8th Standard Mathematics
Exercise 1.1 Solutions
1. Fill in the blanks:
(i) -19/5 lies between the integers _______ and _______.
Converting to mixed fraction: -19/5 = -3 4/5
Answer: -4 and -3
(ii) The decimal form of the rational number 15/-4 is _______.
15/-4 = -3.75
Answer: -3.75
(iii) The rational numbers -8/3 and 8/3 are equidistant from _______.
Both are 2 2/3 units away from zero in opposite directions.
Answer: 0
(iv) The next rational number in the sequence -15/24, 20/-32, -25/40 is _______.
Simplifying each fraction gives -5/8.
Next term with numerator -30: -30/48 (or 30/-48).
Answer: -30/48
(v) The standard form of 58/-78 is _______.
Divide numerator and denominator by 2: 58 ÷ 2/-78 ÷ 2 = 29/-39
Answer: -29/39
2. Say True or False:
(i) 0 is the smallest rational number.
Answer: False
(Negative rational numbers are smaller than 0.)
(ii) -4/5 lies to the left of -3/4.
-4/5 = -0.8 and -3/4 = -0.75. Since -0.8 < -0.75, it lies to the left.
Answer: True
(iii) -19/5 is greater than 15/-4.
-19/5 = -3.8 and 15/-4 = -3.75. Since -3.8 < -3.75:
Answer: False
(iv) The average of two rational numbers lies between them.
Answer: True
(v) There are an unlimited number of rational numbers between 10 and 11.
Answer: True
3. Find the rational numbers represented by each of the question marks marked on the following number lines.
(i) Question mark between -3 and -4 (divided into 3 parts, at 2nd mark from -3):
Value = -3 - 2/3 = -11/3
Answer: -11/3
(ii) Question mark between 0 and -1 (divided into 5 parts, at 2nd mark to the left of 0):
Value = -2/5
Answer: -2/5
(iii) Question mark between 1 and 2 (divided into 4 parts, at 3rd mark to the right of 1):
Value = 1 + 3/4 = 7/4
Answer: 7/4
4. The points S, Y, N, C, R, A, T, I and O on the number line...
Interval between -1 and -2 is divided into 3 equal parts (length = 1/3 each):
C = -1
N = -1 - 1/3 = -4/3
Y = -1 - 2/3 = -5/3
Interval between 2 and 3 is divided into 4 equal parts (length = 1/4 each):
R = 2
A = 2 + 1/4 = 9/4
T = 2 + 2/4 = 10/4 = 5/2
I = 2 + 3/4 = 11/4
6. Write the decimal form of the following rational numbers.
(i) 1/11
0.090909... (or 0.09)
(ii) 13/4
3.25
(iii) -18/7
-2.571428...
(iv) 1 2/5
1 + 0.4 =
1.4
(v) -3 1/2
-(3 + 0.5) =
-3.5
7. List any five rational numbers between the given rational numbers.
(i) -2 and 0
Rewrite as -12/6 and 0:
Five numbers: -1/6, -2/6, -3/6, -4/6, -5/6
(ii) -1/2 and 3/5
Equalize denominator to 10: -5/10 and 6/10
Five numbers: -4/10, -3/10, 0/10, 1/10, 2/10
8. Use the method of averages to write 2 rational numbers between 14/5 and 16/3.
First Number (q1):
q1 = ½ × (14/5 + 16/3) = ½ × (42 + 80/15) = ½ × 122/15 = 61/15
Second Number (q2):
q2 = ½ × (14/5 + 61/15) = ½ × (42 + 61/15) = 103/30
Answer: 61/15 and 103/30
9. Compare the following pairs of rational numbers.
(i) -11/5, -21/8
Cross multiply: -11 × 8 = -88 and -21 × 5 = -105
Since -88 > -105:
-11/5 > -21/8
(ii) 3/-4, -1/2
-3/4 and -2/4
3/-4 < -1/2
(iii) 2/3, 4/5
2 × 5 = 10, 4 × 3 = 12 (10 < 12):
2/3 < 4/5
10. Arrange the rational numbers in ascending and descending order.
(i) -5/12, -11/8, -15/24, -7/-9, 12/36
Simplify/standardize: -5/12, -11/8, -5/8, 7/9, 1/3
Common denominator LCM(12, 8, 9, 3) = 72:
-30/72, -99/72, -45/72, 56/72, 24/72
Ascending Order: -11/8, -15/24, -5/12, 12/36, -7/-9
Descending Order: -7/-9, 12/36, -5/12, -15/24, -11/8
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