Ordering and comparing numbers
🎯 In this topic you will
- Compare positive and negative numbers using the symbols <, >, and =.
- Order positive and negative numbers correctly on a number line.
🧠 Key Words
- negative number
- order
Show Definitions
- negative number: A number less than zero, usually written with a minus sign, used to represent values below zero.
- order: The arrangement of numbers from smallest to largest or from largest to smallest based on their value.
📍 Heights and Depths
T his picture shows the height above sea level and the depth below sea level of an iceberg.
🔢 Ordering Numbers
Y ou can order numbers starting with the smallest or the largest. Numbers are arranged according to their size.
📉 Examples of Order
F or example, starting with the smallest: −90, −80, −70, −60. Starting with the largest: 10, 0, −10, −20.
⚖️ Comparing Numbers
Y ou can compare two numbers using the symbols < and >. For example, −30 < 0 and −50 > −60.
❓ EXERCISES
1. Put these numbers in order starting with the smallest.
👀 Show answer
2. The table shows the minimum temperature on four days.
| Day | Temperature °C |
|---|---|
| Monday | $-2$ |
| Tuesday | $-1$ |
| Wednesday | $3$ |
| Thursday | $-4$ |
a. Which temperature is colder than $-2^\circ\text{C}$?
b. Write the temperatures in order, starting with the coldest temperature.
👀 Show answer
a. $-4^\circ\text{C}$
b. $-4^\circ\text{C},\,-2^\circ\text{C},\,-1^\circ\text{C},\,3^\circ\text{C}$
3.
a. Put this set of numbers in order starting with the smallest.
b. Describe the number pattern.
c. The pattern continues in the same way. Will $121$ be in the pattern? How do you know?
👀 Show answer
a. $-18,\,-12,\,-6,\,0,\,6,\,12$
b. The numbers increase by $6$ each time.
c. Yes, because $121$ is not a multiple of $6$ added to $0$, so it will not appear in this pattern.
4. Write each pair of numbers using the symbol $>$ or $<$.
a. $-3 \ \square \ 9$
b. $10 \ \square \ -1$
c. $-15 \ \square \ 7$
d. $-6 \ \square \ -9$
👀 Show answer
a. $-3 < 9$
b. $10 > -1$
c. $-15 < 7$
d. $-6 > -9$
5. If $-5 < \square < -2$ what whole number could $\square$ be?
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6. Here are six number cards. Three cards are blank. Write a whole number on each blank card so that the six numbers are in order.
👀 Show answer
7. Here are four temperatures. Use each temperature once to make this statement correct.
$-4^\circ\text{C},\ 0^\circ\text{C},\ 5^\circ\text{C},\ -2^\circ\text{C}$
$\square < \square < \square < \square$
👀 Show answer
🧠 Think like a Mathematician
Five negative whole numbers can be arranged to form a number pattern. The numbers obey these rules:
- one number is between $-4$ and $-6$
- one number is between zero and $-3$ but is closer to zero than to $-3$
- one number is next to $-8$ and also next to $-10$
- one number is halfway between $-5$ and $-9$
- one number is halfway between $0$ and $-6$
Task: Arrange the numbers in order. Describe the pattern you have made.
👀 show answer
Step-by-step:
- Between $-4$ and $-6$ is $-5$.
- Between $0$ and $-3$ and closer to $0$ is $-1$.
- A number next to $-8$ and also next to $-10$ must be $-9$ (it sits between them).
- Halfway between $-5$ and $-9$ is $\dfrac{-5+(-9)}{2}=-7$.
- Halfway between $0$ and $-6$ is $\dfrac{0+(-6)}{2}=-3$.
Five numbers:$-1,\,-3,\,-5,\,-7,\,-9$
In order (least to greatest):$-9,\,-7,\,-5,\,-3,\,-1$
Pattern description: This is an arithmetic pattern that increases by $2$ each time (all the numbers are negative odd integers).