Answered

First, rewrite [tex]\frac{7}{8}[/tex] and [tex]\frac{9}{10}[/tex] so that they have a common denominator.

Then, use [tex]\ \textless \ , =,[/tex] or [tex]\ \textgreater \ [/tex] to order [tex]\frac{7}{8}[/tex] and [tex]\frac{9}{10}[/tex].

[tex]
\frac{7}{8} = \frac{\square}{\square} \quad ; \quad \frac{9}{10} = \frac{\square}{\square}
[/tex]

[tex]
\frac{7}{8} \square \frac{9}{10}
[/tex]



Answer :

GinnyAnswer
To compare the fractions [tex]\(\frac{7}{8}\)[/tex] and [tex]\(\frac{9}{10}\)[/tex], we first rewrite them with a common denominator.

Step 1: Find the common denominator.
The denominators are 8 and 10. The common denominator can be found by multiplying the two denominators:
[tex]\[ 8 \times 10 = 80 \][/tex]

Step 2: Rewrite each fraction with the common denominator of 80.

For [tex]\(\frac{7}{8}\)[/tex]:
[tex]\[ \frac{7}{8} = \frac{7 \times 10}{8 \times 10} = \frac{70}{80} \][/tex]

For [tex]\(\frac{9}{10}\)[/tex]:
[tex]\[ \frac{9}{10} = \frac{9 \times 8}{10 \times 8} = \frac{72}{80} \][/tex]

Step 3: Compare the numerators of the rewritten fractions:
[tex]\[ \frac{70}{80} \quad \text{and} \quad \frac{72}{80} \][/tex]

Since 70 is less than 72, we have:
[tex]\[ \frac{70}{80} < \frac{72}{80} \][/tex]

Thus, we can order the original fractions as follows:
[tex]\[ \frac{7}{8} < \frac{9}{10} \][/tex]

Therefore:
[tex]\[ \frac{7}{8} = \frac{70}{80} \quad ; \quad \frac{9}{10} = \frac{72}{80} \][/tex]

And in terms of comparison:
[tex]\[ \frac{7}{8} < \frac{9}{10} \][/tex]

So, the final answer is:
[tex]\[ \frac{7}{8} = \frac{70}{80} \quad ; \quad \frac{9}{10} = \frac{72}{80} \][/tex]
[tex]\[ \frac{7}{8} < \frac{9}{10} \][/tex]