Illustrate by applying the following properties of addition, using sums up to 20: - the sum of zero and any number is equal to the number; and - changing the order of the addends d... Illustrate by applying the following properties of addition, using sums up to 20: - the sum of zero and any number is equal to the number; and - changing the order of the addends does not change the sum.
Understand the Problem
The question is asking to illustrate two properties of addition using examples where the sums do not exceed 20. The first property states that the sum of zero and any number is equal to the number. The second property states that changing the order of the addends does not change the sum. To solve it, we will provide examples for each property.
Answer
1. For the property of zero: $0 + 5 = 5$, $0 + 10 = 10$, $0 + 15 = 15$. 2. For the commutative property: $2 + 3 = 5$ and $3 + 2 = 5$, $7 + 8 = 15$ and $8 + 7 = 15$, $4 + 6 = 10$ and $6 + 4 = 10$.
Answer for screen readers
The examples illustrating the properties of addition are:
- For the property of zero:
- $0 + 5 = 5$
- $0 + 10 = 10$
- $0 + 15 = 15$
- For the commutative property:
- $2 + 3 = 5$ and $3 + 2 = 5$
- $7 + 8 = 15$ and $8 + 7 = 15$
- $4 + 6 = 10$ and $6 + 4 = 10$
Steps to Solve
- Illustrate the property of zero
To show that the sum of zero and any number equals the number, we can use examples like:
- $0 + 5 = 5$
- $0 + 10 = 10$
- $0 + 15 = 15$
These examples clearly demonstrate that adding zero to any number does not change the value of that number.
- Demonstrate the commutative property of addition
To illustrate that changing the order of the addends does not change the sum, we can use several pairs of numbers:
- $2 + 3 = 5$ and $3 + 2 = 5$
- $7 + 8 = 15$ and $8 + 7 = 15$
- $4 + 6 = 10$ and $6 + 4 = 10$
Each pair shows that the result remains the same regardless of the order of the numbers being added.
The examples illustrating the properties of addition are:
- For the property of zero:
- $0 + 5 = 5$
- $0 + 10 = 10$
- $0 + 15 = 15$
- For the commutative property:
- $2 + 3 = 5$ and $3 + 2 = 5$
- $7 + 8 = 15$ and $8 + 7 = 15$
- $4 + 6 = 10$ and $6 + 4 = 10$
More Information
These properties of addition are fundamental in mathematics. The first property emphasizes that zero is the identity element for addition, while the second property highlights the flexibility in adding numbers, which is essential for simplifying expressions and solving equations easily.
Tips
Common mistakes include:
- Forgetting to verify that the sum remains the same when switching the order of the addends. Always check both combinations for clarity.
- Miscalculating the result when adding. Double-checking basic arithmetic can help avoid these errors.
