Problem 51 - Prealgebra

Question

Evaluate each expression for the given value. (lesson \(1-3\) ) $$19 u ; u=5$$

Step-by-Step Solution

Answer

The expression evaluates to 95.

Step 1: Substitute the given value

We are given the expression \( 19u \) and the value \( u = 5 \). Substitute \( u = 5 \) into the expression. So we have \( 19 \times 5 \).

Step 2: Perform the multiplication

Multiply the constant \( 19 \) by the substituted value \( 5 \). This means we calculate \( 19 \times 5 \).

Step 3: Calculate the result

The product of \( 19 \times 5 \) is \( 95 \). So, the expression evaluates to \( 95 \).

Key Concepts

Basic Multiplication

Multiplication is one of the fundamental operations in mathematics. It is essentially repeated addition. For instance, when we multiply two numbers, we are adding one of the numbers to itself a number of times as dictated by the other number. In our exercise, we multiplied 19 by 5, which means we added 19, five times together:

• 19 + 19 + 19 + 19 + 19

Both addition and multiplication are operations that help us simplify calculations. Instead of adding 19 repeatedly, multiplication allows us to quickly calculate the answer. The multiplication operation is denoted by symbols such as "\( \times \)", and it is a crucial technique for evaluating expressions efficiently.

Mathematical Expressions

Mathematical expressions are combinations of numbers, variables, and operations. In our example, the expression \( 19u \) combines a constant (19) with a variable (u). A mathematical expression does not contain an equality sign, distinguishing it from an equation. In an expression, we can replace variables with numbers to simplify or evaluate them. Mathematical expressions can involve different operations like addition, subtraction, multiplication, and division. Each operation affects the value of the expression in a specific way, necessitating a clear understanding of how these operations work. For example, knowing the role of multiplication in adjusting values is key when working with expressions like \( 19u \).

Evaluating Expressions

Evaluating an expression means finding its value after substituting any variables with their given numbers. This process often involves the following steps:

• Identify the expression and the value of any variables involved.
• Replace the variable with the assigned number.
• Carry out the operations as per the rules of arithmetic.

For instance, in the problem \( 19u \), where \( u = 5 \), we substituted \( 5 \) for \( u \), resulting in \( 19 \times 5 \). Following that, we performed the calculation, which led to the expression evaluating to 95. This substitution technique is particularly useful in simplifying expressions and solving algebraic problems. Ultimately, evaluating expressions helps us understand the relationships between numbers and variables, allowing us to solve mathematical problems efficiently.