Problem 27 - Prealgebra

Question

Subtract. $$-35-(-14)$$

Step-by-Step Solution

Answer

The result of \(-35 - (-14)\) is \(-21\).

Step 1: Understand Negative Subtraction

When you see two negative signs together, such as in \(-35 - (-14)\), you need to understand that subtracting a negative is the same as adding a positive because the double negatives cancel each other out.

Step 2: Rewrite the Expression

Using the information from Step 1, rewrite the problem by changing the subtraction of a negative to addition: \(-35 + 14\).

Step 3: Perform the Addition

Now perform the addition calculation: \(-35 + 14\). Since \(35\) is larger in absolute value and negative, you will perform \(35 - 14 = 21\), and keep the negative sign: \(-35 + 14 = -21\).

Key Concepts

Subtracting Negative Numbers

Subtracting a negative number is an interesting but often confusing concept in math, especially when dealing with integers. The main rule to remember here is that subtracting a negative number is equivalent to adding the positive version of that number. This happens because two negatives make a positive.

For example, if you have the expression \(-35 - (-14)\), the two negative signs (- and -) become a plus (\(+\)). So the expression becomes \(-35 + 14\).

This is comparable to borrowing money and then being told you don't need to pay it back anymore—you're effectively in a better position. Remembering this can simplify many seemingly complicated integer operations.

Integer Operations

Understanding integer operations is the key to mastering basic arithmetic involving whole numbers. Integers include all positive and negative numbers, as well as zero. When performing operations with integers, such as addition and subtraction, it's important to consider the signs of the numbers involved.

Here are some tips to help you with integer operations:

• Addition: When both numbers have the same sign, add their absolute values and keep the same sign.
• Subtraction: Subtracting is often easier if you think of it as adding the opposite. Convert the subtraction of a negative into the addition of a positive.
• Negative and positive together: Always evaluate the absolute values first, and then apply the rules for addition or subtraction accordingly.

By practicing these rules, you'll find that dealing with integers becomes much simpler and more intuitive.

Addition and Subtraction of Integers

The addition and subtraction of integers follow some specific rules that can help simplify calculations.

When adding integers:

• If the numbers have the same sign, add their absolute values and give the sum the same sign.
• If the numbers have different signs, subtract the smaller absolute value from the larger absolute value and use the sign of the number with the larger absolute value.

When subtracting integers:

• Remember that subtracting a negative is the same as adding the positive.
• Convert any subtraction into addition by changing the sign of the number being subtracted.
• Apply the rules of addition for further simplification.

By remembering these guidelines, you'll be better prepared to handle all sorts of integer calculations, making math homework much less daunting.