Class 8 Maths Chapter 1 Rational Numbers Exam
2023
Find:
-2/3 × 3/5 + 5/2 - 3/5 × 1/6 - ANS--2/3 × 3/5 + 5/2 - 3/5 × 1/6
= -2/3 × 3/5- 3/5 ×
... [Show More] 1/6+ 5/2 (by commutativity)
= 3/5 (-2/3 - 1/6)+ 5/2
= 3/5 ((- 4 - 1)/6)+ 5/2
= 3/5 ((-5)/6)+ 5/2 (by distributivity)
= - 15 /30 + 5/2
= - 1 /2 + 5/2
= 4/2
= 2
2/5 × (- 3/7) - 1/6 × 3/2 + 1/14 × 2/5 - ANS-2/5 × (- 3/7) - 1/6 × 3/2 + 1/14 × 2/5
= 2/5 × (- 3/7) + 1/14 × 2/5 - (1/6 × 3/2) (by commutativity)
= 2/5 × (- 3/7 + 1/14) - 3/12
= 2/5 × ((- 6 + 1)/14) - 3/12
= 2/5 × ((- 5)/14)) - 1/4
= (-10/70) - 1/4
= - 1/7 - 1/4
= (- 4- 7)/28
= - 11/28
Write the additive inverse of
2/8
-5/9
-6/-5
2/-9
19/-16 - ANS-- 2/8
-5/9
6/5
-2/9
-19/16
Verify that: -(-x) = x for
x = 11/15 - ANS-x = 11/15
The additive inverse of x is - x (as x + (-x) = 0)
Then, the additive inverse of 11/15 is - 11/15 (as 11/15 + (-11/15) = 0)
The same equality 11/15 + (-11/15) = 0, shows that the additive inverse of -11/15 is 11/15.
Or, - (-11/15) = 11/15
i.e., -(-x) = x
Verify that: -(-x) = x for x= -13/17 - ANS-x = -13/17
The additive inverse of x is - x (as x + (-x) = 0)
Then, the additive inverse of -13/17 is 13/17 (as 11/15 + (-11/15) = 0)
The same equality (-13/17 + 13/17) = 0, shows that the additive inverse of 13/17 is -13/17.
Or, - (13/17) = -13/17,
i.e., -(-x) = x
Find ten rational numbers between 3/5 and ¾, - ANS-Let us make the denominators same, say 80.
3/5 = (3 × 16)/(5× 16) = 48/80
3/4 = (3 × 20)/(4 × 20) = 60/80
Ten rational numbers between 3/5 and ¾ = ten rational numbers between 48/80 and 60/80
Therefore, ten rational numbers between 48/80 and 60/80 = 49/80, 50/80, 51/80, 52/80, 54/80, 55/80,
56/80, 57/80, 58/80, 59/80
Write five rational numbers greater than -2. - ANS--2 can be written as - 20/10
Hence, we can say that, the five rational numbers greater than -2 are
-10/10, -5/10, -1/10, 5/10, 7/10
Find the rational numbers between -2/5 and ½. - ANS-Let us make the denominators same, say 50.
-2/5 = (-2 × 10)/(5 × 10) = -20/50
½ = (1 × 25)/(2 × 25) = 25/50
Ten rational numbers between -2/5 and ½ = ten rational numbers between -20/50 and 25/50
Therefore, ten rational numbers between -20/50 and 25/50 = -18/50, -15/50, -5/50, -2/50, 4/50, 5/50, 8/50,
12/50, 15/50, 20/50
Find the rational numbers between 2/3 and 4/5 - ANS-(i) 2/3 and 4/5
Let us make the denominators same, say 60
i.e., 2/3 and 4/5 can be written as:
2/3 = (2 × 20)/(3 × 20) = 40/60
4/5 = (4 × 12)/(5 × 12) = 48/60
Five rational numbers between 2/3 and 4/5 = five rational numbers between 40/60 and 48/60
Therefore, Five rational numbers between 40/60 and 48/60 = 41/60, 42/60, 43/60, 44/60, 45/60
Find the rational numbers between 3/2 and 5/3 - ANS-3/2 and 5/3
Let us make the denominators same, say 6
i.e., -3/2 and 5/3 can be written as:
-3/2 = (-3 × 3)/(2× 3) = -9/6
5/3 = (5 × 2)/(3 × 2) = 10/6
Five rational numbers between -3/2 and 5/3 = five rational numbers between -9/6 and 10/6
Therefore, Five rational numbers between -9/6 and 10/6 = -1/6, 2/6, 3/6, 4/6, 5/6
Find the rational numbers between ¼ and ½ - ANS-Let us make the denominators same, say 24.
i.e., ¼ and ½ can be written as:
¼ = (1 × 6)/(4 × 6) = 6/24
½ = (1 × 12)/(2 × 12) = 12/24
Five rational numbers between ¼ and ½ = five rational numbers between 6/24 and 12/24
Therefore, Five rational numbers between 6/24 and 12/24 = 7/24, 8/24, 9/24, 10/24, 11/24
Write five rational numbers which are smaller than 2 - ANS-The number 2 can be written as 20/10
Hence, we can say that, the five rational numbers which are smaller than 2 are:
Continues... [Show Less]