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Pre-Algebra : Commutative Property of Addition

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Example Questions

Example Question #1 : Identities And Properties

What property can be applied to the following expression?

$2 + \sqrt{x} = \sqrt{x} + 2$ $\displaystyle 2 + \sqrt{x} = \sqrt{x} + 2$

Possible Answers:

Additive Inverse

Commutative of Addition

Commutative of Multiplication

Additive Identity

Associative of Addition

Correct answer:

Commutative of Addition

Explanation:

The rule for Commutative Property of Addition is $\displaystyle a + b = b + a$

Expression given in the question is: $2 + \sqrt{x} = \sqrt{x} + 2$ $\displaystyle 2 + \sqrt{x} = \sqrt{x} + 2$

Hence the property is Commutative of Addition.

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Example Question #2 : Identities And Properties

Identify the property being applied.

$\displaystyle 10.5+6.2+3.7=6.2+3.7+10.5$

Possible Answers:

Associative Inverse Property

Additive Property of Addition

Communitive Property of Addition

Order of Operations

Associative Property of Addition

Correct answer:

Communitive Property of Addition

Explanation:

Correct Answer: Communitive Property of Addition

This property states that any set of terms can be added together in any order to achieve the same solution.

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Example Question #2 : How To Add Fractions

Which of the following statements demonstrates the commutative property of addition?

Possible Answers:

$\frac{7}{8} + \left (- \frac{7}{8} \right ) = 0$ $\displaystyle \frac{7}{8} + \left (- \frac{7}{8} \right ) = 0$

$\frac{3}{4} +\left ( \frac{7}{8} + \frac{1}{6} \right )= \left (\frac{3}{4} + \frac{7}{8} \right ) + \frac{1}{6}$ $\displaystyle \frac{3}{4} +\left ( \frac{7}{8} + \frac{1}{6} \right )= \left (\frac{3}{4} + \frac{7}{8} \right ) + \frac{1}{6}$

$\frac{3}{4} +0 = \frac{3}{4}$ $\displaystyle \frac{3}{4} +0 = \frac{3}{4}$

None of the examples in the other responses demonstrates the commutative property of addition.

$\frac{3}{4} + \frac{7}{8} = \frac{7}{8} + \frac{3}{4}$ $\displaystyle \frac{3}{4} + \frac{7}{8} = \frac{7}{8} + \frac{3}{4}$

Correct answer:

$\frac{3}{4} + \frac{7}{8} = \frac{7}{8} + \frac{3}{4}$ $\displaystyle \frac{3}{4} + \frac{7}{8} = \frac{7}{8} + \frac{3}{4}$

Explanation:

The commutative property of addition states that two numbers can be added in either order to obtain the same sum. Of the given responses, only

$\frac{3}{4} + \frac{7}{8} = \frac{7}{8} + \frac{3}{4}$ $\displaystyle \frac{3}{4} + \frac{7}{8} = \frac{7}{8} + \frac{3}{4}$

demonstrates this property, so it is the correct choice.

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Example Question #372 : Operations And Properties

Which of the following best represents the commutative property of addition?

Possible Answers:

$\displaystyle 1+3 = 5-1$

$\displaystyle 30+1 = 1+30$

$\displaystyle 1+3+5 = 1+(3+5)$

$5\times 2+3 = 3+2\times 5$ $\displaystyle 5\times 2+3 = 3+2\times 5$

$\displaystyle 1+3+5 = 9$

Correct answer:

$\displaystyle 30+1 = 1+30$

Explanation:

The property is defined as:

X+Y=Y+X $\displaystyle X+Y=Y+X$

Switching the order of the numbers and adding the numbers will yield the same result.

The only answer is: $\displaystyle 30+1 = 1+30$

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Example Question #3 : Identities And Properties

Which of the following choices best represent the commutative property of addition?

Possible Answers:

$\displaystyle A+B+C = A +(B+C)$

$\displaystyle 1+3+5+7 = 16$

$\displaystyle (2+3) +4 = 2+(3+4)$

$\displaystyle 20+1 = 1+20$

$\displaystyle 5(x+y) = 5x+5y$

Correct answer:

$\displaystyle 20+1 = 1+20$

Explanation:

Write the rule for the commutative property of addition, letting $\displaystyle x$ and $\displaystyle y$ be any number.

$\displaystyle x+y = y+x$

Changing the order of these two numbers will not affect the final answer.

The best choice is: $\displaystyle 20+1 = 1+20$

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Pre-Algebra : Commutative Property of Addition

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #1 : Identities And Properties

Example Question #2 : Identities And Properties

Example Question #2 : How To Add Fractions

Example Question #372 : Operations And Properties

Example Question #3 : Identities And Properties

All Pre-Algebra Resources

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