# What happens when you subtract two negatives?

• Last Updated : 29 Nov, 2021

Algebra is the branch of mathematics dealing with arithmetic operations and their associated symbols. The symbols are termed as variables that may take different values when subjected to different constraints. The variables are mostly denoted such as x, y, z, p, or q, which can be manipulated through different arithmetic operations of addition, subtraction, multiplication, and division, in order to compute the values.

Negative Numbers

Negative numbers are denoted by integers prepended by a minus sign. It represents the opposite. Or in other words, negative numbers are those numbers that are less than 0 and they are generally used to represent the loss or deficiency. For instance, -4, -2, -11 are negative numbers. The negative numbers can be easily added or subtracted by using both the negative operands.

Subtracting two negative numbers

When we subtract a negative number from another negative number, then these minus signs turn into a plus sign. Or in other words, subtraction of a negative number from another negative number is simply an addition of negative and positive numbers. This is because, according to the known rule, – (-4) becomes +4. The resultant operation becomes positive in nature. The final operation may be positive or negative in nature. However, the magnitude of the final output is greater than both the operands, in case none of the operands is 0. In the case of subtracting negative numbers, the following scenarios may arise where we are subtracting the second operand from the first operand :

1. Second operand > First operand

In case the magnitude of the second operand is greater than the first operand, the final output has a positive sign associated with it. For example, we have, -2 – –4. This equation is equivalent to -2 + 4, which boils down to the addition of 4 to -2 and produces 2. Or we can say -2 – (-4) = 2.

2. Second operand < First operand

In case the magnitude of the second operand is greater than the first operand, the final output has a negative sign associated with it. For example, we have, -4 – –2. This equation is equivalent to -4 + 2, which boils down to the addition of 2 to -4 and produces -2. Or we can say -4 – (–2) = -2.

3. Second operand = First operand

In case the magnitude of the second operand is equal to the first operand, the final output is 0. For example, we have, -2 – –2. This equation is equivalent to -2 + 2, which boils down to the addition of 2 to -2 and produces 0. Or we can say -2 – –2 = 0.

Examples

Question 1. Evaluate -3 – 8 – 10 – 0 – 5 – 1?

Solution:

Here we have to evaluate

= -3 – 8 – 10 – 0 – 5 – 1

Taking the negative sign outside the bracket

= -(3 + 8 + 10 + 0 + 5 + 1)

= -(27)

= -27

Question 2. Evaluate (-23 – 3 – 30 – 44) + (-10 – 6 – 8)?

Solution:

Here we have to evaluate

= (-23 – 3 – 30 – 44) + (-10 – 6 – 8)

First solve the brackets

= (-100) + (-24)

Now opening the brackets

= -100 – 24

= -124

Question 3. Evaluate (25 + 88 + 55) – (26 + 13 – 24)?

Solution:

Here we have to evaluate

= (25 + 88 + 55) – (26 + 13 – 24)

First solve the brackets

= (168) – (15)

Now opening the brackets

= 168 – 15

= 153

Question 4. Find out the answer to the following expression will be negative or positive?

{-22x – (-32x) + 58x + (-66x)}

Solution:

Here we have to find the answer of the expression will be negative or positive

= {-22x – (-32x) + 58x + (-66x)}

First opening the brackets

= (-22x + 32x + 58x – 66x)

Now we add and subtract negative and positive numbers with each other

= -22x – 66x + 32x + 58x

= -88x + 90x

= 2x

Therefore, on solving the expression the answer is positive.

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