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ZingPath: Whole Numbers and Integers

Number Relationships among Operations

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Whole Numbers and Integers

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Lesson Focus

Number Relationships among Operations

Math Foundations

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You will use your understanding of number relationships to solve problems.

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Now You Know

After completing this tutorial, you will be able to complete the following:

  • Understand the effect of addition, subtraction, multiplication, and division on numbers and the relationship among these operations.
  • Describe the Identity Element of Addition, the Identity Element of Multiplication, and the Multiplication Property of Zero.
  • Use the Identity Element of Addition, the Identity Element of Multiplication, and the Multiplication Property of Zero in solving problems involving whole number integers.
  • Use the basic properties of operations to solve problems.

Everything You'll Have Covered

The problems can be solved using number relationships.

Students can solve the puzzles in this Activity Object by examining the relationships between numbers. Every number can be broken down into smaller numbers. For example, 7 can be created by adding several combinations of numbers -2 + 5, 3 + 4, and 6 + 1. Students use information about number relationships to determine the placement of the numbers in the problems.

Example:

Using numbers 1 through 9, A must be 1, 2, 3, or 4. When each of these numbers is doubled (or added to itself), the sum is less than ten. B must be 2, 4, 6, or 8 as these numbers are the only possible sums of 1, 2, 3 or 4 doubled. Using number relationships to solve this example allows us to narrow the possible options.

When multiple problems are solved in Level 2 and 3, students will be able to eliminate options more easily as they analyze the number relationships.

The Identity Property of Addition states that when any number is added to zero the sum is the number.

Students should be able to quickly recognize this property when solving the problems in this Activity Object.

Algebraically, this can be expressed as: a + 0 = a

Zero is called the Identify Element of Addition.

Example:

Using the Identity Property of Addition, we can see that the number added to C must be zero since the sum of the addition problem is C. Therefore, D is zero.

The Identity Property of Multiplication states that when any number is multiplied by one the product is the number.

Again, most students should be able to quickly recognize this property when solving the problems in this Activity Object.

Algebraically, this can be expressed as: a 1 = a

One is called the Identity Element of Multiplication.

Example:

Using the Identity Property of Multiplication, we can see that E must be one since the product of the multiplication problem is F. Therefore, E is one.

The Multiplication Property of Zero states that when any number is multiplied by zero the product is zero.

This property is also easily recognizable when solving problems.

Algebraically, this can be expressed as: a 0 = 0

Example:

Using the Multiplication Property of Multiplication, we can see that H must be zero, since the product of the multiplication is H. Therefore, H is zero.

Tutorial Details

Approximate Time 10 Minutes
Pre-requisite Concepts Students should be familiar with basic whole number computation, identity element of addition, identity element of multiplication, and the multiplication property of zero.
Course Math Foundations
Type of Tutorial Skills Application
Key Vocabulary numbers, operations, properties of operations