Problem 62 - Prealgebra

Question

Find each difference. $$104-82$$

Step-by-Step Solution

Answer

The difference is 22.

Step 1: Understand the Problem

We need to find the difference between two numbers: 104 and 82. This means we will subtract 82 from 104.

Step 2: Set Up the Calculation

Write the subtraction problem as \( 104 - 82 \). This expression represents the difference we are trying to find.

Step 3: Subtract the Ones Place

Subtract the ones place digits: 4 minus 2 equals 2. Write 2 as the ones place digit of the result.

Step 4: Subtract the Tens Place

Subtract the tens place digits: 10 minus 8 equals 2. Write 2 as the tens place digit of the result.

Step 5: Combine the Results

The digits we found in the tens and ones places give us our final answer. Therefore, \( 104 - 82 = 22 \).

Key Concepts

Place Value

Place value is a fundamental concept in the world of mathematics, especially when dealing with subtraction. Each digit in a number has a specific position that determines its value. For example, in the number 104:

• The "1" is in the hundreds place, representing 100.
• The "0" is in the tens place, representing 0 actually.
• The "4" is in the ones place, representing 4.

When performing subtraction, it is crucial to line up numbers according to their place values. This ensures accuracy as each digit is subtracted from its corresponding place. Misplacing digits can lead to incorrect results. For instance, if you align the tens with the hundreds, you get a completely different number. Always remember to keep each digit "in its lane" as you work through problems. This careful alignment helps you subtract accurately, especially when the numbers are not straightforward.

Arithmetic Operations

Arithmetic operations are the basic building blocks of mathematics. Subtraction is one of the four main operations, along with addition, multiplication, and division. It involves finding the difference between two numbers. In our exercise, we subtract 82 from 104. This process can be thought of as removing 82 from 104, leaving behind what remains.

• Subtraction is often visualized on a number line, showing the decrease from the larger number down to the smaller one.
• Think of subtraction as "taking away," which might be helpful if you use physical objects like counters.
• Subtraction can also be checked by addition. For example, if 104 - 82 = 22, then adding 82 + 22 should return you back to 104.

Mastering subtraction is essential for understanding other areas of mathematics. It plays a vital role in solving equations, calculating change, and even dividing large quantities into smaller, manageable parts.

Two-Digit Numbers

Two-digit numbers are numbers that have both tens and ones places. They range from 10 to 99. Understanding how to work with these, especially in subtraction, is crucial for solving more complex problems later on. In a subtraction problem like 104 - 82:

• The focus first is usually on the ones place which includes single-digit subtractions, like 4 minus 2.
• The next focus is on the tens place. If the upper number in the tens place is smaller than the bottom, sometimes borrowing from the hundreds place is necessary.
• Handling carries (borrowing) efficiently is a skill that comes with practice, but it’s important to reinforce the understanding that it helps simplify the subtraction when the top digit isn’t large enough to subtract the bottom digit directly.

e.g. In this problem, no borrowing was needed since the tens place of the top number (10) was larger than that of the bottom number (8). Mastery of two-digit subtractions will make working with larger numbers far less intimidating going forward.