Question

Simplify each expression. If an expression cannot be simplified, so state. $12\left(\frac{1}{6}+\frac{d}{4}\right)+5 d$

Name: Problem 49, Chapter 2: Intermediate Algebra for College Students
Uploaded: 2020-03-18T10:32:30-08:00
Duration: 1 min 30 s
Channel: Ashley High
Description: Simplify each expression. If an expression cannot be simplified, so state. 12((1)/(6)+(d)/(4))+5 d

   Simplify each expression. If an expression cannot be simplified, so state. $12\left(\frac{1}{6}+\frac{d}{4}\right)+5 d$

Intermediate Algebra for College Students

Allen R. Angel;… 10th Edition

Chapter 2, Problem 49

Instant Answer

Solved by Expert Ashley High

03/18/2020

Step 1

First, we can distribute the 12 to both terms inside the parentheses: $12\left(\frac{1}{6}\right) + 12\left(\frac{d}{4}\right) + 5d$ Now, we can simplify the fractions: $2 + 3d + 5d$ Show more…

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Simplify each expression. If an expression cannot be simplified, so state. $12\left(\frac{1}{6}+\frac{d}{4}\right)+5 d$

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Key Concepts

Distributive Property

The distributive property allows you to multiply a single term by each term inside a parenthesis, effectively removing the parenthesis and simplifying the expression. This property, expressed as a(b + c) = ab + ac, is fundamental when working with algebraic expressions that include multiplication distributed over addition.

Operations with Fractions

Working with fractions involves understanding how to perform arithmetic operations such as addition, subtraction, multiplication, and division. When fractions are part of an algebraic expression, it's important to ensure they have a common denominator or are simplified correctly before combining them with other terms.

Combining Like Terms

Combining like terms is the process of consolidating terms in an algebraic expression that have identical variable components. After applying the distributive property, similar terms are grouped together to produce a simplified form of the original expression.

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