ACT Math Pre-Algebra: Drill 3, Problem 5. Simplify the expression.
|Foreign Language||Arabic Subtitled|
|Fractions and Decimals||Fractions|
Number problems (operations using whole numbers, fractions, decimals, and integers)
|Product Type||ACT Math|
No need to feel overwhelmed though. We just have to pick this one apart piece by piece.
The big skill set being tested here is all about common denominators.
So for starters we just add 3/4 and 5/8. The common denominator here should be clear...
all we have to do is turn that 4 into an 8 and we're all good.
We make 3/4 into 6/8... and 6/8 plus 5/8 is 11/8.
Now to the numerator, where we have 4 minus 2/3.
4 is the same as 4 over 1... so we can multiply top and bottom by 3 to get a common denominator...
...and we have 12 over 3 minus 2 over 3 to get 10 over 3 in the numerator.
So the simplified problem thus far looks like this:
Now remember that dividing by a fraction is the same as multiplying by its inverse.
So we multiply 10 over 3 by 8 over 11 to get 80 over 33.
Oh joy -- we have a 33 in the denominator in the answer set.
To get our mixed number, we reduce... 33 goes into 80 twice 14 leftover... that is, it reduces
to 2 and 14/33.
The answer is B.
As in "Bling."