Name the property that justifies each step.
[(2x100)+(3x10)]+[(1x100)+(5x10)]
= (2x100)=[(3x10)+(1x100)]+(5x10) I think this is Commutative
= (2x100)+[(1x100)+(3x10)]+(5x10) I think this is Distributive property
=[(2x100)+(1x100)]+[(3x10)+(5x10)] I think that this is Associative property.
=[(2+1)x100]+[(3+5)x10] I think that this is the Distributive property.
= (3x100)+(8x10) This is Basic facts.
=380 Expanded form to standard form.
Is this all correct? Thanks for your help.
No
Then can you help me with it?
Let's go through each step and identify the properties used:
Step 1: [(2x100)+(3x10)]+[(1x100)+(5x10)]
In this step, you are only rearranging the terms. It is not any specific property, but just using the associative property of addition, since we are grouping the terms.
Step 2: (2x100)=[(3x10)+(1x100)]+(5x10)
Here, you are using the commutative property of addition to rearrange the terms within the parentheses. So, your answer of Commutative property is correct.
Step 3: (2x100)+[(1x100)+(3x10)]+(5x10)
This step is correct, but it is not using the distributive property. It is still using the associative property of addition, just like in Step 1.
Step 4: [(2x100)+(1x100)]+[(3x10)+(5x10)]
You are correct again. This step is using the associative property of addition, rearranging the terms within the parentheses.
Step 5: [(2+1)x100]+[(3+5)x10]
Here, you are correct in identifying the property used. It is the distributive property of multiplication over addition. You have distributed the factors outside the parentheses.
Step 6: (3x100)+(8x10)
This step does not involve any specific property, but it is simply evaluating the expressions by performing the multiplication and addition.
Step 7: 380
Finally, this is the simplified expression in standard form.
To summarize, your reasoning in Steps 2, 5, and 7 is correct. However, Steps 1, 3, and 4 do not involve commutative, distributive, or associative properties. Instead, they just involve rearranging terms without using any specific property.