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Recap

In maths there are different types of numbers:

• Natural numbers: Also called counting numbers, Natural numbers are greater than zero i.e. {1, 2, 3, 4 ….}

• Whole numbers: Whole numbers are the numbers 0, 1, 2, 3 and so on. Note that decimal numbers and fractions are not whole numbers i.e. {0, 1, 2, 3 ….}

• Real numbers: This is the set of all possible numbers.

• Integers: Integers are the set of negative, zero and positive whole numbers. i.e. { …..-3, -2, -1, 0, 1, 2, 3 ….. }

Negative numbers

Negative numbers are represented with a ‘-’ sign ahead of the number.

Example:

-3, -9, -67

The number ‘- 9’ represents a negative value with the magnitude of nine.

Representation on the Number line

The relationship between positive numbers, zero and negative numbers can be represented as

As we can see on the number line, the numbers greater than zero on the right are called positive and the numbers less than zero on the left are called negative numbers. Zero does not have any sign.

In case of positive numbers, the further a number is from 0 on the number line, the greater is its value.

In case of negative numbers, the further a number is from 0 on the number line, the lower is its value.

Example: 8 > 5 but -8 < -5

Two numbers whose sum is zero are called the Additive Inverse of each other. For example 4 and -4 are additive inverse of each other.

• Adding two negative numbers is the same as adding two positive numbers but the resulting number will be a negative number.

Example:

(-12) + (-5) = -17.

• When adding a set of positive and negative numbers you can consider the negative numbers as positive numbers that have to be subtracted.

Example:

12 + (-5) = 12 - 5 = 7.

Subtracting negative numbers

• When you subtract two negative numbers, you must convert the sign of the second number and then add the two numbers

Example:

(-12) - (-5) = -12 + 5 = -7

Subtraction can be considered as addition of the additive inverse of the number to be subtracted.

Multiplying negative numbers

• When you multiply two numbers the answer is the product of the two magnitudes. The sign of the product is determined by the following rules:

The product of a positive number and the negative number is always negative.

The product of two negative numbers is always positive.

Example:

3 * (-4) = -12

(-7) * (-3) = 21

Dividing negative numbers

• When you divide two numbers, the rules for the sign of the quotient of division are the same as that for multiplication.

Example:

21 ÷ (-3) = -7

(-21) ÷ (-3) = 7

Tip: If the dividend and the divisor have the same sign the result is positive. If one of the numbers in the division is negative, the result will be negative.

Negative Numbers Worksheet

1. 9 + ( - 7)

2. 4 + (-12)

3. (-2) + (-6)

4. (-1) + 3

A1: a) 2, b) -8, c) -8, d) 2

Q2. Subtract the following integers

1. 4 - (-2)

2. (-3) - (- 4)

3. (-3) - (4)

4. 4 - (2)

A2: a) 6, b) 1, c) -7, d) 2

Q3: Subtract the following:

1. 3 from -1

2. -2 from -6

3. 7 from 9

4. -7 from 6

A3:

1. -1 - (3) = -4

2. -6 - (-2) = -6 + 2 = -4

3. 9 - 7 = 2

4. 6 - (-7) = 6 + 7 = 13

Q4. Multiply the following numbers:

1. 12 * 3

2. -12 * 3

3. 12 * -3

4. -12 * -3

A4: a) 36, b) -36, c) -36, d) 36

Q5: Divide the following numbers:

1. 18 ÷ 2

2. 18 ÷ (-2)

3. (-18) ÷2

4. (-18) ÷ (-2)

A5: a) 9, b) -9, c) -9, d) 9

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