Which Of The Following Equations Uses The Commutative Property Of Addition To Rewrite $\frac{1}{4}+\frac{2}{5}$?A. $\frac{2}{5}+\frac{1}{4}=\frac{13}{20}$ B. $ 2 4 + 1 5 = 14 20 \frac{2}{4}+\frac{1}{5}=\frac{14}{20} 4 2 + 5 1 = 20 14 [/tex] C.
The commutative property of addition is a fundamental concept in mathematics that states that the order of the numbers being added does not change the result. In other words, when we add two numbers, we can swap their positions and still get the same answer. This property is denoted by the equation a + b = b + a, where a and b are any two numbers.
In the context of fractions, the commutative property of addition can be applied to rewrite an expression in a different order. For example, if we have the expression $\frac{1}{4}+\frac{2}{5}$, we can use the commutative property to rewrite it as $\frac{2}{5}+\frac{1}{4}$.
Rewriting the Expression using the Commutative Property
To rewrite the expression $\frac{1}{4}+\frac{2}{5}$ using the commutative property, we need to swap the positions of the two fractions. This gives us $\frac{2}{5}+\frac{1}{4}$.
Now, let's examine the options provided to see which one uses the commutative property to rewrite the expression.
Option A: $\frac{2}{5}+\frac{1}{4}=\frac{13}{20}$
This option correctly uses the commutative property to rewrite the expression. By swapping the positions of the two fractions, we get $\frac{2}{5}+\frac{1}{4}$, which is equal to $\frac{13}{20}$.
Option B: $\frac{2}{4}+\frac{1}{5}=\frac{14}{20}$
This option does not use the commutative property to rewrite the expression. Instead, it simplifies the fractions by dividing the numerator and denominator of the first fraction by 2, resulting in $\frac{1}{2}+\frac{1}{5}$, which is equal to $\frac{7}{10}$, not $\frac{14}{20}$.
Option C: (Not Provided)
Since option C is not provided, we cannot evaluate it.
Conclusion
In conclusion, the correct answer is option A, $\frac{2}{5}+\frac{1}{4}=\frac{13}{20}$, which uses the commutative property of addition to rewrite the expression $\frac{1}{4}+\frac{2}{5}$.
Understanding the Commutative Property in Real-Life Scenarios
The commutative property of addition is not limited to mathematical expressions. It can be applied to real-life scenarios where we need to add two or more quantities. For example, if we have two boxes containing different numbers of apples, we can use the commutative property to swap the contents of the boxes and still get the same total number of apples.
Real-Life Applications of the Commutative Property
The commutative property of addition has numerous real-life applications in various fields, including:
- Cooking: When measuring ingredients for a recipe, we can use the commutative property to swap the positions of two ingredients and still get the same result.
- Finance: calculating the total cost of two or more items, we can use the commutative property to swap the positions of the items and still get the same result.
- Science: When measuring the volume of two or more liquids, we can use the commutative property to swap the positions of the liquids and still get the same result.
Conclusion
In conclusion, the commutative property of addition is a fundamental concept in mathematics that has numerous real-life applications. By understanding and applying this property, we can simplify complex mathematical expressions and solve problems more efficiently.
Frequently Asked Questions
Q: What is the commutative property of addition?
A: The commutative property of addition is a fundamental concept in mathematics that states that the order of the numbers being added does not change the result.
Q: How is the commutative property used in real-life scenarios?
A: The commutative property is used in real-life scenarios where we need to add two or more quantities. For example, when measuring ingredients for a recipe, we can use the commutative property to swap the positions of two ingredients and still get the same result.
Q: What are some real-life applications of the commutative property?
A: Some real-life applications of the commutative property include cooking, finance, and science.
Q: How can the commutative property be used to simplify complex mathematical expressions?
A: The commutative property can be used to simplify complex mathematical expressions by swapping the positions of two or more quantities and still getting the same result.
Conclusion
The commutative property of addition is a fundamental concept in mathematics that has numerous real-life applications. However, many people still have questions about this property and how it can be used to simplify complex mathematical expressions. In this article, we will answer some of the most frequently asked questions about the commutative property of addition.
Q: What is the commutative property of addition?
A: The commutative property of addition is a fundamental concept in mathematics that states that the order of the numbers being added does not change the result. In other words, when we add two numbers, we can swap their positions and still get the same answer.
Q: How is the commutative property used in real-life scenarios?
A: The commutative property is used in real-life scenarios where we need to add two or more quantities. For example, when measuring ingredients for a recipe, we can use the commutative property to swap the positions of two ingredients and still get the same result.
Q: What are some real-life applications of the commutative property?
A: Some real-life applications of the commutative property include:
- Cooking: When measuring ingredients for a recipe, we can use the commutative property to swap the positions of two ingredients and still get the same result.
- Finance: Calculating the total cost of two or more items, we can use the commutative property to swap the positions of the items and still get the same result.
- Science: When measuring the volume of two or more liquids, we can use the commutative property to swap the positions of the liquids and still get the same result.
Q: How can the commutative property be used to simplify complex mathematical expressions?
A: The commutative property can be used to simplify complex mathematical expressions by swapping the positions of two or more quantities and still getting the same result. For example, if we have the expression $\frac{1}{4}+\frac{2}{5}$, we can use the commutative property to rewrite it as $\frac{2}{5}+\frac{1}{4}$.
Q: What are some common mistakes to avoid when using the commutative property?
A: Some common mistakes to avoid when using the commutative property include:
- Not understanding the concept of the commutative property: Before using the commutative property, it's essential to understand the concept and how it applies to different mathematical expressions.
- Not following the correct order of operations: When using the commutative property, it's essential to follow the correct order of operations to avoid errors.
- Not checking the result: Before accepting the result of a mathematical expression, it's essential to check the result to ensure that it's correct.
Q: How can the commutative property be used in algebraic expressions?
A: The commutative property can be used in algebraic expressions to simplify complex equations. For example, if we have the equation $2x + 3 = 5$, can use the commutative property to rewrite it as $3 + 2x = 5$.
Q: What are some advanced applications of the commutative property?
A: Some advanced applications of the commutative property include:
- Group theory: The commutative property is used in group theory to study the properties of groups and their elements.
- Ring theory: The commutative property is used in ring theory to study the properties of rings and their elements.
- Field theory: The commutative property is used in field theory to study the properties of fields and their elements.
Conclusion
In conclusion, the commutative property of addition is a fundamental concept in mathematics that has numerous real-life applications. By understanding and applying this property, we can simplify complex mathematical expressions and solve problems more efficiently.