Chapter 2: Q62. (page 102)

Find the value of $n$ . Then name the property used in each step. (Lesson 1-3)
$12 \cdot n = 12 \cdot 6$

Short Answer

Expert verified

The value of $n$ is $6$ . The main properties used are the multiplicative property of zero and the distributive property.

Step by step solution

Step 1. State the property.

The multiplicative property of zero states that for any number $a$ , the product of $a$ and $0$ is $0$ .

So, $a \cdot 0 = 0$ .

The distributive property states that multiplication is distributive over addition or subtraction.

So, $a (b \pm c) = a b \pm a c$ .

Step 2. Write the given equation.

The given equation is $12 \cdot n = 12 \cdot 6$ .

Step 3. Solve the given equation.

$12 \cdot n = 12 \cdot 6$ (Given equation)

$12 \cdot n - 12 \cdot 6 = 12 \cdot 6 - 12 \cdot 6$ (Subtract $12 \cdot 6$ from both sides)

$12 \cdot n - 12 \cdot 6 = 0$ (Simplify)

$12 \cdot (n - 6) = 0$ (Distributive property)

$n - 6 = 0$ (Multiplicative property of zero)

$n - 6 + 6 = 0 + 6$ (Add 6 to both sides)

$n = 6$ (Simplify)

So, the solution of the given equation is $n = 6$ and the main properties used are the multiplicative property of zero and the distributive property.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Find the value of $n$ . Then name the property used in each step. (Lesson 1-3)
$12 \cdot n = 12 \cdot 6$

Short Answer

Step by step solution

Step 1. State the property.

Step 2. Write the given equation.

Step 3. Solve the given equation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Theoretical and Mathematical Physics

Mechanics Maths

Pure Maths

Logic and Functions

Geometry

Study anywhere. Anytime. Across all devices.

Find the value of n. Then name the property used in each step. (Lesson 1-3)12⋅n=12⋅6

Short Answer

Step by step solution

Step 1. State the property.

Step 2. Write the given equation.

Step 3. Solve the given equation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Theoretical and Mathematical Physics

Mechanics Maths

Pure Maths

Logic and Functions

Geometry

Study anywhere. Anytime. Across all devices.

Find the value of $n$ . Then name the property used in each step. (Lesson 1-3)
$12 \cdot n = 12 \cdot 6$