Advanced Arithmetic Operations

More arithmetic rules: subtraction of a sum, subtraction of a difference, division by product, and division by quotient

In this article, we will dive into the world of essential arithmetic rules that are fundamental for tackling a wide variety of mathematical exercises. Mastering these rules will provide you with a solid foundation and allow you to solve problems with greater confidence and precision. From basic operations like addition and subtraction to more advanced concepts like the division of products and quotients, we will explore each of these rules in detail. Are you ready to deepen your mathematical skills?
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Test yourself on additional arithmetic rules!

$$ 100-(5+55)= $$

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Subtraction of a sum

Sometimes we need to subtract a sum of elements from another element.
Rule:
$a−(b+c)=a−b−c$

This is also true in algebraic expressions.

We can operate according to the rule: apply the subtraction sign to each of the elements included in the parentheses.
Likewise, we can act according to the order of mathematical operations starting with the parentheses - calculate the sum and only then subtract it.

For example, in the exercise:
$21-(7+2)=$

Option 1 - according to the rule:

We will subtract each element in the parentheses separately and it will give us:
$21-7-2=12$

Option 2 - according to the order of operations:

$21-9=12$

Click here for a more detailed explanation about subtracting a sum.

Subtraction of a difference

It is valid when we need to subtract a difference of elements from another element.
Rule:
$a−(b-c)=a-b+c$

This is also valid in algebraic expressions.

We can operate according to the rule: apply the subtraction sign to each of the elements included in the parentheses and always remember that, minus times minus gives plus.
Likewise, we can act according to the order of mathematical operations starting with the parentheses - calculate the difference and only then subtract it.

For example, in the exercise:
$33-(9-3)=$

Option 1 - according to the rule:

We will separately subtract each element in the parentheses and it will give us:
$33-9+3=$

$24+3=27$

Option 2 - according to the order of operations:

$33-6=27$

Click here for a more detailed explanation about subtracting a difference.

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Test your knowledge

Question 1

$70:(14\times5)=$

Question 2

$300:(5\times6)=$

Question 3

$$ 21-(6-13)= $$

Division by product

It is also true when we need to divide a certain element by the product of others.
Rule:
$a:(b\cdot c)=a:b:c$

This is also valid in algebraic expressions.

We can operate according to the rule: apply the division to each of the elements included in the parentheses.
Likewise, we can act according to the order of mathematical operations starting with the parentheses - calculate the multiplication and only then divide by the product.

For example, in the exercise:
$50:(2\cdot5)$

Option 1 - according to the rule:

We will divide separately for each element of the parentheses and it will give us:
$50:2:5=$
First, we will divide $50:2$ and rewrite the exercise:
$25:5=5$

Option 2 - according to the order of operations:

$50:10=5$

Click here for a more detailed explanation about division by product.

Division by quotient

It is valid when we need to divide a certain element by the quotient of others.
Rule:
$a:(b:c)=a:b\cdot c$

This is also valid in algebraic expressions.

We can operate according to the rule: apply the division to the first element inside the parentheses and then apply the multiplication to the second element of the parentheses.
Likewise, we can act according to the order of mathematical operations starting with the parentheses - calculate the quotient and only then divide by it.

For example, in the exercise:
$48:(6:2)=$

Option 1 - according to the rule:

We will apply division to the first element inside the parentheses and then multiply by the second element of the parentheses.

$48:6\cdot2=$
First, we will divide $48:6$ and rewrite the exercise:
$8\cdot 2=16$

Option 2 - according to the order of operations:

$48:(6:2)=$
$48:3=16$

Click here for a more detailed explanation about division by quotient.

Examples and exercises with solutions of arithmetic rules

Exercise #1

$100-(5+55)=$

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

Step 1: Calculate the sum inside the parentheses.
Step 2: Subtract the result of the sum from 100.

Now, let's work through each step:
Step 1: Calculate $5 + 55$ , which gives $60$ .
Step 2: Perform the subtraction $100 - 60$ , which equals $40$ .

Therefore, the solution to the problem is $40$ .

Answer

Exercise #2

$70:(14\times5)=$

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

Step 1: Calculate the product of $14$ and $5$ .
Step 2: Use this product to divide $70$ .
Step 3: Compare the calculated result with the given choices.

Now, let's work through each step:
Step 1: First, calculate the product of $14$ and $5$ . Using basic multiplication:
$14 \times 5 = 70$ Step 2: Divide $70$ by the product, which is also $70$ :
$70 \div 70 = 1$

Therefore, the solution to the problem is $1$ . This matches choice 1 from the provided options.

Answer

Exercise #3

$300:(5\times6)=$

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

Step 1: Compute the product $5 \times 6$ .
Step 2: Perform the division operation $300 \div 30$ .

Now, let's work through each step:

Step 1: Calculate $5 \times 6$ .

$5 \times 6 = 30$

Step 2: Divide 300 by the result from Step 1.

$300 \div 30 = 10$

Therefore, the solution to the problem is $\boxed{10}$ .

This matches the choice: 10.

Answer

Exercise #4

$21-(6-13)=$

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

Step 1: Evaluate the inner expression $6 - 13$
Step 2: Substitute the result from Step 1 into $21 - \text{result from Step 1}$

Now, let's work through each step:

Step 1: Calculate $6 - 13$ . In this calculation, we subtract 13 from 6. The result is $-7$ , because when subtracting a larger number from a smaller one, the result is negative.

Step 2: Substitute $-7$ into the outer expression $21 - (-7)$ . Since subtracting a negative is equivalent to adding the positive opposite, this simplifies to $21 + 7$ .

Now, compute $21 + 7$ , which equals 28.

Therefore, the solution to the problem is $28$ .

Answer

Exercise #5

$99:(33:10)=$

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

Step 1: Perform the inner division operation.
Step 2: Use the result of Step 1 in the outer division operation.

Now, let's work through each step:

Step 1: Calculate $33:10$ .
This operation is equivalent to dividing 33 by 10, which gives us:
$\frac{33}{10} = 3.3$ .

Step 2: Use the result from Step 1 to perform the division $99:3.3$ .
This operation now becomes:
$\frac{99}{3.3} = 30$ .

Therefore, the solution to the problem is $30$ .

Answer

Do you know what the answer is?

Question 1

$$ 99:(33:10)= $$

Question 2

$$ 2-(1+1)= $$

Question 3

$$ 19-(5+11)= $$

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Advanced Arithmetic Operations

More arithmetic rules: subtraction of a sum, subtraction of a difference, division by product, and division by quotient

Test yourself on additional arithmetic rules!

Subtraction of a sum

Option 1 - according to the rule:

Option 2 - according to the order of operations:

Subtraction of a difference

Option 1 - according to the rule:

Option 2 - according to the order of operations:

Division by product

Option 1 - according to the rule:

Option 2 - according to the order of operations:

Division by quotient

Option 1 - according to the rule:

Option 2 - according to the order of operations:

Examples and exercises with solutions of arithmetic rules

Exercise #1

Video Solution

Step-by-Step Solution

Answer

Exercise #2

Video Solution

Step-by-Step Solution

Answer

Exercise #3

Video Solution

Step-by-Step Solution

Answer

Exercise #4

Video Solution

Step-by-Step Solution

Answer

Exercise #5

Video Solution

Step-by-Step Solution

Answer

More Questions

Additional Arithmetic Rules