Question

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

Answer 1

To simplify the expression \( 18 - 9 \frac{4}{9} + \frac{7}{9} - 8 \) for easier addition, we should group like terms together.

First, let's rewrite the expression to separate the whole numbers from the fractional terms:

1. **Combine Whole Number Terms**:
- \( 18 - 8 \)

2. **Combine Fractional Terms**:
- \( -9 \frac{4}{9} + \frac{7}{9} \)

Now, we can handle each section:

### 1. Whole Number Terms:
- \( 18 - 8 = 10 \)

### 2. Fractional Terms:
First, convert \( -9 \frac{4}{9} \) to an improper fraction:
- \( -9 \frac{4}{9} = -\left(9 \times 9 + 4\right)/9 = -\frac{85}{9} \)

Now, add the fractional terms:
- Combine the fractions:
\[
-\frac{85}{9} + \frac{7}{9} = \frac{-85 + 7}{9} = \frac{-78}{9} = -\frac{26}{3}
\]

### Final Result:
Now we can combine the results:
\[
10 - \frac{26}{3}
\]

To make it easier, convert \( 10 \) to a fraction with a denominator of \( 3 \):
- \( 10 = \frac{30}{3} \)

So, we have:
\[
\frac{30}{3} - \frac{26}{3} = \frac{30 - 26}{3} = \frac{4}{3}
\]

Thus, the expression simplifies to:
\[
\frac{4}{3}
\]

In summary, the best way to group the expression is:
\[
(18 - 8) + \left(-9 \frac{4}{9} + \frac{7}{9}\right)
\]

This approach allows you to clearly handle whole numbers and fractions separately for simple addition.