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Every fraction is a rational number....

Every fraction is a rational number.

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**Step-by-Step Solution:** 1. **Understanding Rational Numbers**: - A rational number is defined as any number that can be expressed in the form of a fraction \( \frac{P}{Q} \), where \( P \) and \( Q \) are integers and \( Q \neq 0 \). 2. **Defining Fractions**: - A fraction is a mathematical expression that represents the division of one integer by another. It is written in the form \( \frac{a}{b} \), where \( a \) (the numerator) and \( b \) (the denominator) are integers, and \( b \neq 0 \). 3. **Connecting Fractions to Rational Numbers**: - Since a fraction can be expressed as \( \frac{a}{b} \) and both \( a \) and \( b \) are integers with \( b \neq 0 \), it fits the definition of a rational number. 4. **Conclusion**: - Therefore, every fraction is indeed a rational number because it can be expressed in the form \( \frac{P}{Q} \) where \( P \) and \( Q \) are integers and \( Q \neq 0 \). **Final Answer**: True, every fraction is a rational number. ---
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In each of the following state if the statement is true (T) or false (F): (i) The quotient of two integers is always an integer. (ii) Every integer is a rational number. (iii) Every rational number is an integer. (iv) Every fraction is a rational number. (v) Every rational number is a fraction. (vi) If a/b is a rational number and m any integer, then a/b=(axxm)/(bxxm) (vii) Two rational numbers with different numerators cannot be equal. (viii) 8 can be written as a rational number with any integer as denominator. (ix) 8 can be written as a rational number with any integer as numerator. (x) 2/3 is equal to 4/6dot

Are the following statements true or false? Give reasons for your answers. (i) Every whole number is a natural number. (ii)Every integer is a rational number. (iii)Every rational number is an integer.

Is the following statements true or false ? Every integer is a rational number.

(0)/(1) is a rational number.

(1)/(0) is a rational number.

State true or false: (i) Negative of an irrational number is irrational . (ii) The product of a non- zero rational number and an irrational number is a rational number.

For each pair of rational numbers, verify commutative property of addition of rational numbers : (vi) -2 "and" (3)/(-5)

For each pair of rational numbers, verify commutative property of addition of rational numbers : (ii) (-5)/(9) "and" (5)/(-12)

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ICSE-RATIONAL NUMBERS -EXERCISE 2A
  1. What are rational numbers? Give four examples of each of positive rati...

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  2. Which of the following are rational numbers? (i) 5/15, (ii) -6/23, (...

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  3. Write down the numerator and the denominator of each of the following ...

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  4. Which of the following are positive rational numbers? (i) -7/8, (ii)...

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  5. Which of the following are negative rational numbers? (i) -16/5, (ii...

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  6. Find four rational numbers equivalent to each of the following: (i) ...

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  7. Write each of the following rational numbers with positive denominator...

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  8. Express 4/9 as a rational number with numerator (i) 24 (ii) -20

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  9. Express 3/8 as a rational number with denominator (i) 48 (ii) -32

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  10. Express -6/11 as a rational number with numerator (i) -36 (ii) 42

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  11. Express 2/(-7) as a rational number with denominator (i) 42 (ii) -28

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  12. Express -48/36 as a rational number with numerator (i) -4(ii) 8

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  13. Express 78/(-117) as a rational number with numerator (i) -6 (ii) 2

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  14. Write each of the following rational numbers in standard form : (i) ...

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  15. Find the value of x such that: (i) -2/3=14/x, (ii) 8/-3 = x/6, (iii)...

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  16. State whether the given statement is true or false : The quotient of...

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  17. Every rational number is a fraction.

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  18. Zero is the smallest rational number.

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  19. Every fraction is a rational number.

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