Sure! Let's match each equation on the left with the appropriate mathematical property on the right. We'll discuss each equation step-by-step to identify the property it uses.
1. Equation: [tex]\((7 + 3) + 2 = 2 + (7 + 3)\)[/tex]
- This equation is illustrating the commutative property of addition. The commutative property states that the order of addition does not change the sum. Therefore, [tex]\((a + b) + c = c + (a + b)\)[/tex].
2. Equation: [tex]\(3(2x + 4) = 6x + 12\)[/tex]
- This equation is illustrating the distributive property. The distributive property states that multiplying a number by a sum is the same as multiplying each addend by the number and then adding the products: [tex]\(a(b + c) = ab + ac\)[/tex].
3. Equation: [tex]\((9 \cdot x) \cdot 3 = 9 \cdot (x \cdot 3)\)[/tex]
- This equation is illustrating the associative property of multiplication. The associative property states that the way in which factors are grouped does not change the product. So, [tex]\((a \cdot b) \cdot c = a \cdot (b \cdot c)\)[/tex].
4. Equation: [tex]\((8 \cdot x \cdot 2) = (8 \cdot 2 \cdot x)\)[/tex]
- This equation is illustrating the commutative property of multiplication. The commutative property states that the order of factors does not change the product. Hence, [tex]\(a \cdot b = b \cdot a\)[/tex].
5. Equation: [tex]\((4 + 5) + 1 = 4 + (5 + 1)\)[/tex]
- This equation is illustrating the associative property of addition. The associative property states that the way in which addends are grouped does not change the sum. Therefore, [tex]\((a + b) + c = a + (b + c)\)[/tex].
Here's the complete matching:
- [tex]\((7 + 3) + 2 = 2 + (7 + 3)\)[/tex] → commutative property of addition
- [tex]\(3(2x + 4) = 6x + 12\)[/tex] → distributive property
- [tex]\((9 \cdot x) \cdot 3 = 9 \cdot (x \cdot 3)\)[/tex] → associative property of multiplication
- [tex]\((8 \cdot x \cdot 2) = (8 \cdot 2 \cdot x)\)[/tex] → commutative property of multiplication
- [tex]\((4 + 5) + 1 = 4 + (5 + 1)\)[/tex] → associative property of addition
