Problem 68 Evaluate. $$ 20 \div a \cdot... [FREE SOLUTION]

Chapter 1: Problem 68

Evaluate. $$ 20 \div a \cdot 4, \text { for } a=5 $$

Short Answer

Expert verified

Step by step solution

- Substitute the value of a

Replace the variable $ a $ in the expression with the given value $ 5 $: $ 20 \div a \cdot 4 $ becomes $ 20 \div 5 \cdot 4 $

- Perform division first

According to the order of operations (PEMDAS), perform the division before multiplication. Compute $ 20 \div 5 $: $ 20 \div 5 = 4 $

- Perform the multiplication

Now, multiply the result from Step 2 by $ 4 $: $4 \cdot 4 $ This gives $ 16 $

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Substitution

Substitution is a fundamental concept in algebra. It involves replacing variables in an equation or expression with their given values. Let's delve into the exercise where we begin with the original expression:

$$ 20 \div a \cdot 4 $$

We are asked to evaluate this expression for the value of $$ a = 5 $$. By substituting $$ 5 $$ for $$ a $$, the expression transforms into:

$$ 20 \div 5 \cdot 4 $$
Substitution simplifies the problem and sets the stage for the next steps. It's crucial because it replaces abstract variables with concrete numbers, making the arithmetic operations straightforward.

Division

Division is one of the core arithmetic operations. In the context of the given exercise, the first step after substitution is to perform the division. According to the order of operations (PEMDAS/BODMAS), division is carried out before multiplication.

After substituting, the expression we have is:

$$ 20 \div 5 \cdot 4 $$

Let's perform the division first:
$$ 20 \div 5 = 4 $$
Here, 20 is divided by 5, resulting in 4. This outcome is crucial as it simplifies the expression further, making the next stage of multiplication easier to handle. Properly handling division at this step ensures accurate results.

Multiplication

Multiplication is another key arithmetic operation. Once we have simplified the expression through division, we move on to multiplication. From our earlier steps, we have:

$$ 4 \cdot 4 $$

Now, perform the multiplication:
$$ 4 \cdot 4 = 16 $$
This step is straightforward after the division. It is important to follow the order of operations to get the correct result.

Checking your answers by re-evaluating the steps can also be helpful. In summary, knowing when to apply each arithmetic operation through the proper order leads to the right solution. Multiplication consolidates our previous steps and delivers the final answer.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Evaluate. $$ 20 \div a \cdot 4, \text { for } a=5 $$

Short Answer

Step by step solution

- Substitute the value of a

- Perform division first

- Perform the multiplication

Key Concepts

Substitution

Division

Multiplication

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Geometry

Probability and Statistics

Logic and Functions

Decision Maths

Statistics

Study anywhere. Anytime. Across all devices.