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 can group the whole numbers and the fractions separately.

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

Now, convert \( -9 \frac{4}{9} \) into an improper fraction to make it easier to handle with the other fraction:
\[
-9 \frac{4}{9} = -\left(9 \cdot 9 + 4\right)/9 = -\frac{81 + 4}{9} = -\frac{85}{9}
\]

Now rewrite the expression:
\[
18 - 8 - \frac{85}{9} + \frac{7}{9}
\]

You can now group the whole numbers and the fractions:
1. Whole numbers: \( 18 - 8 \)
2. Fractions: \( -\frac{85}{9} + \frac{7}{9} \)

Now calculate both groups:
- Whole numbers:
\[
18 - 8 = 10
\]

- Fractions:
\[
-\frac{85}{9} + \frac{7}{9} = -\frac{85 - 7}{9} = -\frac{78}{9} = -\frac{26}{3} \quad \text{(Simplifying)}
\]

Now combine the results:
\[
10 - \frac{26}{3}
\]

To subtract, convert \( 10 \) to a fraction with a denominator of 3:
\[
10 = \frac{30}{3}
\]

Now we can subtract:
\[
\frac{30}{3} - \frac{26}{3} = \frac{30 - 26}{3} = \frac{4}{3}
\]

Thus, the final result of the expression \( 18 - 9 \frac{4}{9} + \frac{7}{9} - 8 \) is:
\[
\frac{4}{3}
\]

In conclusion, to make it easiest to add, group the expression as follows:
\[
(18 - 8) + (-9 \frac{4}{9} + \frac{7}{9})
\]