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Chapter 1: Problem 6

Evaluate the expression when \(y=6\). $$ \frac{24}{y} $$

Short Answer

Expert verified
Therefore, the evaluated expression when \(y=6\) is 4.

Step by step solution

01

Identify and Substitute Variable Y into Expression

First, identify the variable \(y\) in the given expression \(\frac{24}{y}\). Substitution means replacing the variable with the provided value. Here, the value for \(y\) is 6. So we replace \(y\) in the given expression with 6. This results in \(\frac{24}{6}\).
02

Perform Division

After the substitution, perform the division operation. 24 divided by 6 equals 4.

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Key Concepts

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

Substitution
In mathematics, substitution is a technique used to simplify expressions by replacing variables with specific values. This process helps to solve equations or evaluate expressions, making it easier to understand and manage. For example, when evaluating the expression \(\frac{24}{y}\) given \(y = 6\), substitution requires us to replace the variable \(y\) with 6.
  • Locate the variable in the expression.
  • Replace it with the given value.
This turns the expression into \(\frac{24}{6}\), which can then be easily calculated. Substitution is a powerful tool because it helps bridge the gap between abstract algebraic expressions and concrete numbers.
Division
Division is a fundamental operation in mathematics, often used to find out how many times a number, called the divisor, is contained within another number, known as the dividend. The result of the division is termed the quotient. In our example, the expression \(\frac{24}{6}\) means we need to determine how many times 6 fits into 24.
  • Identify the dividend (24) and the divisor (6).
  • Calculate the quotient, which in this case is 4.
Understanding division is crucial not only in arithmetic but also in solving more complex algebraic equations and expressions.
Variables
Variables are symbols, often letters, used to represent unknown or changeable values in mathematical expressions and equations. They serve as placeholders that can stand for actual numbers. In algebra, variables allow us to work with expressions abstractly until given specific values, like in the problem \(\frac{24}{y}\).
  • Variables can change depending on the context or problem.
  • Substitution involves assigning a specific number to a variable.
Using variables helps to model real-world situations and solve problems systematically. Variables are a cornerstone in developing algebraic thinking, which further models relationships and changes.
Algebraic Expressions
Algebraic expressions are mathematical phrases that can include numbers, variables, and operation symbols. They can be simple or complex, depending on the number of elements and operations involved. For instance, the expression \(\frac{24}{y}\) is an algebraic expression that includes a division operation and a variable \(y\).
  • They don't contain an equality sign, hence not making them equations.
  • They can be evaluated by substituting variables with numbers.
Understanding algebraic expressions is essential in algebra as they form the basis from which equations and functions are built. They represent and solve many real-life situations by expressing relationships between quantities.

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Most popular questions from this chapter

Match the problem with the formula needed to solve the problem. Then use the Guess, Check, and Revise strategy or another problem-solving strategy to solve the problem. Area of a rectangle \(\quad A=l w \quad\) Distance \(\quad d=r t\) Simple interest \(\quad I=P r t \quad\) Volume of a cube Temperature \(\quad C=\frac{5}{9}(F-32)\) Surface area of a cube \(S=6 s^{2}\) A cubic storage box is made with 96 square feet of wood. What is the length of each edge?

You are shopping for school supplies. A store is offering a \(10 \%\) discount on binders and a \(20 \%\) discount on packages of paper. You want to buy 5 binders originally marked $$ 2.50\( each and 10 packages of paper originally marked $$ 1.30 each. a. Write an expression that shows how much you will save after the discounts. b. Evaluate the expression. c. Writing If you have $$ 25\) to spend on supplies, how much money will you have left over? Explain how you arrived at your answer.

Evaluate the expression for the given value of the variable. (Review 1.1) $$\frac{5}{16}-p \text { when } p=\frac{3}{8}$$

Evaluate the expression for the given value of the variable. \(12 x\) when \(x=5\)

Compare using \(<,=,\) or \(>.\) $$0.333 \underline{?} 0.3333$$
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