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Which of the following are improper frac...

Which of the following are improper fractions ?
`(1)/(2),(3)/(5),(10)/(7), 2,(15)/(8),(16)/(16),(10)/(11),(23)/(10)`

Text Solution

AI Generated Solution

The correct Answer is:
To determine which of the given fractions are improper fractions, we need to understand what an improper fraction is. An improper fraction is defined as a fraction where the numerator (the top number) is greater than or equal to the denominator (the bottom number). Let's analyze each of the given fractions step by step: 1. **Fraction: \( \frac{1}{2} \)** - Numerator: 1 - Denominator: 2 - Since 1 < 2, this is **not** an improper fraction. 2. **Fraction: \( \frac{3}{5} \)** - Numerator: 3 - Denominator: 5 - Since 3 < 5, this is **not** an improper fraction. 3. **Fraction: \( \frac{10}{7} \)** - Numerator: 10 - Denominator: 7 - Since 10 > 7, this **is** an improper fraction. 4. **Fraction: 2** - This can be written as \( \frac{2}{1} \). - Numerator: 2 - Denominator: 1 - Since 2 > 1, this **is** an improper fraction. 5. **Fraction: \( \frac{15}{8} \)** - Numerator: 15 - Denominator: 8 - Since 15 > 8, this **is** an improper fraction. 6. **Fraction: \( \frac{16}{16} \)** - Numerator: 16 - Denominator: 16 - Since 16 = 16, this **is** an improper fraction. 7. **Fraction: \( \frac{10}{11} \)** - Numerator: 10 - Denominator: 11 - Since 10 < 11, this is **not** an improper fraction. 8. **Fraction: \( \frac{23}{10} \)** - Numerator: 23 - Denominator: 10 - Since 23 > 10, this **is** an improper fraction. Now, let's summarize the improper fractions we found: - \( \frac{10}{7} \) - 2 (or \( \frac{2}{1} \)) - \( \frac{15}{8} \) - \( \frac{16}{16} \) - \( \frac{23}{10} \) ### Final Answer: The improper fractions from the list are: \( \frac{10}{7}, 2, \frac{15}{8}, \frac{16}{16}, \frac{23}{10} \).
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Knowledge Check

  • Which of the following is an improper fraction? 7/10 , 7/9 , 9/7 , 7/7

    A
    `7/10`
    B
    `7/9`
    C
    `9/7`
    D
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    A
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    B
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    C
    `3 3/10`
    D
    `5/8`
  • Which of the following relations are functions ? R_1 {(1,1),(2,2),(3,3),(4,4),(4,5)} R_2 = {(1,1),(2,3),(3,5),(4,7)} R_3 = {(1,1),(2,4),(3,9),(4,16),(5,25)}

    A
    `R_1` and `R_2`
    B
    `R_2` and `R_3`
    C
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    D
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