Problem 76 - Algebra 1

Question

Evaluate the expression. \(y \div 8\) when \(y=32\)

Step-by-Step Solution

Answer

The result when y=32 is divided by 8 is 4

Step 1: Identify required values

From the equation, the value of y is given as 32. Also, we are required to divide y by 8

Step 2: Substitute the value of y

Substitute y=32 into the equation to get \(32 \div 8\)

Step 3: Perform the division operation

Performing the division operation gives \(32 \div 8 = 4\)

Key Concepts

Understanding Division

Division is one of the four basic arithmetic operations. It is the process of finding out how many times one number, the divisor, is contained within another number, the dividend. In our example, the operation division is carried out as \( y \div 8 \). Here, 32 is the dividend and 8 is the divisor. Think of it as having 32 apples, and you want to distribute them equally into 8 baskets.

To perform division, you can ask yourself: How many times does 8 fit into 32? The answer to this is 4, because 8 multiplied by 4 equals 32. This is how we obtain that \( 32 \div 8 = 4 \).

• Dividend: The number to be divided (32 in this case)
• Divisor: The number with which we divide (8 here)
• Quotient: The result of the division (4 here)

Remember, division is essentially the opposite of multiplication. It checks how many times a number fits into another.

Variable Substitution in Mathematics

Variable substitution is a useful method in mathematics to simplify expressions by replacing variables with their given values. In the original exercise, you are given \( y = 32 \) and asked to evaluate the expression \( y \div 8 \).

Here, the process involves substituting the value of the variable \( y \) with 32. This transforms the expression \( y \div 8 \) into \( 32 \div 8 \).

To do this, follow these simple steps:

• Identify the variable (\( y \) in this case)
• Find the given value of the variable (32)
• Replace every occurrence of the variable in the expression with its corresponding value

Making substitutions correctly is critical to solving the problem accurately, as it sets the stage to perform other operations like division or multiplication. Hence, always double-check to ensure the correct values are substituted!

Evaluating Mathematical Expressions

Mathematical expression evaluation involves calculating the value of a mathematical expression when all variable values are provided. This process can include one or more operations such as addition, subtraction, multiplication, or division.

In our example, once the variable \( y \) is replaced with 32, the expression becomes \( 32 \div 8 \). The evaluation step is simple: carry out the division operation to find its value, which is 4.

• Start by substituting any variables in your expression with their given numeric values.
• Follow the correct order of operations (parentheses, exponents, multiplication & division, addition & subtraction).
• Step-by-step, handle each operation sequentially to simplify the expression.

Remember, careful and correct evaluation is necessary to solve the problem at hand accurately. It ensures your final answer is reliable and meaningful.