Question

Which of the two rational numbers in each of the following pairs of rational number is greater?

(i) (-3/8), 0

(ii) (5/2), 0

(iii) (– 4/11), (3/11)

(iv) (– 7/12), (5/- 8)

(v)  (4/-9), (– 3/- 7)

(vi) (– 5/8), (3/- 4)

(vii) (5/9), (-3/- 8)

(viii)  (5/- 8), (-7/12)

Answer 1

(i) Given (-3/8), 0

We know that every positive rational number is greater than zero and every negative

rational number is smaller than zero. Thus, – (3/8) > 0

(ii)  Given (5/2), 0

We know that every positive rational number is greater than zero and every negative rational number is smaller than zero. Thus, (5/2) > 0

(iii) Given (– 4/11), (3/11)

We know that every positive rational number is greater than zero and every negative rational number is smaller than zero, also the denominator is same in given question now we have to compare the numerator, thus – 4/11 < 3/11.

(iv) Given (– 7/12), (5/- 8)

Consider (– 7/12)

Multiply both numerator and denominator by 2 then we get

(-7/12) × (2/2) = (-14/24)…… (1)

Now consider (5/-8)

Multiply both numerator and denominator by 3 we get

(5/-8) × (3/3) = (15/-24)…… (2)

The denominator is same in equation (1) and (2) now we have to compare the numerator, thus (– 7/12) > (5/- 8)

(v) Given (4/-9), (– 3/- 7)

Consider (4/-9)

Multiply both numerator and denominator by 7 then we get

(4/-9) × (7/7) = (28/-63)…… (1)

Now consider (-3/-7)

Multiply both numerator and denominator by 9 we get

(-3/-7) × (9/9) = (-27/-63)…… (2)

The denominator is same in equation (1) and (2) now we have to compare the numerator, thus (4/-9) < (– 3/- 7)

(vi) Given (– 5/8), (3/- 4)

Now consider (3/-4)

Multiply both numerator and denominator by 2 we get

(3/-4) × (2/2) = (6/-8)

The denominator is same in above equation now we have to compare the numerator, thus (– 5/8) > (3/- 4)

(vii) Given (5/9), (-3/- 8)

Consider (5/9)

Multiply both numerator and denominator by 8 then we get

(5/9) × (8/8) = (40/72)…… (1)

Now consider (5/-8)

Multiply both numerator and denominator by 9 we get

(-3/-8) × (9/9) = (-27/-72)…… (2)

The denominator is same in equation (1) and (2) now we have to compare the numerator, thus (5/9) > (-3/- 8)

(viii) Given (5/- 8), (-7/12)

Consider (5/-8)

Multiply both numerator and denominator by 3 then we get

(5/-8) × (3/3) = (15/-24)…… (1)

Now consider (-7/12)

Multiply both numerator and denominator by 2 we get

(-7/12) × (2/2) = (-14/24)…… (2)

The denominator is same in equation (1) and (2) now we have to compare the numerator, thus (5/- 8) < (-7/12)