To determine the best way to group the expression \( 18 - 9\frac{4}{9} + \frac{7}{9} - 8 \) for easier addition or subtraction, let's evaluate the given options:
**A. \((18 - 8) - (9\frac{4}{9} + \frac{7}{9})\)**
**Breaking it down:**
- First, simplify inside the first parenthesis:
\( 18 - 8 = 10 \).
- Then, simplify inside the second parenthesis:
\( 9\frac{4}{9} + \frac{7}{9} \).
Converting \( 9\frac{4}{9} \) to an improper fraction:
\( 9 + \frac{4}{9} = \frac{81}{9} + \frac{4}{9} = \frac{85}{9} \).
Now adding \( \frac{85}{9} + \frac{7}{9} = \frac{92}{9} \).
- Combining results:
\[ 10 - \frac{92}{9} = 10 - \left(\frac{90}{9} + \frac{2}{9}\right) = 10 - \left(10 + \frac{2}{9}\right) = 10 - 10 - \frac{2}{9} = -\frac{2}{9} \].
**B. \((18 - 8 - 9)\)**
This option excludes fractions and groups only the integers. Simplifying:
- \[ 18 - 8 - 9 = 10 - 9 = 1 \].
It doesn’t consider fractions and so isn’t properly aligned with the given problem.
**C. \((18 - 9 - 8) + (-\frac{4}{9} + \frac{7}{9})\)**
**Breaking it down:**
- Simplify inside the first parenthesis:
\[ 18 - 9 - 8 = 9 - 8 = 1 \].
- Simplify inside the second parenthesis:
\[ -\frac{4}{9} + \frac{7}{9} = \frac{3}{9} = \frac{1}{3} \].
- Combining results:
\[ 1 + \frac{1}{3} = \frac{3}{3} + \frac{1}{3} = \frac{4}{3} \].
**D. \((8 - 18) + (\frac{4}{9} + \frac{7}{9})\)**
**Breaking it down:**
- Simplify inside the first parenthesis:
\[ 8 - 18 = -10 \].
- Simplify inside the second parenthesis:
\[ \frac{4}{9} + \frac{7}{9} = \frac{11}{9} \].
- Combining results:
\[ -10 + \frac{11}{9} = -10 + 1\frac{2}{9} = -10 + \frac{11}{9} \].
From the options provided, Option C appears to systematically group the terms while keeping the arithmetic logical and straightforward:
\((18 - 9 - 8) + (-\frac{4}{9} + \frac{7}{9})\).
So, the best grouping to make the addition easier is:
**C. \((18 - 9 - 8) + (-4/9 + 7/9)\)**.
How would you group the following expression to make it easier to add?
18 - 9 4/9 + 7/9 - 8
A. (18 - 8) - (9 4/9 + 7/9)
B. (18 - 8 - 9)
C. (18 - 9 - 8) + (-4/9 + 7/9)
D. (8 - 18) + (4/9 + 7/9)
1 answer
1 answer