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Answer :
To change the improper fraction [tex]\(\frac{107}{20}\)[/tex] into a mixed number, we follow these steps:
1. Divide the numerator by the denominator:
- Divide 107 by 20. Since 20 goes into 107 five times (because 20 x 5 = 100), the whole number part of the mixed number is 5.
2. Find the remainder:
- After 100, we have 7 left over, as 107 - 100 = 7. This 7 is the remainder.
3. Express the remainder as a fraction:
- The remainder 7 becomes the numerator of the fractional part. The denominator remains the same, which is 20. So the fractional part is [tex]\(\frac{7}{20}\)[/tex].
4. Combine the whole number and the fractional part:
- Therefore, the mixed number is [tex]\(5 \frac{7}{20}\)[/tex].
5. Convert the mixed number to a decimal:
- To find the decimal equivalent of [tex]\(\frac{7}{20}\)[/tex], divide 7 by 20, which equals 0.35.
- Add this to the whole number part, 5, to get 5.35.
Hence, the improper fraction [tex]\(\frac{107}{20}\)[/tex] expressed as a mixed number and a decimal is [tex]\(5 \frac{7}{20}\)[/tex] or 5.35. Therefore, the correct choice from the given options is 5.35.
1. Divide the numerator by the denominator:
- Divide 107 by 20. Since 20 goes into 107 five times (because 20 x 5 = 100), the whole number part of the mixed number is 5.
2. Find the remainder:
- After 100, we have 7 left over, as 107 - 100 = 7. This 7 is the remainder.
3. Express the remainder as a fraction:
- The remainder 7 becomes the numerator of the fractional part. The denominator remains the same, which is 20. So the fractional part is [tex]\(\frac{7}{20}\)[/tex].
4. Combine the whole number and the fractional part:
- Therefore, the mixed number is [tex]\(5 \frac{7}{20}\)[/tex].
5. Convert the mixed number to a decimal:
- To find the decimal equivalent of [tex]\(\frac{7}{20}\)[/tex], divide 7 by 20, which equals 0.35.
- Add this to the whole number part, 5, to get 5.35.
Hence, the improper fraction [tex]\(\frac{107}{20}\)[/tex] expressed as a mixed number and a decimal is [tex]\(5 \frac{7}{20}\)[/tex] or 5.35. Therefore, the correct choice from the given options is 5.35.
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