Problem

Explain the difference between $2^{3}$ and $3^{2}…

00:33

Problem 122 Hard Difficulty

Scrabble. Write an expression to determine the number of points received for playing the word QUARTZY and then evaluate it. (The number on each tile gives the point value of the letter.

Answer

The Order of Operations is very important when simplifying expressions and equations. The Order of Operations is a standard that defines the order in which you should simplify different operations such as addition, subtraction, multiplication and division.

This standard is critical to simplifying and solving different algebra problems. Without it, two different people may interpret an equation or expression in different ways and come up with different answers. The Order of Operations is shown below.

Parentheses and Brackets - - Simplify the inside of parentheses and brackets before you deal with the exponent (if any) of the set of parentheses or remove the parentheses. Exponents - - Simplify the exponent of a number or of a set of parentheses before you multiply, divide, add, or subtract it. Multiplication and Division - - Simplify multiplication and division in the order that they appear from left to right. Addition and Subtraction - - Simplify addition and subtraction in the order that they appear from left to right. Before we begin simplifying problems using the Order of Operations, let's examine how failure to use the Order of Operations can result in a wrong answer to a problem.
$2+5 \cdot x$
Without the Order of Operations one might decide to simplify the problem working left to right. He or she would add two and five to get seven, then multiply seven by $x$ to get a final answer of $7 x$. Another person might decide to make the problem a little easier by multiplying first. He or she would have first multiplied 5 by $x$ to get $5 x$ and then found that you can't add 2 and $5 x$ so his or her final answer would be $2+5 x$. Without a standard like the Order of Operations, a problem can be interpreted many different ways.

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Video Transcript

so for being asked to write an expression to dirt to determine the number of points we would receive if he played this word court, see, and then we're gonna find it. And so they tell us that the number on each tile gives the point per letter. So let's take a look at this. R Q is worth 10 points to us one. The A is one. The R is one. The tea is 10 or sorry, The tea's should just be one. What's a race? That that should be a one There Z is 10 and the Y is equal before. So if we want to find the total for this whole word, we would have to add up all these tiles. But we also have to recognize that we have a couple of special letters. So when I start to go ahead and add these all up, I'm gonna have 10 for the Q plus, the one for the U plus one for the A plus Well, for the R is a triple letter score, so I have to multiply that one by three. Then I can add the one for the tea and then the Z is a double letter. So I have to do two times 10 and then I can add four for the why now, The other thing we have to recognize is this you is on a triple word score. So what I have to dio is multiply this entire expression by three. So now we have written expression to find the value of this word. Now we want to go ahead and evaluate well, according to the order of operations, you must do the inside first. Amini, take care of those two multiplication Sze while three times one is three and two times 10 is 20. So we're gonna have three times 10 plus one plus one plus three plus one plus 20 plus four. So now we have to simply add up all the values inside the prophecies. During they had 10 plus one plus one plus three plus one plus 20 plus four, which is gonna give us 40. So you have three times 40. So to find the value of the score, you multiply three by 40 so we'll be 120 points

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Alan S. Tussy, R. David Gustafson

Elementary and Intermediate Algebra

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Related Topics

The Language of Algebra

Equations and Inequalities

Functions

Linear Functions

Quadratic Functions

Polynomials

Top Algebra Educators

Anna Marie V.

Campbell University

Kayleah T.

Harvey Mudd College

Kristen K.

University of Michigan - Ann Arbor

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Idaho State University