Question

Lance wants to find the total length of 3 boards. He uses the expression 3 1/2 + ( 2 + 4 1/2 ). How can Lance rewrite the expression using both the Associative and Commutative Properties of Addition?

Answer 1

Answer:

Commutative expression

3 1/2+(2 + 4 1/2) = (2 + 4 1/2)+3 1/2

Associative expression

3 1/2 + (2 + 4 1/2) = (3 1/2 + 2) + 4 1/2

Step-by-step explanation:

Given the expression 3 1/2 + ( 2 + 4 1/2)

Let A= 3 1/2; B = 2+4 1/2

According to commutative law of addition, if A and B are two numbers or sets, then;

A+B = B+A

The expression can then be written commutatively as;

3 1/2+(2 + 4 1/2) = (2 + 4 1/2)+3 1/2

For the commutative property of addition, we will have;

A+(B+C) = (A+B)+C

If A = 3 1/2, B = 2 and C = 4 1/2

The equation can then be written associatively as;

3 1/2 + (2 + 4 1/2) = (3 1/2 + 2) + 4 1/2

This gives a total length of the three boards as 10. :

Answer 2

Associative: (3 1/2 + 2) + 4 1/2
Commutative: (2+ 4 1/2) + 3 1/2