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Answer :
To convert the improper fraction [tex]\(\frac{107}{20}\)[/tex] into a mixed number, follow these steps:
1. Divide the Numerator by the Denominator:
Start by dividing the numerator (107) by the denominator (20).
[tex]\(107 \div 20 = 5\)[/tex] (with a remainder)
2. Find the Whole Number Part:
The whole number part of the mixed number is the quotient you get from the division.
So, the whole number part is [tex]\(5\)[/tex].
3. Calculate the Remainder:
The remainder of the division gives you the fraction part.
The remainder when 107 is divided by 20 is [tex]\(107 - (20 \times 5) = 107 - 100 = 7\)[/tex].
4. Form the Fractional Part:
Use the remainder as the numerator and keep the original denominator for the fraction part.
This gives you the fractional part as [tex]\(\frac{7}{20}\)[/tex].
5. Combine to Form the Mixed Number:
Therefore, the mixed number is [tex]\(5\)[/tex] followed by the fractional part [tex]\(\frac{7}{20}\)[/tex].
Now, to express this mixed number as a decimal for the answer choice:
- Calculate the decimal equivalent of [tex]\(\frac{7}{20}\)[/tex] by dividing 7 by 20, which gives 0.35.
- Combine the whole number with the decimal: [tex]\(5 + 0.35 = 5.35\)[/tex].
So, the mixed number [tex]\(\frac{107}{20}\)[/tex] is equivalent to [tex]\(5.35\)[/tex], corresponding to the answer choice 5.35.
1. Divide the Numerator by the Denominator:
Start by dividing the numerator (107) by the denominator (20).
[tex]\(107 \div 20 = 5\)[/tex] (with a remainder)
2. Find the Whole Number Part:
The whole number part of the mixed number is the quotient you get from the division.
So, the whole number part is [tex]\(5\)[/tex].
3. Calculate the Remainder:
The remainder of the division gives you the fraction part.
The remainder when 107 is divided by 20 is [tex]\(107 - (20 \times 5) = 107 - 100 = 7\)[/tex].
4. Form the Fractional Part:
Use the remainder as the numerator and keep the original denominator for the fraction part.
This gives you the fractional part as [tex]\(\frac{7}{20}\)[/tex].
5. Combine to Form the Mixed Number:
Therefore, the mixed number is [tex]\(5\)[/tex] followed by the fractional part [tex]\(\frac{7}{20}\)[/tex].
Now, to express this mixed number as a decimal for the answer choice:
- Calculate the decimal equivalent of [tex]\(\frac{7}{20}\)[/tex] by dividing 7 by 20, which gives 0.35.
- Combine the whole number with the decimal: [tex]\(5 + 0.35 = 5.35\)[/tex].
So, the mixed number [tex]\(\frac{107}{20}\)[/tex] is equivalent to [tex]\(5.35\)[/tex], corresponding to the answer choice 5.35.
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