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Practice each question, then open the answer or worked solution.
Which of the following does not represent an integer?
(a) 0 ÷ (– 7) (b) 20 ÷ (– 4) (c) (– 9) ÷ 3 (d) (– 12) ÷ 5
(d) (– 12) ÷ 5
0 ÷ (– 7) = 0, an integer
20 ÷ (– 4) = -5, an integer
(– 9) ÷ 3 = -3, an integer
But, (– 12) ÷ 5 = -2.4, which is a decimal and not an integer
Which of the following is different from the others?
(a) 20 + (–25) (b) (– 37) – (– 32) (c) (– 5) × (–1) (d) ( 45 ) ÷ (– 9)
(c) (– 5) × (–1)
As all the remaining options give a value of -5
20 + (–25) = (– 37) – (– 32) = ( 45 ) ÷ (– 9) = -5
But, (– 5) × (–1) = 5
Which of the following shows the maximum rise in temperature?
(a) 23° to 32° (b) – 10° to + 1° (c) – 18° to – 11° (d) – 5° to 5°
(b) – 10° to + 1°
As the difference in the temperature = 1° – (10°) = 11° (maximum)
Whereas,
23° to 32° = 32° – 23° = 9°
– 18° to – 11° = -11° – (-18)° = 7°
– 5° to 5° = 5° – (-5)° = 10°
If a and b are two integers, then which of the following may not be an integer?
(a) a + b (b) a – b (c) a × b (d) a ÷ b
(d) a ÷ b
If a and b are two integers, then
a + b will always be an integer
a – b will always be an integer
a × b will always be an integer
For a non-zero integer a, which of the following is not defined?
(a) a ÷ 0 (b) 0 ÷ a (c) a ÷ 1 (d) 1 ÷ a
(a) a ÷ 0
a ÷ 0 = a/0 is undefined
Encircle the odd one of the following (Questions 26 to 30).
(a) (–3, 3) (b) (–5, 5) (c) (–6, 1) (d) (–8, 8)
(c) (–6, 1)
–3 + 3 = 0
–5 + 5 = 0
–8 + 8 = 0
–6 + 1 = -5
Hence, (–6, 1) is the odd one.
(a) (–1, –2) (b) (–5, +2) (c) (–4, +1) (d) (–9, +7)
(d) (–9, +7)
–1 + (–2) = -3
–5 + 2 = -3
–4 + 1 = -3
–9 + 7 = -2
Hence, (–9, +7) is the odd one.
(a) (–9) × 5 × 6 × (–3) (b) 9 × (–5) × 6 × (–3)
(c) (–9) × (–5) × (–6) × 3 (d) 9 × (–5) × (–6) × 3
(c) (–9) × (–5) × (–6) × 3
(–9) × 5 × 6 × (–3) = 810
9 × (–5) × 6 × (–3) = 810
(–9) × (–5) × (–6) × 3 = -810
9 × (–5) × (–6) × 3 = 810
Hence, (–9) × (–5) × (–6) × 3 is the odd one.
(a) (–100) ÷ 5 (b) (–81) ÷ 9 (c) (–75) ÷ 5 (d) (–32) ÷ 9
(d) (–32) ÷ 9
Since, only (–32) ÷ 9 doesn’t give an integer i.e. -32/9 = -3.5555555556
Hence, (–32) ÷ 9 is the odd one.
(a) (–1) × (–1) (b) (–1) × (–1) × (–1)
(c) (–1) × (–1) × (–1) × (–1) (d) (–1) × (–1) × (–1) × (–1) × (–1) × (–1)
(b) (–1) × (–1) × (–1)
Since,
(–1) × (–1) = 1
(–1) × (–1) × (–1) × (–1) = 1
(–1) × (–1) × (–1) × (–1) × (–1) × (–1) = 1
But, (–1) × (–1) × (–1) = -1
Hence, (–1) × (–1) × (–1) is the odd one.
In Questions 31 to 71, fill in the blanks to make the statements true.