Problem 9 Simplify. Show your steps. $$\... [FREE SOLUTION]

Chapter 1: Problem 9

Simplify. Show your steps. $$\frac{39}{13}+6-2^{3}$$

Short Answer

Expert verified

Question: Simplify the given expression: $\frac{39}{13} + 6 - 2^3$ Answer: 1

Step by step solution

Simplification of fraction

First, simplify the fraction $\frac{39}{13}$. Both the numerator and the denominator can be divided by 13, so the fraction simplifies to: $$\frac{39\div 13}{13\div 13} = \frac{3}{1} = 3$$

simplification of exponentiation

Next, simplify the exponentiation part, which is $2^3$. Raise 2 to the power of 3: $$2^3 = 2 \times 2 \times 2 = 8$$

Substitute the simplified values in the equation

Now, substitute the simplified values from steps 1 and 2 back into the original expression: $$3 + 6 - 8$$

Summation and subtraction of integers

Finally, perform the addition and subtraction of the integers: $$3 + 6 - 8 = 9 - 8 = 1$$ The simplified expression is 1.

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.

Simplify Fractions

Simplifying fractions is like cleaning up your desk; you want the simplest form to work with. A fraction has a numerator (top number) and a denominator (bottom number). To simplify, we look for common factors that can both divide the numerator and the denominator. This makes the fraction smaller, but it holds the same value.
For example, let's take $\frac{39}{13}$. Both 39 and 13 are divisible by 13, which is their greatest common factor. When we divide them both by 13, we find:

$39 \div 13 = 3$
$13 \div 13 = 1$

So, $\frac{39}{13}$ simplifies to $\frac{3}{1}$, which is just 3. Remember, simplifying fractions makes calculations easier.

Exponentiation

Exponentiation is a way to express repeated multiplication of the same number. When you see something like $2^3$, it means you multiply 2 by itself three times. So, $2^3 = 2 \times 2 \times 2$.
To solve this, break it down:

First, $2 \times 2 = 4$.
Then, multiply that result by 2 again: $4 \times 2 = 8$.

So, $2^3$ equals 8. Using exponentiation helps us to handle large multiplications in an easy way, turning them into simpler problems and saving a lot of time!

Integers Addition and Subtraction

Adding and subtracting integers may sound simple, but it's crucial to follow the right order. First, deal with any addition, and then handle the subtraction part. This ensures your calculations are accurate and quick.
In the expression $3 + 6 - 8$, here's how you'd sort it out:

Start with addition: $3 + 6 = 9$.
Next, subtract: $9 - 8 = 1$.

The final answer is 1. Remembering the correct order of operations鈥攁dding before subtracting鈥攈elps you avoid common mistakes and makes solving such expressions straightforward.

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

Simplify. Show your steps. $$\frac{39}{13}+6-2^{3}$$

Short Answer

Step by step solution

Simplification of fraction

simplification of exponentiation

Substitute the simplified values in the equation

Summation and subtraction of integers

Key Concepts

Simplify Fractions

Exponentiation

Integers Addition and Subtraction

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Calculus

Mechanics Maths

Geometry

Probability and Statistics

Pure Maths

Study anywhere. Anytime. Across all devices.