Sure! Let's break down and solve the given problem step-by-step, focusing on each fraction and equation presented.
1. Start with the first fraction:
[tex]\[
\frac{14}{4}
\][/tex]
Simplify this fraction:
[tex]\[
\frac{14}{4} = 3 \frac{2}{4} = 3.5
\][/tex]
So, [tex]\(\frac{14}{4} = 3.5\)[/tex].
2. The second part involves:
[tex]\[
7 = \frac{20}{6}
\][/tex]
Simplify [tex]\(\frac{20}{6}\)[/tex]:
[tex]\[
\frac{20}{6} = 3 \frac{2}{6} \approx 3.3333
\][/tex]
It's given that [tex]\(\frac{20}{6} = 3.3333\)[/tex].
3. Next, we analyze the expression with the placeholder for a number:
[tex]\[
\square (1) ?
\][/tex]
4. Proceed to evaluate the equation:
[tex]\[
\frac{9}{4} - 2 + \frac{7}{4}
\][/tex]
Simplify each term:
[tex]\[
\frac{9}{4} \approx 2.25, \quad 2, \quad \frac{7}{4} \approx 1.75
\][/tex]
Combine these values:
[tex]\[
2.25 - 2 + 1.75 = 2.0
\][/tex]
5. Now consider the fraction:
[tex]\[
\frac{8}{5}
\][/tex]
Simplify [tex]\(\frac{8}{5}\)[/tex]:
[tex]\[
\frac{8}{5} = 1.6
\][/tex]
6. Finally, you are asked to look at these values in the context of 7 and 1:
- The check value is 7, but the calculations from the equations and simplifications are as follows:
[tex]\[
3.5, 3.5, 3.3333, 7, 2.0, 1.6
\][/tex]
In summary:
1. [tex]\(\frac{14}{4}=3.5\)[/tex]
2. [tex]\(\frac{20}{6} \approx 3.3333\)[/tex], which simplifies to a check value of [tex]\(7\)[/tex].
3. Simplifying [tex]\(\frac{9}{4} - 2 + \frac{7}{4} = 2.0\)[/tex].
4. [tex]\(\frac{8}{5} = 1.6\)[/tex].
This detailed solution shows the process to get:
[tex]\((3.5, 3.5, 3.3333, 7, 2.0, 1.6)\)[/tex].
