Positive and Negative Numbers

Positive and negative numbers are often used to represent quantities like temperature. For example, in winter, a temperature of -2℃ is 2℃ below zero.

When working with arithmetic, it can be helpful to think of positive numbers as something we possess and negative numbers as a debt we owe.

Negative numbers have a minus sign in front of them, such as -2℃. Positive numbers can be written with or without the positive sign in front of the number.

In 10+3, we treat 10 as something we possess and the +3 as something else we possess. So in total, we have 13. Therefore, 10+3=13.

In -10+3, we treat -10 as a debt and the +3 as something we have. After settling the account, we still have a 7 debt. So, -10+3=-7.

In -10-3, we regard -10 as a debt and the -3 as another debt. So in total, we have a 13 debt. Therefore, -10-3=-13.

Calculating sums and differences can also be visualised on a number line. We move to the right if we are adding and to the left if we are subtracting.

For 10+3, start at 10 on the number line and move 3 steps to the right. This gives us 13.

For (-10)+3, start at -10 and move 3 steps to the right.

For (-10)-3, start at -10 and move 3 steps to the left. This takes us to -13. Hence, (-10)-3=-13.

For -10+11, we start at -10 and move 11 steps to the right. This takes us to +1, so -10+11=1.

Keep these rules in mind:

  • + + = +
  • + - = -
  • - + = -
  • - - = +

With larger numbers, using a number line becomes impractical. Instead, visualise what is happening on the number line. For example, consider -57+123.

Start at -57 on the number line and move 123 steps to the right. This takes us to 123-57=66. So, -57+123=66.

To calculate (-57)-123, start at -57 and move 123 steps to the left. This takes us to -(57+123) on the number line. Now, 57+123=180. Therefore, (-57)-123=-180.

With practice, calculations become easier, and visualising the number line may no longer be necessary.

When multiplying numbers (positive, negative), remember these rules:

  • Positive \times positive = positive
  • Positive \times negative = negative
  • Negative \times positive = negative
  • Negative \times negative = positive

Examples

  • 4\times5=20
  • 4\times-5=-20
  • -4\times5=-20
  • -4\times-5=20

The same rules apply for division:

  • 15\div3=5
  • 15\div-3=-5
  • -15\div3=-5
  • -15\div-3 = 5

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