Question

Determine by observation which of the numbers in each pair is the bigger one and which is smaller.

(1) −5, −1
(2) $0,\frac{-8}{7}$
(3) $\frac{4}{3},0$
(4) $\frac{-3}{2},\frac{1}{4}$
(5) $\frac{-11}{6},\frac{-7}{6}$
(6) $\frac{25}{37},\frac{28}{37}$
(7) $\frac{25}{37},\frac{-28}{37}$
(8) $\frac{-7}{10},\frac{-5}{10}$

Answer 1

(1) −5, −1
The number on the left is smaller than the number on the right on the number line.
We know that −5 lies on the left of −1 on the number line.
∴ −5 < −1

(2) $0,\frac{-8}{7}$
All the negative numbers lie on the left of 0 on the number line.
∴ $\frac{-8}{7}$ is on the left of 0.
And we know that a number on the left is smaller than a number on the right on the number line.
$\therefore \frac{-8}{7}<0$

(3) $\frac{4}{3},0$
All the positive numbers lie on the right of 0 on the number line.
∴ 0 is on the left of$\frac{4}{3}$ .
And we know that a number on the left is smaller than a number on the right on the number line.
$\therefore 0<\frac{4}{3}$

(4) $\frac{-3}{2},\frac{1}{4}$
All the positive numbers lie on the right of all the negative numbers on the number line.
∴ $\frac{-3}{2}$ is on the left of$\frac{1}{4}$ .
And we know that a number on the left is smaller than a number on the right on the number line.
$\therefore \frac{-3}{2}<\frac{1}{4}$

(5) $\frac{-11}{6},\frac{-7}{6}$
If two numbers have the same denominator, then the one with the bigger numerator is the bigger number.
We know that −7 > −11 .
$\therefore \frac{-11}{6}<\frac{-7}{6}$

(6) $\frac{25}{37},\frac{28}{37}$
If two numbers have the same denominator, then the one with the bigger numerator is the bigger number.
We know that 25 < 28 .
$\therefore \frac{25}{37}<\frac{28}{37}$

(7) $\frac{25}{37},\frac{-28}{37}$
If two numbers have the same denominator, then the one with the bigger numerator is the bigger number.
We know that −28 < 25 .
$\therefore \frac{-28}{37}<\frac{25}{37}$

(8) $\frac{-7}{10},\frac{-5}{10}$
If two numbers have the same denominator, then the one with the bigger numerator is the bigger number.
We know that −7 < −5 .
$\therefore \frac{-7}{10}<\frac{-5}{10}$