1E Negative integers

Learning intentions

By the end of this topic you will be able to … ✔ compare the value of positive and negative numbers ✔ use negative numbers to represent real-life situations.

Integers

• The set of integers includes all positive whole numbers, negative whole numbers and zero.

• Negative integers are less than zero in value and are preceded by a negative sign, −, placed directly before the first digit.

• Positive integers are greater than zero in value and can be represented by using a positive sign, +. The positive sign can also be left out.

• In the real world, negative numbers are used to represent quantities that lie on a scale that goes below zero. A sign is used to indicate the direction relative to the reference point of zero. For example, a negative temperature indicates that the temperature has dropped below the reference point of 0°.

Ordering numbers

• Numbers are in ascending order when they are arranged in order of increasing value.

• Numbers are in descending order when they are arranged in order of decreasing value.

• ‘Less than’ is shown using the symbol ‘<’

• ‘Greater than’ is shown using the symbol ‘>’

• ‘Equal to’ is shown using the symbol ‘=’

Example 1E.1 Identifying the greater of two integers

Identify which integer is greater in each pair of numbers. Use the following number line to help you.

−4 and −7

THINK a 1 Locate the two numbers on the number line and compare their positions. 2 is to the right of −5, so 2 is greater than −5. b 1 Locate the two numbers on the number line and compare their positions. −4 is to the right of −7, so −4 is greater than −7.

2 Use the ‘greater than’ symbol, >, in your answer.

2 Use the ‘greater than’ symbol, >, in your answer.

Example 1E.2 Representing a situation with an integer

Provide an integer to represent each situation.

a The temperature is 15 degrees above zero.

b A fish swims 4 m below the surface of the water.

c Your bank account is overdrawn by $30.

THINK a 1 The reference point is 0°. b 1 The reference point is the water surface. c 1 The reference point is $0.

2 Determine the sign of the integer based on the number’s position relative to the reference point. ‘15 degrees above zero’ can be indicated using 15.

2 Determine the sign of the integer based on the number’s position relative to the reference point. ‘4 m below’ can be indicated using −4.

2 Determine the sign of the integer based on the number’s position relative to the reference point. ‘Overdrawn by $30’ can be indicated using −30.

WRITE a 15 b −4 c −30

✔ The negative equivalent of a positive number is called the additive inverse. For example, −4 is the additive inverse of 4.

Helpful hints

✔ Don’t get your ‘greater than’ and ‘less than’ symbols mixed up! The ‘mouth’ of the symbol is always trying to ‘eat’ the greater number.

For example, 4 > 3 and 3 < 4