Ordering Quantities and Comparison Symbols

Ordering by Magnitude

To order quantities by magnitude means arranging numbers from least to greatest (ascending) or greatest to least (descending), based on their values.

Before ordering, convert all quantities to the same form (e.g. decimals) if they are in mixed forms like fractions, decimals, or percentages.

Example: To order \( \frac{1}{2}, 0.3, \frac{5}{10}, 45\% \),

first convert: \( \frac{1}{2} = 0.5,\quad 0.3,\quad \frac{5}{10} = 0.5,\quad 45\% = 0.45 \)

Then arrange: \( 0.3 < 0.45 < 0.5 = \frac{1}{2} = \frac{5}{10} \)

Symbols for Comparison

Understanding and using comparison symbols is essential when working with inequalities and ordering values.

= (equals)

Used when two quantities are exactly the same. Example: \( 2 + 3 = 5 \)

≠ (not equal to)

Used when two quantities are not equal. Example: \( 4 \ne 5 \)

> (greater than)

Used when the number on the left is larger than the one on the right. Example: \( 7 > 2 \)

< (less than)

Used when the number on the left is smaller than the one on the right. Example: \( 3 < 8 \)

⩾ (greater than or equal to)

Used when a number is either greater than or exactly equal to the other. Example: \( x \geq 5 \) means \( x = 5 \) or \( x > 5 \)

⩽ (less than or equal to)

Used when a number is either smaller than or equal to another. Example: \( y \leq 10 \) means \( y = 10 \) or \( y < 10 \)