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Important Formulas: Rational Numbers | Mathematics (Maths) Class 7 PDF Download
(1) Numbers that can be expressed in the form p/q, where q is a non-zero integer and p is any integer are called rational numbers.
(2) Every integer is a rational number but a rational number need not be an integer.
(3) Every fraction is a rational number but a fraction need not be a rational number.
(4) A rational number p/q is said to be in the standard form if q is a positive integer and the integers p/q have no common divisor other than 1.
(5) A rational numbers p/q is positive, if p and q are either both positive or both negative.
(6) A rational number p/q is negative, if p and q are of opposite signs.
(7) Two rational numbers are equal if they have the same standard form.
(8) To convert a rational number to an equivalent rational number, either multiply or divide both its numerator and denominator by a non-zero integer.
(9) If x/y is a rational number and m is any non-zero integer, then 
(10) If x/y is a rational number and m is a common divisor of x and y, then 
(11) If x and y are positive integers, then the rational numbers x/y and -x/-y both positive and the rational numbers -x/y and x/-y negative.
(12) 
only when a x d = b x c.
(13) If there are two rational numbers with common denominator, then one with the larger numerator is larger than the other.
(14) Every positive rational number is greater than zero.
(15) Every negative rational number is less than zero.
(16) The rational numbers can be represented on the number line.
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FAQs on Important Formulas: Rational Numbers - Mathematics (Maths) Class 7
| 1. What are rational numbers? |  |
Ans. Rational numbers are numbers that can be expressed as the quotient or fraction of two integers, where the denominator is not zero. This means any number in the form of \( \frac{a}{b} \), where \( a \) and \( b \) are integers and \( b \neq 0 \), is a rational number. Examples include \( \frac{1}{2} \), \( -\frac{3}{4} \), and \( 5 \) (which can be written as \( \frac{5}{1} \)).
| 2. How do you add and subtract rational numbers? | |
Ans. To add or subtract rational numbers, you must have a common denominator. For example, to add \( \frac{1}{3} \) and \( \frac{1}{4} \), find the least common denominator (LCD), which is 12. Convert both fractions: \( \frac{1}{3} = \frac{4}{12} \) and \( \frac{1}{4} = \frac{3}{12} \). Now, add: \( \frac{4}{12} + \frac{3}{12} = \frac{7}{12} \). Subtraction follows the same process.
| 3. What is the process for multiplying rational numbers? | |
Ans. To multiply rational numbers, you multiply the numerators together and the denominators together. For instance, to multiply \( \frac{2}{3} \) and \( \frac{4}{5} \), calculate \( \frac{2 \times 4}{3 \times 5} = \frac{8}{15} \). The result is also a rational number.
| 4. How do you divide rational numbers? | |
Ans. To divide rational numbers, you multiply by the reciprocal of the second number. For example, to divide \( \frac{3}{4} \) by \( \frac{2}{5} \), you would compute \( \frac{3}{4} \times \frac{5}{2} = \frac{15}{8} \). The division of rational numbers results in another rational number.
| 5. Can all integers be considered rational numbers? | |
Ans. Yes, all integers are considered rational numbers because they can be expressed as a fraction with a denominator of 1. For example, the integer \( 7 \) can be written as \( \frac{7}{1} \), which fits the definition of a rational number.
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