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Practice each question, then open the answer or worked solution.
The reciprocal of (-3/8) × (-7/13) is
(a) 104/21 (b) -104/21 (c) 21/104 (d) -21/104
Solution:-
(a) 104/21
= (-3 × -7) / (8 × 13)
= (21/104)
Reciprocal of 21/104 is 104/21
Which of the following is an example of distributive property of multiplication over addition for rational numbers.
Solution:-
(a) – (1/4) × {(2/3) + (-4/7)} = [-(1/4) × (2/3)] + [(-1/4) × (-4/7)]
Because, we know the rule of distributive law, i.e. a × (b + c)] = [(a × b) + (a × c)
Between two given rational numbers, we can find
(a) one and only one rational number.
(b) only two rational numbers.
(c) only ten rational numbers.
(d) infinitely many rational numbers.
Solution:-
(d) infinitely many rational numbers.
(x + y)/2 is a rational number
(a) Between x and y
(b) Less than x and y both.
(c) Greater than x and y both.
(d) Less than x but greater than y
Solution:-
(a) Between x and y
Let us assume the value of x and y is 4 and 8 respectively
Then,
= (4 + 8)/ 2
= 12/2
= 6
Hence, the value 6 is lies between 4 and 8.
Which of the following statements is always true?
Solution:-
(b) (x + y)/2 is a rational number between x and y
Let us assume the value of x and y is 6 and 9 respectively
Then,
= (6 + 9)/ 2
= 14/2
= 7
Hence, the value 7 is lies between 6 and 9.
In questions 26 to 47, fill in the blanks to make the statements true.
The equivalent of 5/7, whose numerator is 45 is .
Solution:-
Form the question it is given that equivalent of 5/7 = 45/denominator
To get 45 in the numerator multiply both numerator and denominator by 9
Then,
= (5 × 9)/ (7 × 9)
= 45/63
So, the equivalent of 5/7, whose numerator is 45 is (45/63)
The equivalent rational number of 7/9, whose denominator is 45 is .
Solution:-
Form the question it is given that equivalent of 7/9 = Numerator/45
To get 45 in the denominator multiply both numerator and denominator by 5
Then,
= (7 × 5)/ (9 × 5)
= 35/45
So, the equivalent rational number of 7/9, whose denominator is 45 is (35/45)
Between the numbers (15/20) and (35/40), the greater number is .
Solution:-
The LCM of the denominators 20 and 40 is 40
∴ (15/20) = [(15×2)/ (20×2)] = (30/40)
and (35/40) = [(35×1)/ (40×1)] = (35/40)
Now, 30 < 35
⇒ (30/40) < (35/40)
Hence, (15/20) < (35/40)
∴ 35/40 is greater.
So, between the numbers (15/20) and (35/40), the greater number is (35/40).
The reciprocal of a positive rational number is .
Solution:-
The reciprocal of a positive rational number is positive rational number.
Let us take positive rational number 2/3
The reciprocal of this positive rational number is 3/2 (positive rational number)
The reciprocal of a negative rational number is .
Solution:-
The reciprocal of a negative rational number is negative rational number.
Let us take negative rational number -3/4
The reciprocal of a negative rational number is 4/-3 = -4/3