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Sagot :
Certainly! Let's convert each given rational number into a fraction in the form [tex]\(\frac{a}{b}\)[/tex], where [tex]\(a\)[/tex] and [tex]\(b\)[/tex] are integers.
1. Convert 0.3 to the form [tex]\(\frac{a}{b}\)[/tex]:
The decimal 0.3 can be written as [tex]\(\frac{3}{10}\)[/tex] because 3 is in the tenths place.
So, [tex]\(0.3 = \frac{3}{10}\)[/tex].
2. Convert [tex]\(2 \frac{2}{8}\)[/tex] to the form [tex]\(\frac{a}{b}\)[/tex]:
First, convert the mixed number to an improper fraction.
[tex]\[ 2 \frac{2}{8} = 2 + \frac{2}{8} \][/tex]
Next, simplify [tex]\(\frac{2}{8}\)[/tex]:
[tex]\[ \frac{2}{8} = \frac{1}{4} \implies 2 + \frac{1}{4} \][/tex]
Convert [tex]\(2\)[/tex] to a fraction with 4 as the denominator:
[tex]\[ 2 = \frac{8}{4} \implies \frac{8}{4} + \frac{1}{4} = \frac{9}{4} \][/tex]
So, [tex]\(2 \frac{2}{8} = \frac{9}{4}\)[/tex].
3. Convert -5 to the form [tex]\(\frac{a}{b}\)[/tex]:
The integer -5 can be written as a fraction with 1 as the denominator.
[tex]\[ -5 = \frac{-5}{1} \][/tex]
4. Convert [tex]\(-1 \frac{3}{4}\)[/tex] to the form [tex]\(\frac{a}{b}\)[/tex]:
First, convert the mixed number to an improper fraction.
[tex]\[ -1 \frac{3}{4} = -1 - \frac{3}{4} \][/tex]
Convert -1 to a fraction with 4 as the denominator:
[tex]\[ -1 = \frac{-4}{4} \implies \frac{-4}{4} - \frac{3}{4} = \frac{-7}{4} \][/tex]
So, [tex]\(-1 \frac{3}{4} = \frac{-7}{4}\)[/tex].
5. Convert -4.5 to the form [tex]\(\frac{a}{b}\)[/tex]:
The decimal -4.5 can be broken down into two parts: -4 and -0.5.
[tex]\[ -4.5 = -4 - 0.5 \][/tex]
Convert -0.5 to a fraction:
[tex]\[ -0.5 = -\frac{1}{2} \][/tex]
Now, convert -4 to a fraction with 2 as the denominator:
[tex]\[ -4 = \frac{-8}{2} \implies \frac{-8}{2} - \frac{1}{2} = \frac{-9}{2} \][/tex]
So, [tex]\(-4.5 = \frac{-9}{2}\)[/tex].
6. Convert 3 to the form [tex]\(\frac{a}{b}\)[/tex]:
The integer 3 can be written as a fraction with 1 as the denominator.
[tex]\[ 3 = \frac{3}{1} \][/tex]
Using the above conversions, we get the following fractions:
1. 0.3 = [tex]\(\frac{3}{10}\)[/tex]
2. [tex]\(2 \frac{2}{8}\)[/tex] = [tex]\(\frac{9}{4}\)[/tex]
3. -5 = [tex]\(\frac{-5}{1}\)[/tex]
4. [tex]\(-1 \frac{3}{4}\)[/tex] = [tex]\(\frac{-7}{4}\)[/tex]
5. -4.5 = [tex]\(\frac{-9}{2}\)[/tex]
6. 3 = [tex]\(\frac{3}{1}\)[/tex]
So, the final results are:
1. [tex]\(0.3 = \frac{3}{10}\)[/tex]
2. [tex]\(2 \frac{2}{8} = \frac{9}{4}\)[/tex]
3. [tex]\(-5 = \frac{-5}{1}\)[/tex]
4. [tex]\(-1 \frac{3}{4} = \frac{-7}{4}\)[/tex]
5. [tex]\(-4.5 = \frac{-9}{2}\)[/tex]
6. [tex]\(3 = \frac{3}{1}\)[/tex]
1. Convert 0.3 to the form [tex]\(\frac{a}{b}\)[/tex]:
The decimal 0.3 can be written as [tex]\(\frac{3}{10}\)[/tex] because 3 is in the tenths place.
So, [tex]\(0.3 = \frac{3}{10}\)[/tex].
2. Convert [tex]\(2 \frac{2}{8}\)[/tex] to the form [tex]\(\frac{a}{b}\)[/tex]:
First, convert the mixed number to an improper fraction.
[tex]\[ 2 \frac{2}{8} = 2 + \frac{2}{8} \][/tex]
Next, simplify [tex]\(\frac{2}{8}\)[/tex]:
[tex]\[ \frac{2}{8} = \frac{1}{4} \implies 2 + \frac{1}{4} \][/tex]
Convert [tex]\(2\)[/tex] to a fraction with 4 as the denominator:
[tex]\[ 2 = \frac{8}{4} \implies \frac{8}{4} + \frac{1}{4} = \frac{9}{4} \][/tex]
So, [tex]\(2 \frac{2}{8} = \frac{9}{4}\)[/tex].
3. Convert -5 to the form [tex]\(\frac{a}{b}\)[/tex]:
The integer -5 can be written as a fraction with 1 as the denominator.
[tex]\[ -5 = \frac{-5}{1} \][/tex]
4. Convert [tex]\(-1 \frac{3}{4}\)[/tex] to the form [tex]\(\frac{a}{b}\)[/tex]:
First, convert the mixed number to an improper fraction.
[tex]\[ -1 \frac{3}{4} = -1 - \frac{3}{4} \][/tex]
Convert -1 to a fraction with 4 as the denominator:
[tex]\[ -1 = \frac{-4}{4} \implies \frac{-4}{4} - \frac{3}{4} = \frac{-7}{4} \][/tex]
So, [tex]\(-1 \frac{3}{4} = \frac{-7}{4}\)[/tex].
5. Convert -4.5 to the form [tex]\(\frac{a}{b}\)[/tex]:
The decimal -4.5 can be broken down into two parts: -4 and -0.5.
[tex]\[ -4.5 = -4 - 0.5 \][/tex]
Convert -0.5 to a fraction:
[tex]\[ -0.5 = -\frac{1}{2} \][/tex]
Now, convert -4 to a fraction with 2 as the denominator:
[tex]\[ -4 = \frac{-8}{2} \implies \frac{-8}{2} - \frac{1}{2} = \frac{-9}{2} \][/tex]
So, [tex]\(-4.5 = \frac{-9}{2}\)[/tex].
6. Convert 3 to the form [tex]\(\frac{a}{b}\)[/tex]:
The integer 3 can be written as a fraction with 1 as the denominator.
[tex]\[ 3 = \frac{3}{1} \][/tex]
Using the above conversions, we get the following fractions:
1. 0.3 = [tex]\(\frac{3}{10}\)[/tex]
2. [tex]\(2 \frac{2}{8}\)[/tex] = [tex]\(\frac{9}{4}\)[/tex]
3. -5 = [tex]\(\frac{-5}{1}\)[/tex]
4. [tex]\(-1 \frac{3}{4}\)[/tex] = [tex]\(\frac{-7}{4}\)[/tex]
5. -4.5 = [tex]\(\frac{-9}{2}\)[/tex]
6. 3 = [tex]\(\frac{3}{1}\)[/tex]
So, the final results are:
1. [tex]\(0.3 = \frac{3}{10}\)[/tex]
2. [tex]\(2 \frac{2}{8} = \frac{9}{4}\)[/tex]
3. [tex]\(-5 = \frac{-5}{1}\)[/tex]
4. [tex]\(-1 \frac{3}{4} = \frac{-7}{4}\)[/tex]
5. [tex]\(-4.5 = \frac{-9}{2}\)[/tex]
6. [tex]\(3 = \frac{3}{1}\)[/tex]
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