Without finding the exact answer, select which of the following numbers is the best estimate of each sum or difference and justify your choices: -2/3, 0, 2/2/3.
a. 1/9 + 2/5 – 1/3 – 3/4
I am confused on where to begin on this question.
1/9 + 2/5 is less than 1/2
-1/3 + -3/4 is more than negative 1.
Which of the three answers comes closest?
-2/3, 0, 2/2/3.
To begin solving this problem, you need to find the best estimate for each sum or difference given the options provided (-2/3, 0, 2/2/3).
Let's start with the first expression, which is:
1/9 + 2/5 - 1/3 - 3/4
Step 1: Simplify the fractions:
1/9 + 2/5 - 1/3 - 3/4 =
(4/36) + (14/36) - (12/36) - (27/36)
Step 2: Combine like terms (numerator and denominator):
(4+14-12-27)/36 = -21/36
Now, we need to determine which of the given options (-2/3, 0, 2/2/3) is the best estimate for the result -21/36.
Option -2/3 is -24/36 when simplified, which is close to -21/36.
Option 0 is 0/36, which is not close to -21/36.
Option 2/2/3 can be written as (6/3) = 2, which is not close to -21/36.
Considering the options, the best estimate for the sum (-21/36) is -2/3.