Question

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

Answer 1

To group the expression \( 18 - 9 \frac{4}{9} + \frac{7}{9} - 8 \) in a way that makes it easier to add, it's best to group the whole numbers together and the fractions together.

1. Identify the whole numbers: \( 18 \) and \( -8 \)
2. Identify the fractions: \( - 9 \frac{4}{9} + \frac{7}{9} \)

So the expression can be grouped as:

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

Now, calculate each group separately:

1. \( 18 - 8 = 10 \)
2. To add the fractions, first convert \( -9 \frac{4}{9} \) into an improper fraction:
\[
-9 \frac{4}{9} = -\frac{85}{9}
\]
Thus, we have:
\[
-\frac{85}{9} + \frac{7}{9} = -\frac{85 - 7}{9} = -\frac{78}{9} = -\frac{26}{3}
\]

Now combine the results from both groups:

\[
10 - \frac{26}{3}
\]

For easier calculations, you can convert \( 10 \) into a fraction:

\[
10 = \frac{30}{3}
\]
Now combine:

\[
\frac{30}{3} - \frac{26}{3} = \frac{30 - 26}{3} = \frac{4}{3}
\]

Thus, the total expression simplifies to \( \frac{4}{3} \).

So, the grouped expression is:

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

This grouping helps in calculating the sum more easily.