# List five rational numbers between: (i) -1 and 0 (ii) -2 and -1 (iii) -⅘ and -⅔ (iv) -½ and ⅔

By Shivank Goel|Updated : August 3rd, 2022

Let us convert the given fractions into like fractions by making their denominators equal.

It can be done by taking the LCM of the denominator or multiplying the numerator and denominator using the same integer.

(i) -1 and 0

Let us multiply both numerator and denominator by 6

(-1 x 6)/(1 x 6) = -6/6

(0 x 6)/(1 x 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

Therefore, the five rational numbers between -1 and 0 are -⅚, -⅔, -1/2;, -⅓, and -⅙.

(ii) -2 and -1

Let us multiply both numerator and denominator by 6

(-2 x 6)/(1 x 6) = (-12/6)

(-1 x 6)/(1 x 6) = -(6/6)

Five rational numbers between -2 and -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

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

(iii) -⅘ and -⅔

Let us convert -⅘ and -⅔ into like fractions

-4/5 = (-4 x 9)/(5 x 9) = -36/45

-2/3 = (-2 x 15)/(3 x 15) = -30/45

Five rational numbers between -⅘ and -⅔ are

-36/45 < -35/45 < -34/45 < -33/45 < -32/45 < -31/45 < -30/45

-4/5 < -35/45 < -34/45 < -33/45 < -32/45 < -31/45 < -2/3

Therefore, the five rational numbers between -⅘ and -⅔ are -7/9, -34/45, -11/15, -32/45, and -31/45.

(iv) -1/2 and ⅔

Let us convert -1/2 and ⅔ into like fractions

-1/2 = (-1 x 3)/(2 x 3) = -3/6

2/3 = (2 x 2)/(3 x 2) = 4/6

Five rational numbers between -1/2 and ⅔ are

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

Therefore, the five rational numbers between -1/2 and ⅔ are -⅓, -⅙, 0, ⅓, and 1/2.

Summary:

## List five rational numbers between: (i) -1 and 0, (ii) -2 and -1, (iii) -⅘ and -⅔, (iv) -1/2 and ⅔.

The five rational numbers between:

(i) -1 and 0 are -⅚, -⅔, -1/2, -⅓ and -⅙.

(ii) -2 and -1 are -11/6, -5/3, -3/2, -4/3 and -7/6.

(iii) -⅘ and -⅔ are -7/9, -34/45, -11/15, -32/45 and -31/45.

(iv) -1/2 and ⅔ are -⅓, -⅙, 0, ⅓, and 1/2.

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