i need to simplify 5 (1/2-3 4/5)-2 (1/6 + 4)

Question

i need to verify if i am doing process correctly. 5 (1/2 - 3 4/5) -2 (1/6 + 4)

Answer 1

Hi Barbara!

5(1/2 - 3 4/5) -2(1/6 +4)

Perhaps the easiest way to do this is first to combine the terms inside the parentheses, but to do that we first have to change the mixed numbers into improper fractions so we can work with them:

3 4/5 becomes 19/5 (that is: 5 times 3, plus 4; and put all of that over 5)

1/6 + 4 becomes 4 1/6 which becomes 25/6  (that is: 6 times 4, plus 1; and put all of that over 6)

So now we have: 5(1/2 - 19/5) -2(25/6)

Now, we need to solve 1/2 -19/5.  For that we have to find a common denominator, which could be 10:

 1(5)/2(5) - 19(2)/5(2) = 5/10 - 38/10 = -33/10

Putting this back into our equation we have 5(-33/10) - 2(25/6) which is looking better!

We can factor out a 5/5 from the first terms and a 3/3 from the second terms and we’ll get

1(-33/2) - 1(25/3) = -33/2 -25/3

Again, we have to find a common denominator which could be 6:

-33(3)/2(3) -25(2)/3(2)

Now we have -99/6 - 50/6 = -149/6 or -24 5/6

 

 

Answer 2

Hi Barbara,

Simplify:
5 (1/2 - 3 4/5) -2 (1/6 + 4)


It's difficult to write formulas like this so they are not ambiguous. This one is no exception.

It looks like it should be:
5*[(1/2) - (3+(4/5)] - 2*[(1/6) + 4)]

(This looks pretty messy, but I don't see any way to make it any less so.)

Working inside the parentheses (my square brackets) first,
convert to improper fractions and go:

5*[(1/2) - (3+(4/5))] - 2*[(1/6) + 4)]
5*[(1/2) - (19/5)] - 2*[(1/6) + (24/6)]
5*[(5/10) - (38/10)] - 2*[(25/6)]
5*[-(33/10)] - [(25/3)]
-(33/2) - (25/3)
-(99/6) - (50/6)
-(149/6)

One way to check is to convert everything to decimal and use a
calculator to evaluate the starting formula and your answer. If
they're the same, you're probably doing it right. If not, you at
least know that you need to check your work.

Here's what I put into Excel to check:

=5 * (0.5 -3.8) - 2*(4+1/6)
= -24.8333

=-149/6
= -24.8333

I hope this helps.