Problem 18 - Elementary Algebra

Question

For exercises 1-80, evaluate. $$ 15-(6-1) $$

Step-by-Step Solution

Answer

10

Step 1: Understand the expression

The given expression is 15 - (6 - 1). This is a subtraction problem within parentheses.

Step 2: Solve inside the parentheses

First, evaluate the expression inside the parentheses: 6 - 1. Calculate this to get 5.

Step 3: Substitute and simplify

Next, substitute the result from step 2 back into the original expression: 15 - 5. Now, perform the subtraction, which yields 10.

Key Concepts

Evaluate Expressions

When we talk about evaluating expressions, we mean performing the required mathematical operations to get a single numerical answer.
Let's break down the given example and understand each step together. First, we need to identify the operations and complete them in the correct order.

In the given problem, we have: 15 - (6 - 1).
Notice that the expression has two main components:

• The subtraction outside the parentheses: 15 - something.
• The subtraction inside the parentheses: 6 - 1.

Solving step-by-step makes it simpler.

Subtraction

Subtraction means finding the difference between numbers. To help you understand better, let's look at the example:

• First, subtract inside the parentheses: 6 - 1

This gives us 5. Now our problem looks like this: 15 - 5.

• Next, subtract 5 from 15. This gives us 10.

So, the final answer is 10.

Remember, subtraction affects the placement of numbers related to each other. Minuend (the first number) minus Subtrahend (the number being subtracted) equals the Result or Difference.
To help:

• Minuend - Subtrahend = Difference.

Parentheses

Parentheses are symbols used to group parts of mathematical expressions. They tell us to perform the operations inside them first.

In the problem 15 - (6 - 1), the parentheses around 6 - 1 tell us to solve this part before doing other operations.

• First, solve inside the parentheses: 6 - 1 = 5.
• Then, use this result to complete the whole expression: 15 - 5 = 10.

Parentheses make sure operations within them get priority. This technique ensures the correct order of calculation.
It's an essential part of the order of operations, which also includes exponents, multiplication, and division before addition and subtraction.