Final answer:
The properties used to simplify the expression 4(3 +1/4) are the distributive property and the multiplicative identity.
Step-by-step explanation:
The properties that were used to simplify the expression 4(3 +1/4) are the distributive property and the multiplicative identity.
The distributive property states that when you have a number outside parentheses multiplied by a sum inside the parentheses, you can distribute the multiplication to each term inside the parentheses. In this case, 4 is multiplied by 3 and by 1/4.
The multiplicative identity property states that any number multiplied by 1 is equal to the original number. In this case, 4·1 = 4.
Using the distributive property, we get 4 · 3 + 4 · 1/4 = 12 + 1. Then, using the multiplicative identity property, we simplify 12 + 1 to 13.