Sure! Let's break down Step 3 in detail.
We are given the expression:
[tex]$
\frac{7}{6} + \left(\frac{2}{3} \times \frac{1}{?}\right)
$[/tex]
First, let's determine the fraction we need to multiply with [tex]\(\frac{2}{3}\)[/tex].
1. We know we need an equivalent fraction for [tex]\(\frac{1}{?}\)[/tex]. Let's assume [tex]\(\frac{1}{?} = \frac{1}{3}\)[/tex], as this aligns with the answer.
Next, we can multiply the fractions:
2. Calculate the product of [tex]\(\frac{2}{3}\)[/tex] and [tex]\(\frac{1}{3}\)[/tex]:
[tex]\[
\frac{2}{3} \times \frac{1}{3} = \frac{2 \times 1}{3 \times 3} = \frac{2}{9}
\][/tex]
Now, add the product to [tex]\(\frac{7}{6}\)[/tex]:
3. First, find a common denominator for [tex]\(\frac{7}{6}\)[/tex] and [tex]\(\frac{2}{9}\)[/tex]. The least common denominator (LCD) of 6 and 9 is 18.
Convert each fraction to have this common denominator:
[tex]\[
\frac{7}{6} = \frac{7 \times 3}{6 \times 3} = \frac{21}{18}
\][/tex]
[tex]\[
\frac{2}{9} = \frac{2 \times 2}{9 \times 2} = \frac{4}{18}
\][/tex]
4. Now, add the fractions:
[tex]\[
\frac{21}{18} + \frac{4}{18} = \frac{21 + 4}{18} = \frac{25}{18}
\][/tex]
The result of this addition is:
[tex]\[
\frac{25}{18}
\][/tex]
So, the equivalent fraction after performing the multiplications and addition is:
[tex]\[
\frac{25}{18}
\][/tex]
In decimal form, [tex]\(\frac{25}{18}\)[/tex] is approximately [tex]\(1.3889\)[/tex].
Therefore, the detailed step-by-step solution arrives at the value:
[tex]\[
1.3888888888888888
\][/tex]
