Problem 21 - Prealgebra

Question

Find the value of each expression. \frac{15+9}{32-20}

Step-by-Step Solution

Answer

The value of the expression is 2.

Step 1: Identify the Numerator and Denominator

In the expression \( \frac{15+9}{32-20} \), the numerator is \( 15 + 9 \) and the denominator is \( 32 - 20 \). Our job is to calculate these separately.

Step 2: Calculate the Numerator

The numerator of the expression is \( 15 + 9 \). Add these two numbers together: \( 15 + 9 = 24 \).

Step 3: Calculate the Denominator

The denominator of the expression is \( 32 - 20 \). Subtract 20 from 32 to find the denominator: \( 32 - 20 = 12 \).

Step 4: Divide the Numerator by the Denominator

With the numerator as 24 and the denominator as 12, divide the numerator by the denominator: \( \frac{24}{12} = 2 \).

Key Concepts

Understanding Numerical Expressions

Numerical expressions are mathematical phrases that involve numbers and operations. They can include addition, subtraction, multiplication, and division, among others. In a numerical expression, you do not have any equation sign (like equals `=`) showing a specific value.
For example, in the given expression \( \frac{15+9}{32-20} \), the operations inside the parentheses and the fraction bar tell us what to do. Here, you must solve the operations in the numerator \( 15+9 \) and the denominator \( 32-20 \) before performing the division.

• The expression only involves numbers and does not have any variables like x or y.
• Order of operations is vital to correctly solve numerical expressions.
• Each part of the expression needs to be calculated separately before proceeding to other operations.

Learning Addition in Expressions

Addition is one of the basic arithmetic operations that combines two or more numbers into a single sum. In the context of numerical expressions, addition often appears as part of a larger calculation, such as in the numerator or denominator of a fraction.
When you see an expression like \( 15 + 9 \), you add the two numbers to find the sum, which gives you 24 in this case.

• Addition helps simplify parts of an expression, particularly when grouping numbers together.
• It's often the first operation performed in the simplification process if dictated by parentheses.
• Learning to add effectively is critical for tackling more complex expressions.

Exploring Subtraction in Expressions

Subtraction is another fundamental arithmetic operation, which involves taking one number away from another. In expressions, subtraction is often used to determine differences that can be part of numerators, denominators, or within parentheses.
In the expression \( 32 - 20 \), you're asked to find the difference between 32 and 20, which results in 12.

• Subtraction is crucial for simplifying expressions, especially when reducing a number by a specified quantity.
• It can be used to uncover the reduced part of a larger problem, such as simplifying within a denominator.
• Mastery of subtraction ensures clarity when expressions require simplification.

Understanding Division in Fractions

Division is a key operation that determines how many times one number is contained within another. Fractions, such as \( \frac{24}{12} \), are a division problem written in a vertical format whereas the numerator 24 is divided by the denominator 12 to find the value of the fraction.
In the problem given, once you have solved the numerator and denominator separately, division allows you to find the overall value of the expression, which in this case results in 2.

• Division is often the last operation after resolving what's inside the numerator and denominator.
• Understanding division in fractions helps solve many types of word problems and equations.
• Mastering this operation is crucial for handling with ease various complexities in mathematics.