Solved Examples on Associative Law

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.

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.