Problem 47 - Prealgebra

Question

Translate each of the following and simplify the result. Subtract \(-6\) from 5

Step-by-Step Solution

Answer

11

Step 1: Translate the Expression to an Equation

To find out what is being asked, we'll translate the phrase 'subtract \(-6\) from 5' into a mathematical expression. 'Subtract \(-6\)' means we are taking away \(-6\), or equivalently adding 6. So, the expression becomes 5 plus 6, or mathematically: \(5 - (-6)\).

Step 2: Simplify the Equation

Now, let's simplify the equation we have. Utilizing the property that subtracting a negative is the same as adding the positive, replace \(-(-6)\) with \(+6\). Thus, the expression \(5 - (-6)\) simplifies to \(5 + 6\).

Step 3: Solve the Simplified Equation

Perform the addition: \(5 + 6 = 11\). Hence, the simplified result of the expression is 11.

Key Concepts

Subtracting Negatives

In mathematics, subtracting a negative number can be a little tricky to wrap your head around at first. Let's simplify the concept. When you see a problem asking to "subtract a negative," it's important to recognize this as similar to adding. For example, if we are to subtract -6 from 5, it is expressed as: \[5 - (-6)\]. But instead of viewing this as subtraction, you can convert it into addition. This is because subtracting a negative is the equivalent of adding the corresponding positive number. So, \[5 - (-6)\] becomes \[5 + 6\]. Think of it this way: If you're taking away a negative, you're adding its positive counterpart.

• Negative of the negative becomes a positive: -(-6) = +6
• Change "subtract a negative" to "add the positive."

This understanding will help when dealing with equations involving more complex subtractions.

Simplifying Expressions

Mathematical expressions often need to be simplified to make them more manageable. Simplifying means making an expression easier to understand or solve. It often involves performing operations or rewriting expressions. Let's take a closer look at how this works. Suppose you have the expression \[5 - (-6)\]. The first step in simplifying is to recognize that subtracting a negative means you should replace it with addition. This gives us \[5 + 6\]. Next, perform the operations to find the most simplified form. In this case:\[5 + 6 = 11\]. What's key here is:

• Recognizing patterns or rules: subtraction of a negative becomes addition.
• Executing math operations: addition or subtraction, as required.

Grasping these steps ensures you can tackle any similar future expression-given task with ease.

Addition of Integers

Adding integers is usually straightforward, especially when both numbers have the same sign. However, it can be confusing when dealing with negative numbers. Here’s a breakdown to help make sense of this concept. When adding integers with different signs, such as \[5 + 6\], just proceed with regular addition. This means simply adding their absolute values. The result is \[11\]. If both integers had been negative, you would actually add the numbers but retain the negative sign. But here, when you change a subtraction into an addition problem like in our example, it's more transparent: \[5 + 6\]. Here are some tips to reliably navigate integer addition:

• For same signs, add absolute values and keep the sign.
• For different signs, subtract the smaller absolute value from the larger and keep the sign of the larger number.

Keep practicing these rules, and soon integer operations will become second nature!