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Sagot :
To fill in the blank spaces with the correct inequality symbols, let's analyze each part step-by-step:
### a. [tex]\(\frac{1}{2} \quad \frac{3}{4}\)[/tex]
[tex]\[ \frac{1}{2} < \frac{3}{4} \][/tex]
So, the correct inequality is:
[tex]\[ \frac{1}{2} < \frac{3}{4} \][/tex]
### b. 8
For [tex]\( \frac{3}{4} - \frac{1}{2} \)[/tex]:
[tex]\[ \frac{3}{4} - \frac{1}{2} = \frac{3}{4} - \frac{2}{4} = \frac{1}{4} = 0.25 \][/tex]
There is no comparison symbol needed in this context; it simply represents the result of the operation. The difference between [tex]\( \frac{3}{4} \)[/tex] and [tex]\( \frac{1}{2} \)[/tex]:
So, we have:
[tex]\[ \frac{3}{4} - \frac{1}{2} = 0.25 \][/tex]
### d. 1
Next, for [tex]\(\frac{1}{2} \quad 18\)[/tex]:
We are comparing [tex]\(\frac{1}{2}\)[/tex] with [tex]\(0.18\)[/tex].
[tex]\[ \frac{1}{2} = 0.5 \quad \text{and} \quad 0.18 \][/tex]
So,
[tex]\[ \frac{1}{2} > 0.18 \][/tex]
### f. [tex]\(\frac{7}{18} \quad \frac{3}{4}\)[/tex]
Comparing [tex]\(\frac{7}{18}\)[/tex] and [tex]\(\frac{3}{4}\)[/tex]:
[tex]\[ \frac{7}{18} \approx 0.388 \quad \text{and} \quad \frac{3}{4} = 0.75 \][/tex]
So,
[tex]\[ \frac{7}{18} < \frac{3}{4} \][/tex]
### g. [tex]\(\frac{3}{4} \quad \frac{6}{8}\)[/tex]
Comparing [tex]\(\frac{3}{4}\)[/tex] with [tex]\(\frac{6}{8}\)[/tex]:
[tex]\[ \frac{3}{4} = \frac{6}{8} = 0.75 \][/tex]
So,
[tex]\[ \frac{3}{4} = \frac{6}{8} \][/tex]
### h. [tex]\(\frac{1}{8} \quad \frac{1}{4}\)[/tex]
Comparing [tex]\(\frac{1}{8}\)[/tex] with [tex]\(\frac{1}{4}\)[/tex]:
[tex]\[ \frac{1}{8} \approx 0.125 \quad \text{and} \quad \frac{1}{4} = 0.25 \][/tex]
So,
[tex]\[ \frac{1}{8} < \frac{1}{4} \][/tex]
### i. [tex]\(\frac{5}{8} \quad \frac{2}{4}\)[/tex]
Comparing [tex]\(\frac{5}{8}\)[/tex] with [tex]\(\frac{2}{4}\)[/tex]:
[tex]\[ \frac{5}{8} = 0.625 \quad \text{and} \quad \frac{2}{4} = 0.5 \][/tex]
So,
[tex]\[ \frac{5}{8} > \frac{2}{4} \][/tex]
### j. [tex]\(\frac{1}{8} \quad \frac{2}{4}\)[/tex]
Comparing [tex]\(\frac{1}{8}\)[/tex] with [tex]\(\frac{2}{4}\)[/tex]:
[tex]\[ \frac{1}{8} \approx 0.125 \quad \text{and} \quad \frac{2}{4} = 0.5 \][/tex]
So,
[tex]\[ \frac{1}{8} < \frac{2}{4} \][/tex]
### Summary of Inequalities
a. [tex]\( \frac{1}{2} < \frac{3}{4} \)[/tex]
b. [tex]\( \frac{3}{4} - \frac{1}{2} = 0.25 \)[/tex]
c. [tex]\( \frac{1}{2} > 0.18 \)[/tex]
d. [tex]\( \frac{7}{18} < \frac{3}{4} \)[/tex]
e. [tex]\( \frac{3}{4} = \frac{6}{8} \)[/tex]
f. [tex]\( \frac{1}{8} < \frac{1}{4} \)[/tex]
g. [tex]\( \frac{5}{8} > \frac{2}{4} \)[/tex]
h. [tex]\( \frac{1}{8} < \frac{2}{4} \)[/tex]
### a. [tex]\(\frac{1}{2} \quad \frac{3}{4}\)[/tex]
[tex]\[ \frac{1}{2} < \frac{3}{4} \][/tex]
So, the correct inequality is:
[tex]\[ \frac{1}{2} < \frac{3}{4} \][/tex]
### b. 8
For [tex]\( \frac{3}{4} - \frac{1}{2} \)[/tex]:
[tex]\[ \frac{3}{4} - \frac{1}{2} = \frac{3}{4} - \frac{2}{4} = \frac{1}{4} = 0.25 \][/tex]
There is no comparison symbol needed in this context; it simply represents the result of the operation. The difference between [tex]\( \frac{3}{4} \)[/tex] and [tex]\( \frac{1}{2} \)[/tex]:
So, we have:
[tex]\[ \frac{3}{4} - \frac{1}{2} = 0.25 \][/tex]
### d. 1
Next, for [tex]\(\frac{1}{2} \quad 18\)[/tex]:
We are comparing [tex]\(\frac{1}{2}\)[/tex] with [tex]\(0.18\)[/tex].
[tex]\[ \frac{1}{2} = 0.5 \quad \text{and} \quad 0.18 \][/tex]
So,
[tex]\[ \frac{1}{2} > 0.18 \][/tex]
### f. [tex]\(\frac{7}{18} \quad \frac{3}{4}\)[/tex]
Comparing [tex]\(\frac{7}{18}\)[/tex] and [tex]\(\frac{3}{4}\)[/tex]:
[tex]\[ \frac{7}{18} \approx 0.388 \quad \text{and} \quad \frac{3}{4} = 0.75 \][/tex]
So,
[tex]\[ \frac{7}{18} < \frac{3}{4} \][/tex]
### g. [tex]\(\frac{3}{4} \quad \frac{6}{8}\)[/tex]
Comparing [tex]\(\frac{3}{4}\)[/tex] with [tex]\(\frac{6}{8}\)[/tex]:
[tex]\[ \frac{3}{4} = \frac{6}{8} = 0.75 \][/tex]
So,
[tex]\[ \frac{3}{4} = \frac{6}{8} \][/tex]
### h. [tex]\(\frac{1}{8} \quad \frac{1}{4}\)[/tex]
Comparing [tex]\(\frac{1}{8}\)[/tex] with [tex]\(\frac{1}{4}\)[/tex]:
[tex]\[ \frac{1}{8} \approx 0.125 \quad \text{and} \quad \frac{1}{4} = 0.25 \][/tex]
So,
[tex]\[ \frac{1}{8} < \frac{1}{4} \][/tex]
### i. [tex]\(\frac{5}{8} \quad \frac{2}{4}\)[/tex]
Comparing [tex]\(\frac{5}{8}\)[/tex] with [tex]\(\frac{2}{4}\)[/tex]:
[tex]\[ \frac{5}{8} = 0.625 \quad \text{and} \quad \frac{2}{4} = 0.5 \][/tex]
So,
[tex]\[ \frac{5}{8} > \frac{2}{4} \][/tex]
### j. [tex]\(\frac{1}{8} \quad \frac{2}{4}\)[/tex]
Comparing [tex]\(\frac{1}{8}\)[/tex] with [tex]\(\frac{2}{4}\)[/tex]:
[tex]\[ \frac{1}{8} \approx 0.125 \quad \text{and} \quad \frac{2}{4} = 0.5 \][/tex]
So,
[tex]\[ \frac{1}{8} < \frac{2}{4} \][/tex]
### Summary of Inequalities
a. [tex]\( \frac{1}{2} < \frac{3}{4} \)[/tex]
b. [tex]\( \frac{3}{4} - \frac{1}{2} = 0.25 \)[/tex]
c. [tex]\( \frac{1}{2} > 0.18 \)[/tex]
d. [tex]\( \frac{7}{18} < \frac{3}{4} \)[/tex]
e. [tex]\( \frac{3}{4} = \frac{6}{8} \)[/tex]
f. [tex]\( \frac{1}{8} < \frac{1}{4} \)[/tex]
g. [tex]\( \frac{5}{8} > \frac{2}{4} \)[/tex]
h. [tex]\( \frac{1}{8} < \frac{2}{4} \)[/tex]
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