Problem 46 - Algebra 2

Question

Find the value of each expression. $$ \frac{1}{2}(34) $$

Step-by-Step Solution

Answer

The value of the expression is 17.

Step 1: Identify the Components of the Expression

The given mathematical expression is \( \frac{1}{2}(34) \). This represents one-half of the number 34. Here, we need to multiply 34 by \( \frac{1}{2} \), which is the same as dividing 34 by 2.

Step 2: Divide the Number by 2

To find \( \frac{1}{2}(34) \), divide 34 by 2: \[ 34 \div 2 = 17 \]. The result of this operation is 17.

Key Concepts

Multiplication

Multiplication is one of the basic operations in mathematics. It's a way to combine equal groups into a single total. When you multiply, you are essentially adding a number to itself a certain number of times.

• For example, 3 multiplied by 4 means you are adding 3, four times (3 + 3 + 3 + 3), which equals 12.
• In the context of fractions, multiplying a number by a fraction like \( \frac{1}{2} \) can be visualized as taking half of that number.
• Here, multiplying by \( \frac{1}{2} \) is equivalent to finding what one part of two equal parts of a number would be.

Multiplication of fractions involves multiplying the numerators and denominators individually. For example, to multiply \( \frac{1}{2} \times 34 \), think of it as halving 34, which results in 17.

Division

Division is another fundamental operation in mathematics. It involves splitting a number into equal parts. When you divide, you are determining how many times a number can fit into another.

• For instance, dividing 34 by 2 is asking, "How many times does 2 fit into 34?"
• Just like subtraction is the opposite of addition, division is the opposite of multiplication.
• Dividing by a number is also the same as multiplying by its reciprocal. Thus, dividing by 2 is the same as multiplying by \( \frac{1}{2} \).

This is why in the expression \( \frac{1}{2}(34) \), we divide 34 by 2 to find one-half of it, resulting in 17.

Mathematical Expressions

Mathematical expressions are a combination of numbers and operation symbols. These expressions can include addition, subtraction, multiplication, and division.

• Expressions provide a way to represent mathematical ideas concisely and can be solved step by step.
• Consider \( \frac{1}{2}(34) \), which represents multiplying 34 by \( \frac{1}{2} \), or finding half of 34.
• The expression involves both multiplication and division, as these operations are closely linked, especially with fractions.

Understanding how to interpret expressions allows you to solve them correctly. Breaking them down into simpler parts, identifying operations, and executing them in sequence is vital in solving expressions like this.