Question

Find 5 rational numbers between: (a)-1and 0 (b)-2and -1 with solutions​

Answer 1

Step-by-step explanation:

a) Rational numbers between -1 and 0:

(-1/1) and (0/1)

Since we need 5 numbers, multiply both the numerator and the denominator by 6.

After multiplication, we get;

-1 and 0

Following five rational numbers:

(-5/6), (-2/3), (-1/2), (-1/3), (-1/6)

b) Rational numbers between -2 and -1:

The given negative integers are written as:

(-2/1) and (-1/1)

Multiplying both the numerator and denominator by 6, we get;

(-12/6) and (-6/6)

Following five rational numbers:

(-11/6), (-5/3), (-3/2), (-4/3), (-7/6)

Answer 2

Answer:

(i) -1 and 0

Multiplying both denominator and numerator by 6, we get:

(-1 × 6) / (1 × 6) = -6/6,

(0 × 6)/(1 × 6) = 0/6

Five rational numbers between -1 and 0 are

-6/6 < -5/6 < -4/6 < -3/6 < -2/6 < -1/6 < 0/6

-1 < -5/6 < -4/6 < -3/6 < -2/6 < -1/6 < 0

Thus five rational numbers between -1 and 0 are

-5/6 , -2/3 , -1/2 , -1/3 , -1/6.

(ii) -2 and -1

Multiplying both numerator and denominator by 6 , we get

(-2 × 6)/(1 × 6) = (-12/6) , (-1 × 6)/(1 × 6) = -(6/6)

Five rational numbers between -2 and -1 -1 are,

-12/6 < -11/6 < -10/6 < -9/6 < -8/6 < -7/6 < -6/6

-2 < -11/6 < -10/6 < -9/6 < -8/6 < -7/6 < -1

Thus, the five rational numbers between -2 and -1 are -11/6, -5/3, -3/2, -4/3, -7/6.