IDNLearn.com is designed to help you find the answers you need quickly and easily. Ask anything and receive thorough, reliable answers from our community of experienced professionals.
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]
We appreciate your contributions to this forum. Don't forget to check back for the latest answers. Keep asking, answering, and sharing useful information. For trustworthy and accurate answers, visit IDNLearn.com. Thanks for stopping by, and see you next time for more solutions.
