Question

PLEASE ANSWER: 3 1/2 + (-7) x (2 2/3 + 1 1/2) = ?

Answer 1

3.5+​(‑7)*​x*​(2.66667+​1.5)

Answer 2

`-(77)/(3)`

Explanation:

So we have the equation:
`3(1)/(2) + (-7) * (2(2)/(3) + 1(1)/(2))`. and I'm assuming you meant to do mixed fractions and not actually multiplying. 2 * 2/3. So the first thing to do is follow PEMDAS which essentially says Parenthesis first, Exponents next, Multiplication or Division, and then Addition or Subtract. So let's start by evaluating the 2 2/3 and 1 1/2. The first step is to combine 2 into the 2/3 and the 1 into 1/2. This is done by multiplying the 2 by the denominator of 3, and adding it to the numerator so:
`2(2)/(3) = > ((2*3)+2)/(3) = > (8)/(3)`. And you do this for the 1/2 as well:
`1(1)/(2) = > ((2*1)+1)/(2)= > (3)/(2)`.

Now when adding fractions, you can only add them when they have the same denominator, so we have the get 3/2 and 8/3 to have the same denominator. You can list the multiplies of 2 and 3 to try to find a LCM, but in this case, I'll just multiply 2 and 3, since they're really small numbers, also because 6 is the LCM.
`(8)/(3) * (2)/(2) = (16)/(6)`. And now do this to the 3/2 you get:
`(3)/(2) * (3)/(3) = (9)/(6)`. Now the inside of the parenthesis is:
`(9)/(6) + (16)/(6) = (25)/(6)`. So now we have the equation:
`3(1)/(2) -7 * (25)/(6)` . Also notice how I got ride of the plus sign and made it negative? Think of it as having a 1 in front and simply distributing that to the -7, 1*(-7) becomes -7.

Now to multiply the fraction by a whole number you simply multiply the denominator and numerator, and you can think of the denominator of a whole number as a 1. So this gives you:
`(-7)/(1) * (25)/(6) = (-7 * 25)/(1 * 6) = -(175)/(6)`. Now we have the equation:
`3(1)/(2) - (175)/(6)`. And to subtract these two numbers I'll make the 3 1/2 a fraction by multiplying the 3 by the denominator and adding it to the 1 which should become 7/2. And after that multiply both sides by 3/3 to get 21/6 so they have the same denominator. This gives you the equation:
`(21)/(6) - (175)/(6) = (21-175)/(6) = -(154)/(6)`. Which can simplify by dividing both sides by 2 to get:
`-(77)/(3)`