To express [tex]\(3.7\)[/tex] as a mixed number, let's go through the steps in detail.
Let [tex]\( x = 3.7 \)[/tex].
First, consider multiplying [tex]\( x \)[/tex] by [tex]\( 10 \)[/tex]:
[tex]\[
10x = 37.0
\][/tex]
Next, we observe the value when [tex]\( x \)[/tex] is multiplied by [tex]\( 9 \)[/tex]:
[tex]\[
9x = 33.3
\][/tex]
By simple subtraction:
[tex]\[
10x - x = 37.0 - 3.7
\][/tex]
[tex]\[
9x = 33.3
\][/tex]
Given that [tex]\( x = 3.7 \)[/tex], we can separate it into an integer part and a fractional part.
Here, the integer part of [tex]\( 3.7 \)[/tex] is:
[tex]\[
\text{Integer part} = 3
\][/tex]
Next, we determine the fractional part:
[tex]\[
\text{Fractional part} = 3.7 - 3 = 0.7
\][/tex]
Now, we convert the fractional part [tex]\( 0.7 \)[/tex] into a fraction:
[tex]\[
0.7 = \frac{7}{10}
\][/tex]
Therefore, the mixed number form of [tex]\( 3.7 \)[/tex] is written as the sum of its integer and fractional parts:
[tex]\[
3.7 = 3 + \frac{7}{10}
\][/tex]
So [tex]\( 3.7 \)[/tex] is equal to:
[tex]\[
3 \frac{7}{10}
\][/tex]
