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Sagot :
Let's solve each part of the question step-by-step:
### Associative Property
1. The associative property holds for addition:
- The associative property for addition states that for any three numbers a, b, and c, the equation [tex]\((a + b) + c = a + (b + c)\)[/tex] always holds.
- Hence, the associative property holds for addition: True
2. The associative property holds for multiplication:
- Similarly, the associative property for multiplication states that for any three numbers a, b, and c, the equation [tex]\((a \cdot b) \cdot c = a \cdot (b \cdot c)\)[/tex] always holds.
- Hence, the associative property holds for multiplication: True
### Simplify
1. [tex]\(|15| + |-7|\)[/tex]
- The absolute value of 15 is 15, and the absolute value of -7 is 7.
- So, [tex]\(|15| + |-7| = 15 + 7 = 22\)[/tex].
2. [tex]\(|-24| - |-46|\)[/tex]
- The absolute value of -24 is 24, and the absolute value of -46 is 46.
- So, [tex]\(|-24| - |-46| = 24 - 46 = -22\)[/tex].
### Find the Sum
Let's find the sum for each expression:
1. [tex]\(-300 + 304\)[/tex]
- [tex]\(-300 + 304 = 4\)[/tex].
2. [tex]\(-13 + (-22)\)[/tex]
- [tex]\(-13 + (-22) = -13 - 22 = -35\)[/tex].
3. [tex]\(143 + (-187) + 250\)[/tex]
- First, sum [tex]\(143 + (-187) = 143 - 187 = -44\)[/tex].
- Then, [tex]\(-44 + 250 = 206\)[/tex].
4. [tex]\(-240 + (-150) + 6\)[/tex]
- First, sum [tex]\(-240 + (-150) = -240 - 150 = -390\)[/tex].
- Then, [tex]\(-390 + 6 = -384\)[/tex].
### Subtract
Now, we'll perform the subtraction step-by-step:
1. Subtract -12 from -15:
- [tex]\(-15 - (-12) = -15 + 12 = -3\)[/tex].
2. Subtract 45 from -51:
- [tex]\(-51 - 45 = -51 - 45 = -96\)[/tex].
3. Subtract 24 from -38:
- [tex]\(-38 - 24 = -38 - 24 = -62\)[/tex].
4. Subtract -58 from 130:
- [tex]\(130 - (-58) = 130 + 58 = 188\)[/tex].
Thus, putting it all together, the detailed solutions are:
- Associative Property for Addition: True
- Associative Property for Multiplication: True
- [tex]\(|15| + |-7| = 22\)[/tex]
- [tex]\(|-24| - |-46| = -22\)[/tex]
- [tex]\((-300) + 304 = 4\)[/tex]
- [tex]\((-13) + (-22) = -35\)[/tex]
- [tex]\(143 + (-187) + 250 = 206\)[/tex]
- [tex]\((-240) + (-150) + 6 = -384\)[/tex]
- [tex]\(-15 - (-12) = -3\)[/tex]
- [tex]\(-51 - 45 = -96\)[/tex]
- [tex]\(-38 - 24 = -62\)[/tex]
- [tex]\(130 - (-58) = 188\)[/tex]
### Associative Property
1. The associative property holds for addition:
- The associative property for addition states that for any three numbers a, b, and c, the equation [tex]\((a + b) + c = a + (b + c)\)[/tex] always holds.
- Hence, the associative property holds for addition: True
2. The associative property holds for multiplication:
- Similarly, the associative property for multiplication states that for any three numbers a, b, and c, the equation [tex]\((a \cdot b) \cdot c = a \cdot (b \cdot c)\)[/tex] always holds.
- Hence, the associative property holds for multiplication: True
### Simplify
1. [tex]\(|15| + |-7|\)[/tex]
- The absolute value of 15 is 15, and the absolute value of -7 is 7.
- So, [tex]\(|15| + |-7| = 15 + 7 = 22\)[/tex].
2. [tex]\(|-24| - |-46|\)[/tex]
- The absolute value of -24 is 24, and the absolute value of -46 is 46.
- So, [tex]\(|-24| - |-46| = 24 - 46 = -22\)[/tex].
### Find the Sum
Let's find the sum for each expression:
1. [tex]\(-300 + 304\)[/tex]
- [tex]\(-300 + 304 = 4\)[/tex].
2. [tex]\(-13 + (-22)\)[/tex]
- [tex]\(-13 + (-22) = -13 - 22 = -35\)[/tex].
3. [tex]\(143 + (-187) + 250\)[/tex]
- First, sum [tex]\(143 + (-187) = 143 - 187 = -44\)[/tex].
- Then, [tex]\(-44 + 250 = 206\)[/tex].
4. [tex]\(-240 + (-150) + 6\)[/tex]
- First, sum [tex]\(-240 + (-150) = -240 - 150 = -390\)[/tex].
- Then, [tex]\(-390 + 6 = -384\)[/tex].
### Subtract
Now, we'll perform the subtraction step-by-step:
1. Subtract -12 from -15:
- [tex]\(-15 - (-12) = -15 + 12 = -3\)[/tex].
2. Subtract 45 from -51:
- [tex]\(-51 - 45 = -51 - 45 = -96\)[/tex].
3. Subtract 24 from -38:
- [tex]\(-38 - 24 = -38 - 24 = -62\)[/tex].
4. Subtract -58 from 130:
- [tex]\(130 - (-58) = 130 + 58 = 188\)[/tex].
Thus, putting it all together, the detailed solutions are:
- Associative Property for Addition: True
- Associative Property for Multiplication: True
- [tex]\(|15| + |-7| = 22\)[/tex]
- [tex]\(|-24| - |-46| = -22\)[/tex]
- [tex]\((-300) + 304 = 4\)[/tex]
- [tex]\((-13) + (-22) = -35\)[/tex]
- [tex]\(143 + (-187) + 250 = 206\)[/tex]
- [tex]\((-240) + (-150) + 6 = -384\)[/tex]
- [tex]\(-15 - (-12) = -3\)[/tex]
- [tex]\(-51 - 45 = -96\)[/tex]
- [tex]\(-38 - 24 = -62\)[/tex]
- [tex]\(130 - (-58) = 188\)[/tex]
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