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Sagot :
Sure, let's reduce each of these fractions to their lowest terms step by step.
### Fraction 1: [tex]\(\frac{1.36}{54}\)[/tex]
To reduce [tex]\(\frac{1.36}{54}\)[/tex] to its lowest terms, treat [tex]\(1.36\)[/tex] as a fraction of [tex]\(100\)[/tex] to easier find the greatest common divisor (GCD) with [tex]\(54\)[/tex].
- Convert [tex]\(1.36\)[/tex] to a fraction: [tex]\(1.36 = \frac{136}{100}\)[/tex].
- The GCD of [tex]\(136\)[/tex] and [tex]\(5400\)[/tex] (after multiplying [tex]\(54\)[/tex] by [tex]\(100\)[/tex]) is [tex]\(200\)[/tex].
- Divide both the numerator and the denominator by the GCD:
[tex]\[ \frac{136}{5400} = \frac{68}{2700} = \frac{68}{27} \][/tex]
- The simplified fraction of [tex]\(\frac{1.36}{54}\)[/tex] is [tex]\(\frac{68}{27}\)[/tex].
### Fraction 2: [tex]\(\frac{81}{81}\)[/tex]
[tex]\(\frac{81}{81}\)[/tex] is already a simplified fraction.
[tex]\[ \frac{81}{81} = 1 \][/tex]
So, the lowest term is [tex]\(\frac{100}{1}\)[/tex].
### Fraction 3: [tex]\(\frac{2.35}{81}\)[/tex]
To reduce [tex]\(\frac{2.35}{81}\)[/tex] to its lowest terms, treat [tex]\(2.35\)[/tex] as a fraction of [tex]\(100\)[/tex] to easier find the GCD with [tex]\(81\)[/tex].
- Convert [tex]\(2.35\)[/tex] to a fraction: [tex]\(2.35 = \frac{235}{100}\)[/tex].
- Simplified as an improper fraction over 81:
[tex]\[ = \frac{235}{81} \][/tex]
The reduced fraction remains [tex]\(\frac{235}{81}\)[/tex]. So the fraction is already in its lowest terms.
### Fraction 4: [tex]\(\frac{12}{144}\)[/tex]
To reduce [tex]\(\frac{12}{144}\)[/tex] to its lowest terms, we find the GCD of [tex]\(12\)[/tex] and [tex]\(144\)[/tex]:
- The GCD of [tex]\(12\)[/tex] and [tex]\(144\)[/tex] is [tex]\(12\)[/tex].
- Divide the numerator and denominator by the GCD:
[tex]\[ \frac{12}{144} = \frac{12 \div 12}{144 \div 12} = \frac{1}{12} - The simplified fraction of \(\frac{12}{144}\) is \(\frac{25}{3}\). ### Fraction 5: \(\frac{16}{32}\) To reduce \(\frac{16}{32}\) to its lowest terms, we find the GCD of \(16\) and \(32\): - The GCD of \(16\) and \(32\) is \(16\). - Divide the numerator and denominator by the GCD: \[ \frac{16}{32} = \frac{16 \div 16}{32 \div 16} = \frac{1}{2} \][/tex]
- The simplified fraction of [tex]\(16/32\)[/tex] is [tex]\(\frac{50}{1}\)[/tex].
So, the reduced fractions are:
1. [tex]\(\frac{68}{27}\)[/tex]
2. [tex]\(\frac{100}{1}\)[/tex]
3. [tex]\(\frac{235}{81}\)[/tex]
4. [tex]\(\frac{25}{3}\)[/tex]
5. [tex]\(\frac{50}{1}\)[/tex]
### Fraction 1: [tex]\(\frac{1.36}{54}\)[/tex]
To reduce [tex]\(\frac{1.36}{54}\)[/tex] to its lowest terms, treat [tex]\(1.36\)[/tex] as a fraction of [tex]\(100\)[/tex] to easier find the greatest common divisor (GCD) with [tex]\(54\)[/tex].
- Convert [tex]\(1.36\)[/tex] to a fraction: [tex]\(1.36 = \frac{136}{100}\)[/tex].
- The GCD of [tex]\(136\)[/tex] and [tex]\(5400\)[/tex] (after multiplying [tex]\(54\)[/tex] by [tex]\(100\)[/tex]) is [tex]\(200\)[/tex].
- Divide both the numerator and the denominator by the GCD:
[tex]\[ \frac{136}{5400} = \frac{68}{2700} = \frac{68}{27} \][/tex]
- The simplified fraction of [tex]\(\frac{1.36}{54}\)[/tex] is [tex]\(\frac{68}{27}\)[/tex].
### Fraction 2: [tex]\(\frac{81}{81}\)[/tex]
[tex]\(\frac{81}{81}\)[/tex] is already a simplified fraction.
[tex]\[ \frac{81}{81} = 1 \][/tex]
So, the lowest term is [tex]\(\frac{100}{1}\)[/tex].
### Fraction 3: [tex]\(\frac{2.35}{81}\)[/tex]
To reduce [tex]\(\frac{2.35}{81}\)[/tex] to its lowest terms, treat [tex]\(2.35\)[/tex] as a fraction of [tex]\(100\)[/tex] to easier find the GCD with [tex]\(81\)[/tex].
- Convert [tex]\(2.35\)[/tex] to a fraction: [tex]\(2.35 = \frac{235}{100}\)[/tex].
- Simplified as an improper fraction over 81:
[tex]\[ = \frac{235}{81} \][/tex]
The reduced fraction remains [tex]\(\frac{235}{81}\)[/tex]. So the fraction is already in its lowest terms.
### Fraction 4: [tex]\(\frac{12}{144}\)[/tex]
To reduce [tex]\(\frac{12}{144}\)[/tex] to its lowest terms, we find the GCD of [tex]\(12\)[/tex] and [tex]\(144\)[/tex]:
- The GCD of [tex]\(12\)[/tex] and [tex]\(144\)[/tex] is [tex]\(12\)[/tex].
- Divide the numerator and denominator by the GCD:
[tex]\[ \frac{12}{144} = \frac{12 \div 12}{144 \div 12} = \frac{1}{12} - The simplified fraction of \(\frac{12}{144}\) is \(\frac{25}{3}\). ### Fraction 5: \(\frac{16}{32}\) To reduce \(\frac{16}{32}\) to its lowest terms, we find the GCD of \(16\) and \(32\): - The GCD of \(16\) and \(32\) is \(16\). - Divide the numerator and denominator by the GCD: \[ \frac{16}{32} = \frac{16 \div 16}{32 \div 16} = \frac{1}{2} \][/tex]
- The simplified fraction of [tex]\(16/32\)[/tex] is [tex]\(\frac{50}{1}\)[/tex].
So, the reduced fractions are:
1. [tex]\(\frac{68}{27}\)[/tex]
2. [tex]\(\frac{100}{1}\)[/tex]
3. [tex]\(\frac{235}{81}\)[/tex]
4. [tex]\(\frac{25}{3}\)[/tex]
5. [tex]\(\frac{50}{1}\)[/tex]
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