Which integer is greater, −45 or −54, and why?

Class 7Integers (Extended)Integers

A−54, because 54 is larger than 45.
BThey are equal in value.
C−54, because it lies further from zero.
D−45, because it lies to the right of −54 on the number line.

Step-by-Step Solution

Values increase to the right on the number line, and −45 sits to the right of −54, so −45 > −54. The trap is ranking negatives by their digits: among negative integers, the bigger the digits the smaller the number. Lying further from zero makes −54 smaller, not greater.

Answer: D) −45, because it lies to the right of −54 on the number line.

Key idea: Multiplying more than two integers

Count the number of negative factors:
- **Even** number of negatives → product is positive.
- **Odd** number of negatives → product is negative.

Examples:

(- 2) \times (- 3) \times (- 4)

has three negatives (odd) → negative. Compute the magnitude:

2 \times 3 \times 4 = 24

. Result: −24.

(- 2) \times (- 3) \times 4

has two negatives (even) → positive. Magnitude:

2 \times 3 \times 4 = 24

. Result: +24.

Master this chapter in 30 minutes a day.

Don't just memorise the answer — build a daily practice habit.

Practice 5 Similar Questions Free →

All Integers (Extended) practice questions

More Class 7 Integers (Extended) practice

Arrange −3, 7, −11, 0 and −8 in ascending order.How many integers lie strictly between −4 and 3?Which integer lies exactly midway between −8 and 2 on the number line?On a builder's survey pole, the top of a compound wall is marked +4 m and the bottom of…Without multiplying anything out, decide the sign of (−3) × (−7) × 2 × (−5) × (−1).