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

Question

Responses

(18 − 8 − 9)
Left Parenthesis 18 minus 8 minus 9 Right Parenthesis

(18 − 9 − 8) + (−4/9 + 7/9)
Left Parenthesis 18 minus 9 minus 8 Right Parenthesis plus Left Parenthesis negative Start Fraction 4 over 9 End Fraction plus Start Fraction 7 over 9 Right Parenthesis

(8 − 18) + (4/9 + 7/9)
Left Parenthesis 8 minus 18 Right Parenthesis plus Left Parenthesis Start Fraction 4 over 9 End Fraction plus Start Fraction 7 over 9 End Fraction Right Parenthesis

(18 − 8) + (−9 4/9 + 7/9)
Left Parenthesis 18 minus 8 Right Parenthesis plus Left Parenthesis negative 9 Start Fraction 4 over 9 End Fraction plus Start Fraction 7 over 9 End Fraction Right Parenthesis

Answer 1

To make the expression easiest to add, let's analyze each grouping:

1. (18 − 8 − 9): This groups whole numbers well, but doesn't account for the fractions.

2. (18 − 9 − 8) + (−4/9 + 7/9): This groups the whole numbers together first, then combines the fractions.

3. (8 − 18) + (4/9 + 7/9): This is not a good grouping because it changes the order (subtraction is not associative) and doesn't lend itself well to computation.

4. (18 − 8) + (−9 4/9 + 7/9): This separates the whole numbers and the fractions but doesn't manage the fractions as cleanly as option 2.

The best way to group for easy computation is option 2:

(18 − 9 − 8) + (−4/9 + 7/9)

This keeps the whole numbers together for easy subtraction and then groups the fractions to make it simple to combine them afterward.