Subtracting Whole Numbers with Subtraction in Parentheses

If you are interested in this article you may also be interested in the following articles:

• Subtraction of whole numbers with parentheses in which there are additions.
• Division of whole numbers in parentheses in which there is multiplication
• Division of integers in parentheses in which there is division

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Task:

Solve the following exercise:

$-30-\left(\left(-41\right)-\left(\left(-4\right)-\left(-8\right)\right)\right)=$

Solution:

First we solve the innermost parentheses.

$-30-\left(\left(-41\right)-\left(\left(-4\right)+8\right)\right)=$

Order the expression in the innermost parentheses and solve it.

$-30-\left(\left(-41\right)-\left(8-4\right)\right)=$

$-30-\left(\left(-41\right)-4\right)=$

We break $41$ down into $2$ numbers to make the calculation easier.

$-30-\left(-40-1-4\right)=$

$-30-\left(-40-1-4\right)=$

$-30-\left(-45\right)=$

We solve according to the rules.

$-30+45=$

$45-30=15$

Answer:

$15$

Task:

$17-\left(3-\left(-7-4\right)\right)=$

Solution:

First, we solve the innermost parentheses and break down$4$ into $2$ terms to make the calculation easier.

$17-\left(3-\left(-7-3-1\right)\right)=$

$17-\left(3-\left(-10-1\right)\right)=$

$17-\left(3-\left(-11\right)\right)=$

After solving the inner parentheses we continue solving the exercise that remains in parentheses.

$17-\left(3+11\right)=$

$17-14=$

We break down the expression to make the calculation easier.

$10+7-10-4=$

We solve the exercise in two parts.

$10-10=0$

$7-4=3$

Answer:

$3$

Task:

$-58-\left(\left(-7\right)-\left(-12\right)\right)=$

Solution:

We solve the expression in parentheses, first reordering the minus and plus signs.

$-58-\left(-7+12\right)=$

Solve the expression in parentheses accordingly.

$-58-\left(12-7\right)=$

Solve according to the rules.

$-58-5=$

We break down $5$ into $2$ terms to make the calculation easier.

$-58-2-3=$

$-60-3=-63$

Answer:

$-63$

Task:

$49-\left(53-18\right)=$

Solution:

First we start with the expression in parentheses and break down the $53$ into $2$ numbers to make the calculation easier.

$49-\left(58-5-18\right)=$

We solve the expression in parentheses and then solve accordingly.

$49-\left(58-18-5\right)=$

$49-\left(40-5\right)=$

$49-35=$

We break down the $49$ into $2$ numbers to make the calculation easier.

$45+4-35=$

We reorder the operations accordingly and solve.

$45-35+4=$

$10+4=14$

Answer:

$14$

Task:

$37-\left(4-7\right)=$

Solution:

First we tackle the expression in parentheses and solve.

$37-\left(-3\right)=$

We reorder the minus and plus signs accordingly, and solve.

$37+3=40$

Answer:

$40$

The parentheses are a grouping sign. As the name implies, they helps us to group operations where certain mathematical operations need to be performed. These parentheses indicate that the operations must be performed from the inside out, that is, first we must solve the operations that are inside the parentheses, in this case the subtraction, and then use that number in our subtraction operation.

In order to be able to solve operations with parenthese, the law of signs for multiplication must be applied. This law can be seen as follows:

$+\times+=+$

$+\times-=-$

$-\times+=-$

$-\times+=-$

To solve an operation with parentheses, all we have to do is complete the operations from the inside out, that is, perform the operations that are inside the parentheses and then the operations outside the parentheses. In this case we will solve the subtractions that are inside the parentheses and then we use sign laws and perform the next operation.

In order to eliminate the parentheses in an addition or a subtraction expression, we first perform the operations that are inside the parentheses, and in this way the parentheses are eliminated, let's see some examples:

Task:

$52-\left(25-11\right)=$

Solution:

We solve the subtraction inside the parentheses.

$52-\left(14\right)=$

We remove the parentheses by applying the law of signs.

$52-14=$

We break down the $14$ into two terms to make the calculations easier.

$52-12-2=40-2=38$

Answer:

$38$

Task:

$36-\left(\left(-3\right)-\left(-8\right)\right)=$

Solution:

Eliminate the innermost parentheses using sign laws.

$36-\left(-3+8\right)=$

Solve the operations inside the parentheses.

$36-\left(8-3\right)=36-\left(5\right)$

Again we eliminate parentheses.

$36-5=31$

Answer:

$31$