Additional Arithmetic Rules Practice Problems & Solutions

Master subtraction of sums, subtraction of differences, division by products, and division by quotients with step-by-step practice problems and solutions.

📚Master Advanced Arithmetic Rules with Interactive Practice

Apply subtraction of sum rule: a-(b+c) = a-b-c in complex expressions
Solve subtraction of difference problems using a-(b-c) = a-b+c formula
Master division by product rule: a:(b·c) = a:b:c with step-by-step solutions
Practice division by quotient problems using a:(b:c) = a:b·c method
Compare multiple solution methods for each arithmetic rule type
Build confidence solving parentheses problems with distributive properties

Understanding Additional Arithmetic Rules

Complete explanation with examples

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?
Let's get started!

Detailed explanation

Practice Additional Arithmetic Rules

Test your knowledge with 40 quizzes

$$ 22-(28-3)= $$

Examples with solutions for Additional Arithmetic Rules

Step-by-step solutions included

Exercise #1

$60:(10\times2)=$

Step-by-Step Solution

We write the exercise in fraction form:

$\frac{60}{10\times2}=$

Let's separate the numerator into a multiplication exercise:

$\frac{10\times6}{10\times2}=$

We simplify the 10 in the numerator and denominator, obtaining:

$\frac{6}{2}=3$

Answer:

$3$

Video Solution

Exercise #2

$12:(2\times2)=$

Step-by-Step Solution

According to the order of operations, we first solve the exercise within parentheses:

$2\times2=4$

Now we divide:

$12:4=3$

Answer:

$3$

Video Solution

Exercise #3

$7-(4+2)=$

Step-by-Step Solution

According to the order of operations, we first solve the exercise within parentheses:

$4+2=6$

Now we solve the rest of the exercise:

$7-6=1$

Answer:

$1$

Video Solution

Exercise #4

$8-(2+1)=$

Step-by-Step Solution

According to the order of operations, we first solve the exercise within parentheses:

$2+1=3$

Now we solve the rest of the exercise:

$8-3=5$

Answer:

$5$

Video Solution

Exercise #5

$13-(7+4)=$

Step-by-Step Solution

According to the order of operations, we first solve the exercise within parentheses:

$7+4=11$

Now we subtract:

$13-11=2$

Answer:

$2$

Video Solution

Frequently Asked Questions

Everything you need to know about Additional Arithmetic Rules

What is the subtraction of a sum rule in arithmetic?

The subtraction of a sum rule states that a-(b+c) = a-b-c. This means when subtracting a sum in parentheses, you can distribute the negative sign to each term inside the parentheses. For example, 21-(7+2) = 21-7-2 = 12.

How do you solve subtraction of difference problems?

Use the rule a-(b-c) = a-b+c. When subtracting a difference, distribute the negative sign: the first term becomes negative and the second term becomes positive. For instance, 33-(9-3) = 33-9+3 = 27.

What is division by product rule and how does it work?

The division by product rule is a:(b·c) = a:b:c. You can divide by each factor separately instead of multiplying first. Example: 50:(2·5) = 50:2:5 = 25:5 = 5, which equals 50:10 = 5.

How is division by quotient different from division by product?

Division by quotient follows the rule a:(b:c) = a:b·c. You divide by the first term and multiply by the second term. For example, 48:(6:2) = 48:6·2 = 8·2 = 16, or solve parentheses first: 48:3 = 16.

Why do these arithmetic rules work with algebraic expressions?

These rules apply to algebraic expressions because they follow the same mathematical properties as numbers. The distributive property, associative property, and order of operations remain consistent whether using numbers or variables.

When should I use the rule vs order of operations?

Both methods give the same result. Use the rule method when you want to practice distributive properties or when parentheses contain complex expressions. Use order of operations when the calculation inside parentheses is simple and quick to compute.

What are common mistakes with subtraction of difference problems?

The most common mistake is forgetting that minus times minus equals plus. In a-(b-c), students often write a-b-c instead of a-b+c. Remember: the negative sign changes both terms in the parentheses.

How can I remember these arithmetic rules easily?

Use these memory aids: 1) Subtraction distributes to all terms, 2) Division by product splits into separate divisions, 3) Division by quotient flips the second operation (division becomes multiplication), 4) Practice with simple numbers first before using variables.

Continue Your Math Journey

Master Additional Arithmetic Rules first, then advance to these related topics that build on your fraction skills

Topics Learned in Later Sections

Subtracting Whole Numbers with Addition in Parentheses Division of Whole Numbers Within Parentheses Involving Division Subtracting Whole Numbers with Subtraction in Parentheses Division of Whole Numbers with Multiplication in Parentheses

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Additional Arithmetic Rules Practice Problems & Solutions

Understanding Additional Arithmetic Rules

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

Practice Additional Arithmetic Rules

Examples with solutions for Additional Arithmetic Rules

Frequently Asked Questions

What is the subtraction of a sum rule in arithmetic?

How do you solve subtraction of difference problems?

What is division by product rule and how does it work?

How is division by quotient different from division by product?

Why do these arithmetic rules work with algebraic expressions?

When should I use the rule vs order of operations?

What are common mistakes with subtraction of difference problems?

How can I remember these arithmetic rules easily?

More Additional Arithmetic Rules Questions