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Using the greatest common factor, simplify the fraction 160200 (1 point) Responses 45 4 fifths 1620 16 over 20 4050 40 over 50...Question
Using the greatest common factor, simplify the fraction 160200
(1 point)
Responses
45
4 fifths
1620
16 over 20
4050
40 over 50
40
(1 point)
Responses
45
4 fifths
1620
16 over 20
4050
40 over 50
40
Answers
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Answered by
GPT-4o mini
To simplify the fraction 160200, we need to find the greatest common factor (GCF) of the numerator and denominator.
However, the fraction appears to be missing a denominator. Assuming it is meant to be written as \( \frac{160}{200} \), let's simplify this.
1. The prime factors of 160 are \( 2^5 \times 5 \).
2. The prime factors of 200 are \( 2^3 \times 5^2 \).
To find the GCF, we take the lowest powers of the common factors:
- For \( 2 \), the minimum power is \( 2^3 \).
- For \( 5 \), the minimum power is \( 5^1 \).
Thus, the GCF is \( 2^3 \times 5^1 = 8 \times 5 = 40 \).
Now, we can simplify \( \frac{160}{200} \) using the GCF:
\[
\frac{160 \div 40}{200 \div 40} = \frac{4}{5}
\]
Therefore, the simplified fraction is \( \frac{4}{5} \).
The correct simplification based on the options provided is:
**4 fifths**.
However, the fraction appears to be missing a denominator. Assuming it is meant to be written as \( \frac{160}{200} \), let's simplify this.
1. The prime factors of 160 are \( 2^5 \times 5 \).
2. The prime factors of 200 are \( 2^3 \times 5^2 \).
To find the GCF, we take the lowest powers of the common factors:
- For \( 2 \), the minimum power is \( 2^3 \).
- For \( 5 \), the minimum power is \( 5^1 \).
Thus, the GCF is \( 2^3 \times 5^1 = 8 \times 5 = 40 \).
Now, we can simplify \( \frac{160}{200} \) using the GCF:
\[
\frac{160 \div 40}{200 \div 40} = \frac{4}{5}
\]
Therefore, the simplified fraction is \( \frac{4}{5} \).
The correct simplification based on the options provided is:
**4 fifths**.
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