Join IDNLearn.com today and start getting the answers you've been searching for. Ask any question and receive timely, accurate responses from our dedicated community of experts.
Sagot :
Let's work through the given problem step-by-step.
### Step 1: Simplify the Numerator
The expression for the numerator is:
[tex]\[ \frac{2}{5} \div \frac{1}{2} \text { of } \frac{4}{9} - 1 \frac{1}{10} \][/tex]
First, we convert the mixed number [tex]\(1 \frac{1}{10}\)[/tex] to an improper fraction:
[tex]\[ 1 \frac{1}{10} = 1 + \frac{1}{10} = \frac{10}{10} + \frac{1}{10} = \frac{11}{10} \][/tex]
Next, we handle the division and multiplication:
[tex]\[ \frac{2}{5} \div \frac{1}{2} = \frac{2}{5} \times 2 = \frac{2 \times 2}{5} = \frac{4}{5} \][/tex]
Then, we multiply by [tex]\(\frac{4}{9}\)[/tex]:
[tex]\[ \frac{4}{5} \times \frac{4}{9} = \frac{4 \times 4}{5 \times 9} = \frac{16}{45} \][/tex]
We now subtract the improper fraction:
[tex]\[ \frac{16}{45} - \frac{11}{10} \][/tex]
To subtract these fractions, we need a common denominator. The least common multiple of 45 and 10 is 90.
Convert each fraction to have a denominator of 90:
[tex]\[ \frac{16}{45} = \frac{16 \times 2}{45 \times 2} = \frac{32}{90} \][/tex]
[tex]\[ \frac{11}{10} = \frac{11 \times 9}{10 \times 9} = \frac{99}{90} \][/tex]
Now subtract:
[tex]\[ \frac{32}{90} - \frac{99}{90} = \frac{32 - 99}{90} = \frac{-67}{90} \][/tex]
### Step 2: Simplify the Denominator
The expression for the denominator is:
[tex]\[ \frac{1}{8} - \frac{1}{6} \times \frac{3}{8} \][/tex]
First, handle the multiplication:
[tex]\[ \frac{1}{6} \times \frac{3}{8} = \frac{1 \times 3}{6 \times 8} = \frac{3}{48} = \frac{1}{16} \][/tex]
Then, we subtract:
[tex]\[ \frac{1}{8} - \frac{1}{16} \][/tex]
To subtract these, we need a common denominator. The least common multiple of 8 and 16 is 16.
Convert each fraction to have a denominator of 16:
[tex]\[ \frac{1}{8} = \frac{1 \times 2}{8 \times 2} = \frac{2}{16} \][/tex]
Now subtract:
[tex]\[ \frac{2}{16} - \frac{1}{16} = \frac{2 - 1}{16} = \frac{1}{16} \][/tex]
### Step 3: Final Division
Now divide the simplified numerator by the simplified denominator:
[tex]\[ \frac{\frac{-67}{90}}{\frac{1}{16}} = \frac{-67}{90} \times 16 = -\frac{67 \times 16}{90} = -\frac{1072}{90} \][/tex]
Simplify the fraction:
[tex]\[ - \frac{1072}{90} = - \frac{536}{45} \][/tex]
Convert it to a mixed number:
[tex]\[ - \frac{536}{45} = -11 \frac{41}{45} \][/tex]
Thus, the final result, as a mixed number in its simplest form, is:
[tex]\[ -11 \frac{41}{45} \][/tex]
### Step 1: Simplify the Numerator
The expression for the numerator is:
[tex]\[ \frac{2}{5} \div \frac{1}{2} \text { of } \frac{4}{9} - 1 \frac{1}{10} \][/tex]
First, we convert the mixed number [tex]\(1 \frac{1}{10}\)[/tex] to an improper fraction:
[tex]\[ 1 \frac{1}{10} = 1 + \frac{1}{10} = \frac{10}{10} + \frac{1}{10} = \frac{11}{10} \][/tex]
Next, we handle the division and multiplication:
[tex]\[ \frac{2}{5} \div \frac{1}{2} = \frac{2}{5} \times 2 = \frac{2 \times 2}{5} = \frac{4}{5} \][/tex]
Then, we multiply by [tex]\(\frac{4}{9}\)[/tex]:
[tex]\[ \frac{4}{5} \times \frac{4}{9} = \frac{4 \times 4}{5 \times 9} = \frac{16}{45} \][/tex]
We now subtract the improper fraction:
[tex]\[ \frac{16}{45} - \frac{11}{10} \][/tex]
To subtract these fractions, we need a common denominator. The least common multiple of 45 and 10 is 90.
Convert each fraction to have a denominator of 90:
[tex]\[ \frac{16}{45} = \frac{16 \times 2}{45 \times 2} = \frac{32}{90} \][/tex]
[tex]\[ \frac{11}{10} = \frac{11 \times 9}{10 \times 9} = \frac{99}{90} \][/tex]
Now subtract:
[tex]\[ \frac{32}{90} - \frac{99}{90} = \frac{32 - 99}{90} = \frac{-67}{90} \][/tex]
### Step 2: Simplify the Denominator
The expression for the denominator is:
[tex]\[ \frac{1}{8} - \frac{1}{6} \times \frac{3}{8} \][/tex]
First, handle the multiplication:
[tex]\[ \frac{1}{6} \times \frac{3}{8} = \frac{1 \times 3}{6 \times 8} = \frac{3}{48} = \frac{1}{16} \][/tex]
Then, we subtract:
[tex]\[ \frac{1}{8} - \frac{1}{16} \][/tex]
To subtract these, we need a common denominator. The least common multiple of 8 and 16 is 16.
Convert each fraction to have a denominator of 16:
[tex]\[ \frac{1}{8} = \frac{1 \times 2}{8 \times 2} = \frac{2}{16} \][/tex]
Now subtract:
[tex]\[ \frac{2}{16} - \frac{1}{16} = \frac{2 - 1}{16} = \frac{1}{16} \][/tex]
### Step 3: Final Division
Now divide the simplified numerator by the simplified denominator:
[tex]\[ \frac{\frac{-67}{90}}{\frac{1}{16}} = \frac{-67}{90} \times 16 = -\frac{67 \times 16}{90} = -\frac{1072}{90} \][/tex]
Simplify the fraction:
[tex]\[ - \frac{1072}{90} = - \frac{536}{45} \][/tex]
Convert it to a mixed number:
[tex]\[ - \frac{536}{45} = -11 \frac{41}{45} \][/tex]
Thus, the final result, as a mixed number in its simplest form, is:
[tex]\[ -11 \frac{41}{45} \][/tex]
Thank you for being part of this discussion. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Trust IDNLearn.com for all your queries. We appreciate your visit and hope to assist you again soon.
