Mr. Howard wrote the following expressions on the board in order to determine which expressions are equivalent and how they are equivalent.
60x+24, 3(20x+8, 4(15x+6)
Explain which of these expressions are equivalent using properties of operations, and then determine how other equivalent expressions could be created using the same properties. Provide at least two examples.
Why are you changing names, and what could you not understand about my answer here:
http://www.jiskha.com/display.cgi?id=1424281591
To determine which expressions are equivalent, we need to apply the properties of operations. Let's take a look at each expression and see how they can be simplified or rearranged.
Expression 1: 60x + 24
Expression 2: 3(20x + 8)
Expression 3: 4(15x + 6)
First, let's simplify Expression 2:
3(20x + 8) can be simplified using the distributive property of multiplication. We multiply 3 with both terms inside the parentheses:
3 * 20x + 3 * 8 = 60x + 24
Expression 1 (60x + 24) is equivalent to Expression 2 (3(20x + 8)) because both expressions simplify to the same result.
Now, let's simplify Expression 3:
4(15x + 6) can also be simplified using the distributive property of multiplication:
4 * 15x + 4 * 6 = 60x + 24
Expression 1 (60x + 24) is also equivalent to Expression 3 (4(15x + 6)) due to the same simplification.
To create other equivalent expressions using the same properties, we can rearrange the terms within the expressions or factor out common factors.
Example 1:
Expression 1: 60x + 24
We can factor out a common factor of 12:
12(5x + 2)
Example 2:
Expression 2: 3(20x + 8)
We can rearrange the terms to get:
3(8 + 20x)
This maintains the same equivalence.
In summary, Expression 1 (60x + 24) is equivalent to Expression 2 (3(20x + 8)) and Expression 3 (4(15x + 6)) through the use of the distributive property of multiplication. Additional equivalent expressions can be created by rearranging terms or factoring out common factors.