The numbers and have some special characteristics when performing basic operations like addition, subtraction, multiplication, and division—including combined calculations.
In this article we will learn what they are and why they are important.
Special Cases 0 and 1 Practice Problems and Exercises
Master the special properties of 0 and 1 in arithmetic operations. Practice identity elements, multiplication by zero, and division rules with step-by-step solutions.
📚Practice Your Understanding of Zero and One Properties
- Apply additive identity property with zero in complex expressions
- Use multiplicative identity property with one to simplify calculations
- Solve problems involving multiplication by zero in combined operations
- Practice division by one and zero division rules correctly
- Work through order of operations with special cases 0 and 1
- Identify when expressions equal zero or remain unchanged using identity elements
Understanding The Numbers 0 and 1 in Operations
Complete explanation with examples
Practice The Numbers 0 and 1 in Operations
Test your knowledge with 19 quizzes
\( \frac{6}{3}\times1=\text{ ?} \)
Examples with solutions for The Numbers 0 and 1 in Operations
Step-by-step solutions included
Exercise #1
Solve the following exercise:
Step-by-Step Solution
According to the order of operations rules, since the exercise only involves addition and subtraction operations, we will solve the problem from left to right:
Answer:
Video Solution
Exercise #2
Solve the following exercise:
Step-by-Step Solution
According to the order of operations rules, since the exercise only involves addition and subtraction, we will solve the problem from left to right:
Answer:
9.5
Video Solution
Exercise #3
Step-by-Step Solution
According to the order of operations rules, we first divide and then add:
Answer:
Video Solution
Exercise #4
Step-by-Step Solution
According to the order of operations rules, we first divide and then add:
Answer:
Video Solution
Exercise #5
Solve the following exercise:
Step-by-Step Solution
According to the order of operations rules, we first divide and then add:
Answer:
Frequently Asked Questions
What happens when you multiply any number by 0?
+When you multiply any number by 0, the result is always 0. This is called the zero property of multiplication. For example: 5 × 0 = 0, (-3) × 0 = 0, and 1000 × 0 = 0.
Why is 1 called the multiplicative identity?
+The number 1 is called the multiplicative identity because multiplying any number by 1 leaves the number unchanged. For instance: 7 × 1 = 7, 253 × 1 = 253. This property makes 1 the neutral element for multiplication.
What is 0 divided by any number?
+Zero divided by any non-zero number equals 0. Examples include: 0 ÷ 5 = 0, 0 ÷ 100 = 0, 0 ÷ (1/2) = 0. However, division by zero is undefined and not allowed in mathematics.
How do special properties of 0 and 1 help in order of operations?
+The special properties of 0 and 1 can simplify complex expressions. If you identify multiplication by 0 (result is 0) or multiplication by 1 (number stays same), you can solve problems faster without computing every step.
What is the additive identity and why is it important?
+Zero is the additive identity because adding 0 to any number leaves it unchanged: a + 0 = a and a - 0 = a. This property is fundamental in algebra and helps maintain equality in equations when adding or subtracting zero.
Can you divide by zero in mathematics?
+No, division by zero is undefined in mathematics. You cannot divide any number by 0. However, you can divide 0 by any non-zero number, and the result will always be 0.
How do identity elements work in combined operations?
+In combined operations, identity elements follow the same rules: 1. Multiplication by 0 anywhere makes the entire product 0 2. Multiplication by 1 leaves factors unchanged 3. Adding or subtracting 0 doesn't change the sum 4. These properties help simplify complex expressions quickly.
What are some common mistakes with 0 and 1 in math problems?
+Common mistakes include: confusing 0 ÷ a = 0 with a ÷ 0 (undefined), forgetting that 0^0 is indeterminate, and not recognizing when expressions automatically equal zero due to multiplication by 0. Always check for these special cases first.