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Fill in the blanks and state the propert...

Fill in the blanks and state the property used.
If a and b are two integers, then their sum is also _______.

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To solve the question, we need to fill in the blank and state the property used regarding the sum of two integers. ### Step-by-Step Solution: 1. **Understanding the Question**: The question states that if \( a \) and \( b \) are two integers, then their sum is also _______. We need to determine what the sum of two integers results in. 2. **Choosing Integers**: Let's choose two integers for our example. For instance, let \( a = 5 \) and \( b = 2 \). 3. **Calculating the Sum**: Now, we calculate the sum of \( a \) and \( b \): \[ a + b = 5 + 2 = 7 \] 4. **Verifying with Reverse Order**: To ensure that the property holds, we can also calculate \( b + a \): \[ b + a = 2 + 5 = 7 \] 5. **Conclusion**: Since both \( a + b \) and \( b + a \) yield the same result, we can conclude that the sum of two integers is also an integer. Therefore, we fill in the blank: \[ \text{If } a \text{ and } b \text{ are two integers, then their sum is also } \text{an integer.} \] 6. **Stating the Property Used**: The property used here is the **Closure Property of Addition** for integers, which states that the sum of any two integers is always an integer. ### Final Answer: If \( a \) and \( b \) are two integers, then their sum is also **an integer**. The property used is the **Closure Property of Addition**.
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Knowledge Check

  • Fill in the blanks and state the property used. If x and y are two integers, then x + y is also _______.

    A
    an integer
    Property used : Closure under subtraction
    B
    an integer
    Property used : commutativity under addition
    C
    an integer
    Property used : Closure under addition
    D
    an integer
    Property used : associativity under addition
  • Fill in the blanks and state the property used. 451+0="_______"+451

    A
    0
    Property used : associative identity
    B
    0
    Property used : multiplicative inverse
    C
    0
    Property used : Additive identity
    D
    451
    Property used : commutative identity
  • Fill in the blanks and state the property used. 0+(-8)=(-8)+"________"

    A
    `0`
    Property used : associative identify
    B
    `0`
    Property used : Additive identify
    C
    `8`
    Property used : Additive identify
    D
    `0`
    Property used : distributive identify
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