraction bars after making the subsitutions in those expressions you posted.

When you end up with expressions on both the top and the bottom of a fraction bar that contain only numbers (i.e., no variables), then often it's easier to just do all of the arithmetic on the top, followed by doing all of the arithmetic on the bottom -- waiting to cancel (if possible) as the last step to write the result as a reduced fraction.

You might also be trying to ask about the second problem you posted, since it's a compound fraction (i.e., a fraction divided by a fraction).

Like

2/3 over 4/5

or

a / 4 / x

which can be thought of as either:

a/4 over x/1

or

a/1 over 4/x

(Whichever you like, because they both mean the same thing.)

The following rule changes a compound fraction into a simple fraction:

Writing a/b over c/d is the same thing as writing a/b multiplied by d/c

In other words, multiply the fraction on top by the reciprocal of the fraction on the bottom. "Reciprocal" means flipped; as in c/d becomes d/c.

(a/b) / (c/d) = (a/b) * (d/c)

So something like:

3x^2 / (x + 6) / (4x - 1)

which can be thought of as the compound fraction:

3x^2 / (x + 6) over (4x - 1) / 1

becomes a simple fraction by flipping (4x - 1) / 1 to get the reciprocal, and then multiplying the fraction on top by it:

3x^2 / (x + 6) multiplied by 1 / (4x - 1)

So, 3x^2 / (x + 6) / (4x - 1) = 3x^2 / [(x + 6) * (4x - 1)]

Maybe you need help with something like simplifying (4r)^3

That's 4r * 4r * 4r

which can be regrouped with numbers together and variables together:

(4 * 4 * 4) * (r * r * r)

(4r)^3 = 64r^3

Or maybe you need help with how to reduce a fraction like 24/64.

Or maybe you need help with something else. :?:

The more specific you can be when you post a request for help, the sooner people can zero in on helping you with exactly what you need to know. Most of us usually do not have time to guess at possibilities and type explanations for them like I just did, sorta.

If you still need help with this problem, please let us know what part you're trying to do. ~ Mark