Problem 71 - Algebra 1

Question

Find the sum. $$4-(-7)+3$$

Step-by-Step Solution

Answer

The sum of \(4-(-7)+3\) is \(14\).

Step 1: Handle the double negative

The problem you are given is \(4-(-7)+3\). In mathematics, subtracting a negative number is the same as adding a positive one. In light of this, the problem can be rewritten as \(4+7+3\).

Step 2: Add the numbers

Now, we do the addition starting from left to right, firstly add 4 with 7 which results in \(11\), then we add the result with the last number. The final sum is \(11+3\) which is 14

Step 3: Final step

So, the sum of the given expression \(4-(-7)+3\) is \(14\)

Key Concepts

Addition

Addition is one of the most basic operations in mathematics. In its simplest form, if you have a group of things and you get another group of things, addition is how you'd figure out how many things you have in total.

For example, in the exercise given, we are adding the numbers: 4, 7, and 3. Here's how it works:

• Start with the first number, which is 4.
• Add the next number, which is 7. This gives us a total of 11.
• Finally, add the last number, which is 3. Now we're up to 14.

To express this in a formula: \[ 4+7+3 = 14 \]

When adding numbers, it doesn't matter how you group them. This is known as the Associative Property of Addition, which states that the way in which numbers are grouped in an addition problem doesn't change the result. So, you could combine (4 + 7) first, as we did, or (7 + 3) first, and you'd still end up with 14.

Subtraction

Subtraction is the process of taking one number away from another. It is essentially the opposite of addition. In simple situations, if you have a number and you take some away, subtraction helps you find out what's left.

In this exercise, subtraction appears as part of a unique operation known as subtracting a negative number. This is a special case in subtraction because math rules tell us that subtracting a negative is the same as adding positive. Therefore, in our exercise \(4 - (-7)\) becomes \(4 + 7\).

This change converts the subtraction into an addition, simplifying our operation. It's a good illustration of how sometimes subtraction is just another form of addition, especially when you're dealing with negative numbers. Keeping track of these rules and concepts is key to mastering subtraction.

Negative Numbers

Negative numbers are numbers less than zero and are often represented with a minus sign (-) in front. They are essential for understanding a wide range of mathematical concepts, especially when dealing with debts, temperatures below zero, or any situation where a quantity is less than nothing.

When working with negative numbers, one of the most common rules is that subtracting a negative number is like adding its positive counterpart. For instance, in the exercise we have \(4 - (-7)\). According to the rule, subtracting \(-7\) is equivalent to adding \(+7\). Therefore, \(4 - (-7)\) simplifies to \(4 + 7\).

Understanding negative numbers also means knowing how they interact with positive numbers. The sum of a positive and its corresponding negative will always result in zero. For example, \(3 + (-3) = 0\). This concept is useful when simplifying expressions and solving equations.

Negative numbers can be tricky at first, but practicing problems that involve them will make you more comfortable and adept at using them in various mathematical operations.