Let's analyze each equation step-by-step.
A. [tex]\( -8 \div (-2) = -4 \)[/tex]
To divide [tex]\(-8\)[/tex] by [tex]\(-2\)[/tex]:
[tex]\[ \frac{-8}{-2} = 4 \][/tex]
Clearly, [tex]\(4\)[/tex] is not equal to [tex]\(-4\)[/tex].
So,
False.
B. [tex]\( 3 \div \left(-\frac{1}{3}\right) = -1 \)[/tex]
To divide [tex]\(3\)[/tex] by [tex]\(-\frac{1}{3}\)[/tex]:
[tex]\[ 3 \div \left(-\frac{1}{3}\right) = 3 \times \left(-3\right) = -9 \][/tex]
Clearly, [tex]\(-9\)[/tex] is not equal to [tex]\(-1\)[/tex].
So,
False.
C. [tex]\( 4.4 \div 12.5 = 3.52 \)[/tex]
To divide [tex]\(4.4\)[/tex] by [tex]\(12.5\)[/tex]:
[tex]\[ \frac{4.4}{12.5} = 0.352 \][/tex]
Clearly, [tex]\(0.352\)[/tex] is not equal to [tex]\(3.52\)[/tex].
So,
False.
D. [tex]\( -1 \frac{1}{6} \div \frac{1}{3} = -3 \frac{1}{2} \)[/tex]
First, convert mixed number to improper fraction:
[tex]\[ -1 \frac{1}{6} = -\left(1 + \frac{1}{6}\right) = -\frac{7}{6} \][/tex]
Now divide by [tex]\(\frac{1}{3}\)[/tex]:
[tex]\[ -\frac{7}{6} \div \frac{1}{3} = -\frac{7}{6} \times 3 = -\frac{21}{6} = -\frac{7}{2} = -3.5 \][/tex]
which is:
[tex]\[ -3 \frac{1}{2} \][/tex]
So,
True.
E. [tex]\( 1 \frac{2}{9} \div -2 \frac{1}{3} = \frac{-11}{21} \)[/tex]
First, convert mixed numbers to improper fractions:
[tex]\[ 1 \frac{2}{9} = 1 + \frac{2}{9} = \frac{11}{9} \][/tex]
[tex]\[ -2 \frac{1}{3} = -\left(2 + \frac{1}{3}\right) = -\frac{7}{3} \][/tex]
Now divide [tex]\(\frac{11}{9}\)[/tex] by [tex]\(-\frac{7}{3}\)[/tex]:
[tex]\[ \frac{11}{9} \div -\frac{7}{3} = \frac{11}{9} \times -\frac{3}{7} = \frac{11 \times -3}{9 \times 7} = \frac{-33}{63} = \frac{-11}{21} \][/tex]
So,
True.
F. [tex]\(-\frac{1}{6} \div -\frac{1}{9} \div \frac{3}{2} = 1 \)[/tex]
First, evaluate the left part:
[tex]\[ -\frac{1}{6} \div -\frac{1}{9} = \frac{-1}{6} \times -9 = \frac{9}{6} = \frac{3}{2} \][/tex]
Now take [tex]\(\frac{3}{2}\)[/tex] and divide it by [tex]\(\frac{3}{2}\)[/tex]:
[tex]\[ \frac{3}{2} \div \frac{3}{2} = 1 \][/tex]
So,
True.
Based on this evaluation, the results are:
A: False
B: False
C: False
D: True
E: True
F: True
