Problem 23 - Prealgebra

Question

Find the value of each expression. $$11(6-1)$$

Step-by-Step Solution

Answer

The value of the expression is 55.

Step 1: Simplify the Expression Inside the Parentheses

Begin by simplifying the expression inside the parentheses of the equation \( 11(6-1) \). This means subtracting 1 from 6. \[ 6 - 1 = 5 \].

Step 2: Multiply the Result by 11

Now that the expression inside the parentheses is simplified, multiply the result by 11. This means computing \( 11 \times 5 \).

Step 3: Calculation

Carry out the multiplication: \( 11 \times 5 = 55 \). Thus, the value of the expression \( 11(6-1) \) is 55.

Key Concepts

Simplifying Expressions

Before tackling any mathematical expression, it's crucial to simplify it as much as possible. Simplifying expressions involves reducing them to their simplest form. This often includes performing operations inside parentheses first. Consider the expression \( 11(6-1) \). Here, we have the operation \( 6 - 1 \) inside the parentheses. When simplifying:

• Look for operations inside brackets or parentheses.
• Perform these operations first, following the rules of arithmetic.
• Simplification makes the expression easier to work with in further calculations.

For our expression, the simplification step is to calculate \( 6 - 1 \), which equals 5. This step is essential as it sets the stage for the next arithmetic operation. Always remember, simplifying makes future steps much easier.

Multiplication

After any necessary simplification, multiplication is the next step if present in the expression. In our example, once we've simplified \( 6 - 1 \) to 5, the expression becomes \( 11 \times 5 \).

• This operation involves multiplying the two numbers to find their product.
• Multiplication is repeated addition; in this case, we add 11 five times.
• For calculations like this, it's often easier to think of the multiplication table or use repeated addition: \( 11 + 11 + 11 + 11 + 11 \).

The result of \( 11 \times 5 \) is 55. Understanding multiplication as a concept of adding a number repeatedly can make it more intuitive and less mechanical.

Basic Arithmetic

Basic arithmetic is all about understanding the fundamental operations: addition, subtraction, multiplication, and division. In our example, we've used subtraction and multiplication, which are two key elements.

• **Subtraction** reduces the value by the number being subtracted, as we saw with \( 6 - 1 = 5 \).
• **Multiplication** scales a number by another, as performed with \( 11 \times 5 = 55 \).

Remember the order of operations to tackle expressions properly:

• Parentheses first.
• Exponents, if any, follow.
• Then, move to multiplication or division (from left-to-right), and finally, addition or subtraction (also from left-to-right).

Mastering these basic operations will provide you with the necessary skills to solve a wide array of mathematical problems effectively. These operations form the foundation of nearly all calculations.