/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 32 Simplify. Show your steps. $$(... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 32

Simplify. Show your steps. $$(19-16) 13+54 \div 9(7-5)$$

Short Answer

Expert verified
Question: Simplify the expression (19-16) 鈰� 13 + 54 梅 9 鈰� (7-5). Answer: 51

Step by step solution

01

Evaluate the expressions in parentheses

We first need to solve the expressions within the parentheses: \((19-16)\) and \((7-5)\). $$(19 - 16) = 3$$ $$(7 - 5) = 2$$ So, the expression becomes: $$3 \cdot 13 + 54 \div 9 \cdot 2$$
02

Perform multiplication and division from left to right

We must now carry out the remaining multiplication and division operations in the expression, going from left to right: First, calculate the multiplication: $$3 \cdot 13 = 39$$ Then, perform the division: $$54 \div 9 = 6$$ And finally, multiply the result of the division by the previously evaluated expression in parentheses \((7-5)\): $$6 \cdot 2 = 12$$ Our expression now looks like this: $$39 + 12$$
03

Perform addition

Finally, we perform the addition operation: $$39 + 12 = 51$$ So, the simplified expression is: $$51$$

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.

Understanding Parentheses
Parentheses are like a signal in math telling you what to calculate first. In the expression \((19 - 16) 13 + 54 \div 9 (7 - 5)\), we identify the operations inside the parentheses first. This means that you'll calculate both \((19 - 16)\) and \((7 - 5)\) before doing any other operations. The subtraction in the parentheses breaks down as follows:

\((19 - 16) = 3\) and \((7 - 5) = 2\).

By solving these, we simplify the larger expression to replace those parentheses with their results, transforming it into \(3 \cdot 13 + 54 \div 9 \cdot 2\). Working with parentheses ensures that you have a clear and ordered starting point.
Multiplication and Division Rules
Once you've dealt with any parentheses, the next step involves multiplication and division. These operations are always performed from left to right as they appear in your expression. From our example, you continue with the expression \(3 \cdot 13 + 54 \div 9 \cdot 2\).

Here's how you break it down:
  • First, multiply \(3 \times 13\) to get \(39\).
  • Next, tackle the division \(54 \div 9\) which equals \(6\).
  • Finally, multiply the result of the division by \(2\) to get \(12\).
After performing these steps, the expression simplifies further to \(39 + 12\). Follow left to right to stay on track with the right order.
Adding Up the Results
The last step in your order of operations is addition. After simplifying through multiplication and division, you're left with something like \(39 + 12\). Addition is the final tidy up, bringing all parts together.

To achieve your final answer, simply add the two numbers together:
  • \(39 + 12 = 51\).
That brings you to your simplified solution. Understanding how to systematically work through each step keeps your math clear and correct.

One App. One Place for Learning.

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

Get started for free

Most popular questions from this chapter

Simplify. Show your steps. $$[485-(68+39)]+4^{5}-24 \cdot 16 \div 8$$

Simplify. Show your steps. $$9 \cdot 4-24 \div 4 \cdot 2-6$$

Write the number in standard form. 9 ten thousands \(+2\) thousands \(+5\) hundreds \(+8\) tens \(+1\) one

Solve. A cell phone has a volume of 90 cubic centimeters. If the length is 9 centimeters and the width is 5 centimeters, find the height.

Write the number in standard form. 4 ten millions \(+9\) hundred thousands \(+8\) ten thousands \(+1\) hundred \(+9\) ones
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Statistics

Read Explanation

Applied Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.