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)

1 answer

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}).