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

Answer:

$-\frac{77}{3}$

Step-by-step explanation:

So we have the equation: $3\frac{1}{2} + (-7) * (2\frac{2}{3} + 1\frac{1}{2})$. 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: $2\frac{2}{3} = > \frac{(2*3)+2}{3} = > \frac{8}{3}$. And you do this for the 1/2 as well: $1\frac{1}{2} = > \frac{(2*1)+1}{2}= > \frac{3}{2}$.

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. $\frac{8}{3} * \frac{2}{2} = \frac{16}{6}$. And now do this to the 3/2 you get: $\frac{3}{2} * \frac{3}{3} = \frac{9}{6}$. Now the inside of the parenthesis is: $\frac{9}{6} + \frac{16}{6} = \frac{25}{6}$. So now we have the equation: $3\frac{1}{2} -7 * \frac{25}{6}$ . 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: $\frac{-7}{1} * \frac{25}{6} = \frac{-7 * 25}{1 * 6} = -\frac{175}{6}$. Now we have the equation: $3\frac{1}{2} - \frac{175}{6}$. 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: $\frac{21}{6} - \frac{175}{6} = \frac{21-175}{6} = -\frac{154}{6}$. Which can simplify by dividing both sides by 2 to get: $-\frac{77}{3}$