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Sagot :
Sure! Let's solve each fraction step-by-step by finding the greatest common factor (GCF) and reducing them to their lowest terms.
### 1. Reduce [tex]\(\frac{1.36}{54}\)[/tex] to its lowest terms:
#### Step 1: Calculate the GCF of 1.36 and 54
- Convert 1.36 to a fraction: [tex]\(\frac{136}{100}\)[/tex]
- The numerator is 136 and the denominator is 5400 (since [tex]\(\frac{1.36}{54} = \frac{1.36100}{54100} = \frac{136}{5400}\)[/tex]).
Use the GCF method:
- [tex]\( \text{GCF}(136, 5400) = 8 \)[/tex]
#### Step 2: Divide both the numerator and the denominator by the GCF:
- Reduced numerator: [tex]\( \frac{136}{8} = 17 \)[/tex]
- Reduced denominator: [tex]\( \frac{5400}{8} = 675 \)[/tex]
Thus, [tex]\(\frac{1.36}{54} = \frac{17}{675}\)[/tex].
### 2. Reduce [tex]\(\frac{81}{81}\)[/tex] to its lowest terms:
#### Step 1: Calculate the GCF of 81 and 81
- Both the numerator and the denominator are 81.
- [tex]\( \text{GCF}(81, 81) = 81 \)[/tex]
#### Step 2: Divide both the numerator and the denominator by the GCF:
- Reduced numerator: [tex]\( \frac{81}{81} = 1 \)[/tex]
- Reduced denominator: [tex]\( \frac{81}{81} = 1 \)[/tex]
Thus, [tex]\(\frac{81}{81} = 1\)[/tex].
### 3. Reduce [tex]\(\frac{35}{81}\)[/tex] to its lowest terms:
#### Step 1: Calculate the GCF of 35 and 81
- The numbers 35 and 81 do not have any common factors other than 1.
- [tex]\( \text{GCF}(35, 81) = 1 \)[/tex]
#### Step 2: Since the GCF is 1, the fraction is already in its lowest terms:
- Fraction remains: [tex]\(\frac{35}{81}\)[/tex]
Thus, [tex]\(\frac{35}{81}\)[/tex] remains [tex]\(\frac{35}{81}\)[/tex].
### 4. Reduce [tex]\(\frac{12}{144}\)[/tex] to its lowest terms:
#### Step 1: Calculate the GCF of 12 and 144
- Both are divisible by 12.
- [tex]\( \text{GCF}(12, 144) = 12 \)[/tex]
#### Step 2: Divide both the numerator and the denominator by the GCF:
- Reduced numerator: [tex]\( \frac{12}{12} = 1 \)[/tex]
- Reduced denominator: [tex]\( \frac{144}{12} = 12 \)[/tex]
Thus, [tex]\(\frac{12}{144} = \frac{1}{12}\)[/tex].
### 5. Reduce [tex]\(\frac{16}{32}\)[/tex] to its lowest terms:
#### Step 1: Calculate the GCF of 16 and 32
- Both are divisible by 16.
- [tex]\( \text{GCF}(16, 32) = 16 \)[/tex]
#### Step 2: Divide both the numerator and the denominator by the GCF:
- Reduced numerator: [tex]\( \frac{16}{16} = 1 \)[/tex]
- Reduced denominator: [tex]\( \frac{32}{16} = 2 \)[/tex]
Thus, [tex]\(\frac{16}{32} = \frac{1}{2}\)[/tex].
### Summary
Here are the reduced forms of each given fraction:
1. [tex]\(\frac{1.36}{54}\)[/tex] reduces to [tex]\(\frac{17}{675}\)[/tex].
2. [tex]\(\frac{81}{81}\)[/tex] reduces to [tex]\(1\)[/tex].
3. [tex]\(\frac{35}{81}\)[/tex] remains [tex]\(\frac{35}{81}\)[/tex].
4. [tex]\(\frac{12}{144}\)[/tex] reduces to [tex]\(\frac{1}{12}\)[/tex].
5. [tex]\(\frac{16}{32}\)[/tex] reduces to [tex]\(\frac{1}{2}\)[/tex].
These are the fractions in their lowest terms!
### 1. Reduce [tex]\(\frac{1.36}{54}\)[/tex] to its lowest terms:
#### Step 1: Calculate the GCF of 1.36 and 54
- Convert 1.36 to a fraction: [tex]\(\frac{136}{100}\)[/tex]
- The numerator is 136 and the denominator is 5400 (since [tex]\(\frac{1.36}{54} = \frac{1.36100}{54100} = \frac{136}{5400}\)[/tex]).
Use the GCF method:
- [tex]\( \text{GCF}(136, 5400) = 8 \)[/tex]
#### Step 2: Divide both the numerator and the denominator by the GCF:
- Reduced numerator: [tex]\( \frac{136}{8} = 17 \)[/tex]
- Reduced denominator: [tex]\( \frac{5400}{8} = 675 \)[/tex]
Thus, [tex]\(\frac{1.36}{54} = \frac{17}{675}\)[/tex].
### 2. Reduce [tex]\(\frac{81}{81}\)[/tex] to its lowest terms:
#### Step 1: Calculate the GCF of 81 and 81
- Both the numerator and the denominator are 81.
- [tex]\( \text{GCF}(81, 81) = 81 \)[/tex]
#### Step 2: Divide both the numerator and the denominator by the GCF:
- Reduced numerator: [tex]\( \frac{81}{81} = 1 \)[/tex]
- Reduced denominator: [tex]\( \frac{81}{81} = 1 \)[/tex]
Thus, [tex]\(\frac{81}{81} = 1\)[/tex].
### 3. Reduce [tex]\(\frac{35}{81}\)[/tex] to its lowest terms:
#### Step 1: Calculate the GCF of 35 and 81
- The numbers 35 and 81 do not have any common factors other than 1.
- [tex]\( \text{GCF}(35, 81) = 1 \)[/tex]
#### Step 2: Since the GCF is 1, the fraction is already in its lowest terms:
- Fraction remains: [tex]\(\frac{35}{81}\)[/tex]
Thus, [tex]\(\frac{35}{81}\)[/tex] remains [tex]\(\frac{35}{81}\)[/tex].
### 4. Reduce [tex]\(\frac{12}{144}\)[/tex] to its lowest terms:
#### Step 1: Calculate the GCF of 12 and 144
- Both are divisible by 12.
- [tex]\( \text{GCF}(12, 144) = 12 \)[/tex]
#### Step 2: Divide both the numerator and the denominator by the GCF:
- Reduced numerator: [tex]\( \frac{12}{12} = 1 \)[/tex]
- Reduced denominator: [tex]\( \frac{144}{12} = 12 \)[/tex]
Thus, [tex]\(\frac{12}{144} = \frac{1}{12}\)[/tex].
### 5. Reduce [tex]\(\frac{16}{32}\)[/tex] to its lowest terms:
#### Step 1: Calculate the GCF of 16 and 32
- Both are divisible by 16.
- [tex]\( \text{GCF}(16, 32) = 16 \)[/tex]
#### Step 2: Divide both the numerator and the denominator by the GCF:
- Reduced numerator: [tex]\( \frac{16}{16} = 1 \)[/tex]
- Reduced denominator: [tex]\( \frac{32}{16} = 2 \)[/tex]
Thus, [tex]\(\frac{16}{32} = \frac{1}{2}\)[/tex].
### Summary
Here are the reduced forms of each given fraction:
1. [tex]\(\frac{1.36}{54}\)[/tex] reduces to [tex]\(\frac{17}{675}\)[/tex].
2. [tex]\(\frac{81}{81}\)[/tex] reduces to [tex]\(1\)[/tex].
3. [tex]\(\frac{35}{81}\)[/tex] remains [tex]\(\frac{35}{81}\)[/tex].
4. [tex]\(\frac{12}{144}\)[/tex] reduces to [tex]\(\frac{1}{12}\)[/tex].
5. [tex]\(\frac{16}{32}\)[/tex] reduces to [tex]\(\frac{1}{2}\)[/tex].
These are the fractions in their lowest terms!
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