Problem 60 - Prealgebra

Question

Perform the indicated operations. $$\begin{array}{r} 85 \\ -42 \\ \hline \end{array}$$

Step-by-Step Solution

Answer

The result is 43.

Step 1: Understand the Problem

We need to subtract 42 from 85.

Step 2: Set Up the Equation

Write the subtraction equation: \( 85 - 42 \).

Step 3: Perform the Subtraction

Start subtracting the units (5 - 2 = 3). Then subtract the tens (8 - 4 = 4). This gives us a final result of 43.

Key Concepts

Arithmetic Operations

Arithmetic operations are the fundamental building blocks of mathematics. They include addition, subtraction, multiplication, and division. Each of these operations plays a crucial role in solving mathematical problems. In our exercise, subtraction is the focus, which is the process of calculating the difference between two numbers.
To perform subtraction, align the numbers vertically, ensuring that each digit is in the correct place value column (units, tens, hundreds, etc.). Starting from the rightmost column, subtract the lower digit from the upper digit. If the upper digit is smaller, borrowing may be necessary from the next left column. Understanding these basic steps is essential for mastering subtraction as a foundational arithmetic operation.

Basic Math Skills

Developing basic math skills involves gaining a solid understanding of core concepts like addition, subtraction, multiplication, and division. Mastery of these skills allows students to tackle more complex mathematical problems and scenarios.
Subtraction, as in our exercise, involves finding the difference between numbers. Good subtraction skills require practice in recognizing place values and borrowing when needed. This can be enhanced by:

• Practicing with different sets of numbers to build confidence.
• Utilizing visual aids like number lines or counters to conceptualize the process.
• Checking work by adding the result to the smaller number to see if it equals the original larger number.
  

By continually practicing these skills, students develop fluency in numerical operations and improve their overall mathematical proficiency.

Numerical Calculation

Numerical calculation is the process of using numbers and arithmetic operations to solve problems. It involves careful manipulation of numbers to achieve correct results.
The subtraction of 42 from 85, for instance, requires precise calculation to determine that the result is 43. To ensure accuracy, one should:

• Align digits correctly according to their place values.
• Start subtracting from the rightmost digits and proceed left.
• Verify the result by performing the inverse operation, such as adding the result to the smaller number, to see if it equals the original larger number.
  

By mastering the art of numerical calculation, students can better handle various mathematical tasks and apply these skills in everyday situations, improving their problem-solving abilities.