Problem 66 - Prealgebra

Question

Perform the indicated operations. $$2+45 \times \frac{1}{60}$$

Step-by-Step Solution

Answer

The result of the expression is approximately 2.75.

Step 1: Identify the order of operations

In mathematical expressions, operations are performed in a specific order: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). This is often abbreviated as PEMDAS. Our expression is simple, so we will handle multiplication first, then addition.

Step 2: Perform multiplication

According to the order of operations, we first carry out the multiplication operation: \(45 \times \frac{1}{60}\). Convert \(1/60\) into a decimal by performing the division: \(45 \times 0.0167 \approx 0.75\).

Step 3: Perform addition

Now add the result of the multiplication to 2: \(2 + 0.75 = 2.75\).

Key Concepts

Multiplication in Prealgebra

In prealgebra, multiplication is one of the foundational arithmetic operations you will often encounter. It's essentially a quick way to add the same number a certain number of times. For instance, multiplying 45 by \( \frac{1}{60} \) means you are adding \( 45 \) one-sixtieths, 45 times.

In the example problem, we simplify the fraction \( \frac{1}{60} \) first. Here, \( 45 \times \frac{1}{60} \) becomes \( 45 \times 0.0167 \). A calculator can be helpful for precise multiplication here, and you will see this equals approximately 0.75.

• Consider breaking fractions into decimals for easier multiplication.
• Remember the result represents repeated addition of fractions or decimals.
• Keep track of decimal places during multiplication for accuracy.

Addition in Prealgebra

Addition is the process of bringing two or more numbers together to make a sum. This operation is straightforward once you have your numbers ready. For example, after calculating the multiplication part in our problem, you are left with the task of adding this product to another number.

In the given exercise, you first perform multiplication and then add 2 to the product which is 0.75. This results in the sum of 2.75. This addition is relatively simple as it combines an integer and a decimal.

• Ensure numbers are aligned in their place values (decimal points) before adding.
• Understand that order in simple addition does not matter; 2 + 0.75 is the same as 0.75 + 2.

PEMDAS

PEMDAS is a tool that helps you remember the order of operations in math, ensuring that calculations are performed logically and correctly. The acronym stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). Think of it as a roadmap for solving the types of problems you'll encounter in prealgebra and beyond.

In the exercise, there were no parentheses or exponents, meaning multiplication was the first step. As specified by PEMDAS, multiplication occurred before addition. This order ensures that calculations are performed correctly and you arrive at the correct solution.

• Always apply PEMDAS from left to right for Multiplication/Division and Addition/Subtraction.
• This rule prevents common mistakes in solving math problems.
• Practice consistently to remember the PEMDAS order and become proficient at solving arithmetic problems.