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Chapter 2: Problem 36

Combine as indicated and simplify. $$5.83 y+2.48 y-5.18 y-2.56 y-3.18 y$$

Short Answer

Expert verified
\(-3.61y\)

Step by step solution

01

Combine like terms

Start by adding and subtracting the coefficients of the like terms, which are all the terms with the variable 'y'.
02

Perform the arithmetic operations

Add and subtract the coefficients: \(5.83 + 2.48 - 5.18 - 2.56 - 3.18\).
03

Calculate the result

Perform the additions and subtractions to find the single coefficient for the variable 'y'.

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Key Concepts

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

Simplifying Algebraic Expressions
Simplifying algebraic expressions is like tidying up numbers and letters in a mathematical sentence to make it easier to understand or solve. Think of it as organizing a cluttered room where all similar items are put together. In algebra, we do this by combining like terms. Like terms are algebraic expressions that have the exact same variables raised to the same powers. The process involves adding or subtracting the coefficients (these are the numerical parts) of these like terms. For example, when we have an expression like \(5.83y + 2.48y - 5.18y - 2.56y - 3.18y\), we can make it simpler by combining the terms that are all talking about 'y's.
Arithmetic Operations
Arithmetic operations are the building blocks of math, much like how everyday chores are for keeping a home in order. These operations include addition, subtraction, multiplication, and division. In algebra, we often use addition and subtraction to combine like terms. When we look at an expression such as \(5.83y + 2.48y - 5.18y - 2.56y - 3.18y\), imagine that you're balancing your pocket money; you add some, spend some, and your goal is to figure out how much you have left at the end. By performing these arithmetic operations on the coefficients, you simplify the expression to find out how 'heavy' the 'y' is in the entire expression.
Algebraic Terms
Algebraic terms are like individual puzzle pieces in a bigger picture. Each term can contain numbers, variables (like 'x' or 'y'), and sometimes exponents. In our example, the term \(5.83y\) means '5.83 times y'. If you have several pieces of the same shape, you can put them together, much like how you would combine similar terms in an expression. In the expression \(5.83y + 2.48y - 5.18y - 2.56y - 3.18y\), each term has a 'y' attached, so they're all puzzle pieces of the same shape, representing like terms that can be combined.

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