Question

Arrange the following in ascending order:

• A. |-3| + |7|
• B. |23/3| + 5
• C. |-32/3| + |-7|
• D. |55/3| - 4

Answer 1

Here, the || refers to modulus or absolute value of a number.

So,

1. |-3| + |7| = 3 + 7 = 10

2. |23/3| + 5 = $\frac{23+15}{3}$ = $\frac{38}{3}$

3. |-32/3| + |-7| = 32/3 + 7 = $\frac{32+21}{3}$
= $\frac{53}{3}$

4. |55/3| - 4 = $\frac{55-12}{3}$ = $\frac{43}{3}$

Converting all the above to have the same denominators, we get:
$\frac{30}{3}$ , $\frac{38}{3}$ , $\frac{53}{3}$ ,$\frac{43}{3}$

Hence, in ascending order
$\frac{30}{3}$ < $\frac{38}{3}$ < $\frac{43}{3}$ < $\frac{53}{3}$

i.e., |-3|+|7| < |23/3| + 5 < |55/3| - 4 < |-32/3| + |-7|