Associative Law Worksheet

Associative Law is a fundamental property in mathematics that governs how elements are grouped in a binary operation without changing the result. Associative Law Worksheet helps students learn to group numbers differently in addition or multiplication.

This article explains the Associative Law and provides various practice questions based on the associative property of addition and multiplication.

In mathematics, the associative law states that in a sequence of operations involving three or more elements, the final result remains the same regardless of how the elements are grouped.

• It shows that in terms of addition, the value of (a + b) + c = a + (b + c).
• In the case of multiplication, it means that a × (b × c) = (a × b) × c.

This law is applicable to operations like addition and multiplication, where two elements are combined to produce a single result.

Associative Law of Addition

Associative Law of Addition is a fundamental principle in mathematics, particularly in arithmetic and algebra. It states that the grouping of numbers being added does not affect the result. In simpler terms, it means that when adding three or more numbers together, the order in which they are grouped does not change the result of the sum.

This property holds true for any set of numbers being added. Whether we group them from left to right or right to left, the sum remains unchanged.

Example:

Let us take the numbers 1, 2, and 3:

• First, add 1 and 2, then add 3 to the result: (1 + 2) + 3 = 3 + 3 = 6.
• Alternatively, add 2 and 3, then add 1 to the result: 1 + (2 + 3) = 1 + 5 = 6.

Both ways, you get the sum 6.

Associative Law of Multiplication

Associative Law of Multiplication defines that the associative property holds true when multiplying three or more numbers. It states that the grouping of factors does not affect the product.

In simpler terms, it allows us to regroup numbers for multiplication without changing the final outcome.

Any numbers multiplied should follow this principle.

Example:

Let us take the numbers 2, 3, and 4:

• First, multiply 2 and 3 to get 6, then multiply by 4: (2 × 3) × 4 = 6 × 4 = 24.
• Alternatively, multiply 3 and 4 to get 12, then multiply by 2: 2 × (3 × 4) = 2 × 12 = 24.

Both ways, you get the product 24. Hence, the product remains unchanged irrespective of the order they are placed.

Question 1: Verify the Associative Law of addition for the numbers 3, 4, and 5.

Solution:

The Associative Law of addition states that for any three numbers a, b, and c: (a + b) + c = a + (b + c)

Let us verify this for the numbers 3, 4, and 5.

First, calculate (3 + 4) + 5:

1. Add 3 and 4: 3 + 4 = 7
2. Add the result to 5: 7 + 5 = 12

Next, calculate 3 + (4 + 5):

1. Add 4 and 5: 4 + 5 = 9
2. Add 3 to the result: 3 + 9 = 12

Since (3 + 4) + 5 = 12 and 3 + (4 + 5) = 12, the Associative Law of addition is verified.↥

Question 2: Verify the Associative Law of multiplication for the numbers 2, 3, and 4.

Solution:

The Associative Law of multiplication states that for any three numbers a, b, and c: (a × b) × c = a × (b × c)

Let us verify this for the numbers 2, 3, and 4.

First, calculate (2 × 3) × 4:

1. Multiply 2 and 3: 2 × 3 = 6
2. Multiply the result by 4: 6 × 4 = 24

Next, calculate 2 × (3 × 4):

1. Multiply 3 and 4: 3 × 4 = 12
2. Multiply 2 by the result: 2 × 12 = 24

Since (2 × 3) × 4 = 24 and 2 × (3 × 4) = 24, the Associative Law of multiplication is verified.

Question 3: Verify the Associative Law of addition for the algebraic expressions x, y, and z.

Solution:

The Associative Law of addition states that for any three expressions a, b, and c: (a + b) + c = a + (b + c)

Let us verify this for the expressions x, y, and z.

First, calculate (x + y) + z:

1. Add x and y: (x + y)
2. Add the result to z: (x + y) + z

Next, calculate x + (y + z):

1. Add y and z: (y + z)
2. Add x to the result: x + (y + z)

Since (x + y) + z and x + (y + z) are both equal (they represent the same sum of x, y, and z), the Associative Law of addition is verified for algebraic expressions.

Question 4: Verify the Associative Law of multiplication for the algebraic expressions a, b, and c.

Solution:

The Associative Law of multiplication states that for any three expressions a, b, and c: (a × b) × c = a × (b × c)

Let’s verify this for the expressions a, b, and c.

First, calculate (a × b) × c:

1. Multiply a and b: (a × b)
2. Multiply the result by c: (a × b) × c = abc

Next, calculate a × (b × c):

1. Multiply b and c: (b × c)
2. Multiply a by the result: a × (b × c) = abc

Since (a × b) × c and a × (b × c) are both equal (they represent the same product of a, b, and c), the Associative Law of multiplication is verified for algebraic expressions.

Question 5: Verify the Associative Law of addition for the numbers 6, 7, and 8.

Solution:

First, calculate (6 + 7) + 8 = (13) + 8 = 21

Next, calculate 6 + (7 + 8) = 6 + (15) = 21

Since (6 + 7) + 8 = 21 and 6 + (7 + 8) = 21, the Associative Law of addition is verified for the numbers 6, 7, and 8.

Question 6: Verify the Associative Law of multiplication for the numbers 5, 6, and 7.

Solution:

First, calculate (5 × 6) × 7 = (30) × 7 = 210

Next, calculate 5 × (6 × 7)= 5 × (42) = 210

Since (5 × 6) × 7 = 210 and 5 × (6 × 7) = 210, the Associative Law of multiplication is verified for the numbers 5, 6, and 7.

Question 7: Verify the Associative Law of addition for the algebraic expressions p, q, and r.

Solution:

Let us verify this for the algebraic expressions p, q, and r. First, calculate (p + q) + r: This simplifies to p + q + r.

Next, calculate p + (q + r): This also simplifies to p + q + r.

Since (p + q) + r and p + (q + r) are both equal (they represent the same sum of p, q, and r), the Associative Law of addition is verified for algebraic expressions p, q, and r.

Question 8: Verify the Associative Law of addition for the numbers 9, 10, and 11.

Solution:

First, calculate (9 + 10) + 11 = (19) + 11 = 30

Next, calculate 9 + (10 + 11) = 9 + (21) = 30

Since (9 + 10) + 11 = 30 and 9 + (10 + 11) = 30, the Associative Law of addition holds for the numbers 9, 10, and 11.

Question 9: Verify the Associative Law of multiplication for the numbers 8, 9, and 10.

Solution:

First, calculate (8 × 9) × 10 = (72) × 10 = 720

Next, calculate 8 × (9 × 10) = 8 × (90) = 720

Since (8 × 9) × 10 = 720 and 8 × (9 × 10) = 720, the Associative Law of multiplication holds for the numbers 8, 9, and 10.

Question 1: Using the associative law of addition, simplify the expression: (2 + 3) + 4.

Question 2: Apply the associative law of multiplication to simplify the following expression: (5 x 2) x 3.

Question 3: According to the associative law of addition, which of the following expressions is equivalent to 7 + (9 + 4)?

• (7 + 9) + 4
• 7 + (9 + 4)
• (7 + 4) + 9

Question 4: Determine if the associative law holds true for the given set of numbers: 3, 6, and 9, under the operation of addition.

Question 5: Verify the Associative Law of addition for the numbers 16, 17, and 18.

Question 6: Verify the Associative Law of multiplication for the numbers 14, 15, and 16.

Question 7: Verify the Associative Law of addition for the algebraic expressions “a + b + c”, “d + e + f”, and “g + h + i”.

Question 8: Verify the Associative Law of multiplication for the algebraic expressions “2p”, “3q”, and “4r”.

Question 9: Verify the Associative Law of addition for the numbers 19, 20, and 21.

Question 10: Verify the Associative Law of multiplication for the numbers 17, 18, and 19.

Question 11: Verify the Associative Law of addition for the algebraic expressions “m + n”, “p + q”, and “r + s”.

Read More,

• Commutative Law of Addition
• Commutative Property
• Distributive Property

What is the associative property?

According to the associative property, grouping numbers during an operation has no effect on the outcome. It applies to both addition and multiplication.

How might the Associative Law Worksheet assist students?

It includes activities for rearranging and solving formulas, stressing the idea that grouping does not change the answer.

Is the associative property applicable to subtraction and division?

No, it does not. Changing the grouping in subtraction or division changes the result.

Why is knowing the associative property so important?

It is essential for effectively solving difficult mathematical problems and serves as the foundation for more sophisticated algebra and calculus principles.

How does the Associative Law apply to addition?

The Associative Law for addition states that when adding three or more numbers, the grouping of the numbers does not affect the sum.