To solve this problem, let's carefully analyse the values of each fraction involved.
We need to determine which of the given options fits best in the blank space between [tex]\(\frac{7}{8}\)[/tex] and [tex]\(\frac{3}{5}\)[/tex] in terms of their decimal values. Let's start by converting each fraction to its decimal equivalent for easier comparison.
1. Convert [tex]\(\frac{7}{8}\)[/tex] to a decimal:
[tex]\[
\frac{7}{8} = 0.875
\][/tex]
2. Convert [tex]\(\frac{3}{5}\)[/tex] to a decimal:
[tex]\[
\frac{3}{5} = 0.6
\][/tex]
Now, we need to compare the decimal values of the given options and decide which is suitable to place in between [tex]\(0.875\)[/tex] and [tex]\(0.6\)[/tex].
- Option A: [tex]\(\frac{1}{4}\)[/tex]
[tex]\[
\frac{1}{4} = 0.25
\][/tex]
- Option B: [tex]\(\frac{3}{8}\)[/tex]
[tex]\[
\frac{3}{8} = 0.375
\][/tex]
- Option C: [tex]\(\frac{1}{2}\)[/tex]
[tex]\[
\frac{1}{2} = 0.5
\][/tex]
- Option D: [tex]\(\frac{3}{4}\)[/tex]
[tex]\[
\frac{3}{4} = 0.75
\][/tex]
We now have the decimal equivalents:
- [tex]\(\frac{7}{8} = 0.875\)[/tex]
- [tex]\(\frac{3}{5} = 0.6\)[/tex]
- [tex]\(\frac{1}{4} = 0.25\)[/tex]
- [tex]\(\frac{3}{8} = 0.375\)[/tex]
- [tex]\(\frac{1}{2} = 0.5\)[/tex]
- [tex]\(\frac{3}{4} = 0.75\)[/tex]
The correct fraction to fit between [tex]\(0.875\)[/tex] and [tex]\(0.6\)[/tex] is [tex]\(0.75\)[/tex]. Therefore, the correct choice is:
[tex]\[
\boxed{D\ \frac{3}{4}}
\][/tex]
