Question

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

Answer 1

To make the expression \( 18 - 9 \frac{4}{9} + \frac{7}{9} - 8 \) easier to add, it's helpful to group the whole numbers together and the fractions together.

First, let's rewrite the expression clearly:

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

Now, group the whole numbers (18 and -8) and the fractional terms (-9 \(\frac{4}{9}\) and +\(\frac{7}{9}\)):

1. **Whole numbers**: \( 18 - 8 \)
2. **Fractions**: \( -9 \frac{4}{9} + \frac{7}{9} \)

Now, we can simplify each group:

- Whole numbers: \( 18 - 8 = 10 \)
- For the fractions, remember that \( -9 \frac{4}{9} \) can be expressed as \( -\frac{85}{9} \) (since \( -9 = -\frac{81}{9} \) and adding \( -\frac{4}{9} \) gives us \( -\frac{81}{9} - \frac{4}{9} = -\frac{85}{9} \)).

So we have:

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

Now we can simplify the fractions:

\[
-\frac{85}{9} + \frac{7}{9} = -\frac{85 - 7}{9} = -\frac{78}{9} = -\frac{26}{3}
\]

Finally, we can combine \( 10 \) and \( -\frac{26}{3} \):

Convert \( 10 \) into a fraction with a denominator of 3:

\[
10 = \frac{30}{3}
\]

Now combine:

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

Thus, the final answer after all calculations is:

\[
\frac{4}{3}
\]

In conclusion, when grouping the terms, you should group them as follows for easier addition:

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