Question

use the commutative and associative properties to simplify 429+75+71​

Answer 1

Algebraic properties:

• Commutative property - If a and b be two numbers and addition (+) be defined, then we can write a + b = b + a. This is the Commutative property on addition.
• Associative property - If a, b and c be three numbers and addition (+) be defined, then we can write a + (b + c) = (a + b) + c. This is the Associative property on addition.

Now we try to solve the given problem:

∴ 429 + 75 + 71

= 429 + (75 + 71), grouping the numbers

= 429 + (71 + 75), commutative property

= (429 + 71) + 75, associative property

= 500 + 75

= 575

Thus 429 + 75 + 71 = 575

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Answer 2

Thus the answer is 429 + 75 + 71 = 575

Explanation:

Commutative property: Commutative property says that Let say a and b be two numbers and addition (+) is performed then we can write a + b = b + a. Both sides will be equal .

This is the Commutative property of addition.

Associative property: Associative property says that If a, b and c be three numbers and addition (+) is performed, then we can write a + (b + c) = (a + b) + c.

This is the Associative property of addition.

Now apply the formula:

  429 + 75 + 71

= 429 + (75 + 71), grouping the numbers

• Apply commutative property here:

= 429 + (71 + 75)

• Apply associative property here.

= (429 + 71) + 75

= 500 + 75

= 575

Thus 429 + 75 + 71 = 575