Problem 53 - Beginning and Intermediate Algebra

Question

Find each difference. $$ 4-7 $$

Step-by-Step Solution

Answer

-3

Step 1: Identify the operation

Recognize that this is a subtraction problem where 4 is subtracted by 7.

Step 2: Rewrite the problem

Convert the subtraction into an addition of the opposite. So, rewrite the expression as: 4 - 7 = 4 + (-7).

Step 3: Combine the numbers

Add 4 and -7 together. When you add a positive number and a larger negative number, the result is negative: 4 + (-7) = -3.

Key Concepts

integer operations

Integer operations are fundamental in math and include addition, subtraction, multiplication, and division of whole numbers. Let's focus on subtraction, which often involves dealing with both positive and negative numbers. Integer operations follow specific rules, and mastering them is essential for solving problems effectively.
For addition and subtraction:

• Adding a positive number increases value.
• Adding a negative number decreases value.
• Subtracting a positive number decreases value.
• Subtracting a negative number becomes addition (the two negatives cancel out, making it positive).

Understanding these principles helps in managing operations involving integers, ensuring accuracy in computations and allowing you to solve problems like 4 - 7 confidently.

subtraction of numbers

Subtraction is removing a certain value from another. When dealing with integers, it can produce positive, negative, or zero results. Let's revisit the problem 4 - 7.
To subtract numbers:

• Identify the operation: Here, it's 4 minus 7.
• Transform subtraction into addition of the opposite. So, 4 - 7 becomes 4 + (-7).
• Combine the numbers while paying attention to their signs: 4 plus -7.

Combining them requires adding a positive number (4) to a larger negative number (-7). The larger magnitude sign determines the result's sign. Hence, 4 + (-7) results in -3.
Thinking of subtraction as adding a negative helps simplify calculations, especially when dealing with negative outcomes.

negative results in subtraction

Negative results in subtraction signify that the outcome is less than zero. For instance, in 4 - 7:

• After converting to 4 + (-7), you add opposite-signed numbers.
• A larger negative number (7 in this case) outweighs the positive 4.
• The combination, 4 + (-7), results in a negative value: -3.

Visualize this on a number line:
- Starting at 4, moving left (negative direction) by 7 steps lands you at -3.
Negative results are common in integer operations and imply moving below the zero mark on the number line. Recognizing these results aids in understanding number relationships and better problem-solving.