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, 2/3

1/9 + 2/5 - 1/3 - 3/4

1/9 + 2/5 - 1/3 - 3/4

= (-1/3 + 1/9) + (-3/4 + 2/5) (both terms are negative)
= -2/9 + (-1/3) approx.
= -2/3 approx.

Thanks so much I understand now

To estimate the sum or difference of fractions without finding the exact answer, we can use a strategy called benchmarking. The idea is to identify benchmark fractions (fractions that are easy to work with and commonly used) and then compare the given fractions to these benchmarks.

Now let's look at the expression: 1/9 + 2/5 - 1/3 - 3/4.

1. Benchmark fractions for the denominators:
- 1/2: Below 1/2, we have 0 and 2/3.
- 1: Above 1, we have 2/3.

2. Estimating the fractions:
a) 1/9 is much smaller than 1/2, so we can approximate it as 0.
b) 2/5 is a bit smaller than 1/2, so we can approximate it as - 2/3.
c) 1/3 is smaller than 1/2, so we can approximate it as 0.
d) 3/4 is larger than 1/2, so we can approximate it as 2/3.

3. Plugging in the estimated values:
Our expression becomes: 0 + (-2/3) - 0 - 2/3.

4. Adding and Subtracting:
To sum the fractions, we need to get them over a common denominator. The common denominator of -2/3 and 2/3 is 3.

-2/3 - 2/3 = -4/3.

5. Final estimation:
The best estimate of the sum or difference is -4/3.

Therefore, without finding the exact answer, -4/3 is the best estimate for the sum or difference of the expression.