Question

How should you group the following expression to make it easiest to add?
18 - 9 4/9 + 7/9 + 8
(18 - 8 - 9)
(8 - 18 ) + (4/9 + 7/9)
(18 - 9 - 8) + (-4/9 + 7/9)
(18 - 8 ) + (-9 4/9 + 7/9)

Answer 1

To make the expression \( 18 - 9 \frac{4}{9} + \frac{7}{9} + 8 \) easiest to add, we should look for combinations that simplify the calculations.

Let's break it down:

1. Combine whole numbers: \( 18 \) and \( 8 \).
2. Handle the fractions, which are \( -9 \frac{4}{9} + \frac{7}{9} \).

We can group it as follows:

\[
(18 - 8) + (-9 \frac{4}{9} + \frac{7}{9})
\]

This simplifies to:

- Grouping the whole numbers gives \( 10 \).
- Now, for the fraction \( -9 \frac{4}{9} + \frac{7}{9} \), convert \( -9 \frac{4}{9} \) to its improper fraction, which is \( -\frac{85}{9} \).

So the operation becomes:

\[
10 - \frac{85}{9} + \frac{7}{9}
\]

This grouping allows you to first simplify the numbers, making the fraction addition slightly less confusing afterward.

Thus, the best grouping for adding in the expression is:

\[
(18 - 8) + (-9 \frac{4}{9} + \frac{7}{9})
\]

Which is clear and straightforward to evaluate. So the answer from your options is:
**(18 - 8) + (-9 \frac{4}{9} + \frac{7}{9})**.