Читать книгу Algebra I All-in-One For Dummies - Mary Jane Sterling, Mary Sterling Jane - Страница 29

Before a car manufacturer puts together a car, several different things have to be done first. The engine experts have to construct the engine with all its parts. The body of the car then has to be mounted onto the chassis and also secured. Other car assemblers have to perform the tasks that they specialize in as well. When these tasks are all accomplished in order, the car can be put together. The same is true with algebra. You have to do what’s inside the grouping symbol before you can use the result in the rest of the equation.

Grouping symbols tell you that you have to deal with the terms inside the grouping symbols before you deal with the larger problem. If the problem contains grouped items, do what’s inside a grouping symbol first, and then follow the order of operations. The grouping symbols are as follows.

 Parentheses ( ): Parentheses are the most commonly used symbols for grouping.

 Brackets [ ] and braces { }: Brackets and braces are also used frequently for grouping and have the same effect as parentheses. Using the different types of symbols helps when there’s more than one grouping in a problem. It’s easier to tell where a group starts and ends.

 Radical : This is used for finding roots.

 Fraction line (called the vinculum): The fraction line also acts as a grouping symbol — everything above the line (in the numerator) is grouped together, and everything below the line (in the denominator) is grouped together.

Even though the order of operations and grouping-symbol rules are fairly straightforward, it’s hard to describe, in words, all the situations that can come up in these problems. The explanations and examples in Chapters 3 and 7 should clear up any questions you may have.

Q. What are the operations found in the expression: ?

A. The operations, in order from left to right, are multiplication, subtraction, division, addition, multiplication, and square root. The term 3y means to multiply 3 times y. The subtraction symbol separates the first and second terms. Writing y over 4 in a fraction means to divide. Then that term has the radical added to it. The 2 and y are multiplied under the radical, and then the square root is taken.

Q. Identify the grouping symbols shown in .

A. The first grouping symbol to recognize is the fraction line. It separates the term in the numerator, , from the terms in the denominator, . Next, you see the brackets, which contain the two terms forming a subtraction, . The last grouping symbols are the parentheses, which have a multiplier of 2 and, inside, the sum of two terms.

16 Write the expression using the correct symbols: “The square root of x is subtracted from 3 times y.”

17 Write the expression using the correct symbols: “Add 2 and y; then divide that sum by 11.”

18 Identify the grouping symbols in .