Problem 69 - Prealgebra

Question

Write a numerical expression for each verbal phrase. twelve divided into sixty

Step-by-Step Solution

Answer

The expression is \( 60 \div 12 \).

Step 1: Understand the Operation

The phrase 'twelve divided into sixty' suggests a division operation, with 'sixty' being divided by 'twelve.' When you 'divide into,' it means the divisor will be the number after the phrase.

Step 2: Identify the Numbers

In this phrase, the dividend is sixty (the number being divided), and the divisor is twelve (the number that goes into the dividend).

Step 3: Write the Expression

Using the division operation identified in Step 1, write the numerical expression as \( 60 \div 12 \).

Key Concepts

Division Operation

The division operation is a fundamental arithmetic process where one number, known as the "dividend," is divided by another number, referred to as the "divisor," to yield a result called the "quotient." In your exercise, the phrase "twelve divided into sixty" indicates a division operation. Here, the number sixty is divided by twelve. To express this operation mathematically, you write it as a division formula: \( 60 \div 12 \). This essentially asks, "How many times does twelve fit into sixty?" Understanding division is crucial in solving many mathematical problems, and it simplifies scenarios where you need to partition or share quantities.
Keep in mind:

• The dividend is the total or quantity that is being divided. Here, it is sixty.
• The divisor is the part or quantity you are dividing by, which is twelve in this expression.

Mathematical Phrases

In mathematics, verbal phrases are used to describe mathematical operations. Understanding these phrases is essential in converting words into numerical expressions. The phrase "twelve divided into sixty" is a verbal cue for performing a division operation. It is a common way to verbally express a mathematical operation without directly stating numerical values or symbols.
When approaching such phrases in math:

• Translate the words into a mathematical operation. Here, "divided into" indicates division, and the order in which numbers are mentioned determines dividend and divisor.
• Pay attention to the phrasing as it can alter the meaning; for instance, "sixty divided by twelve" is equivalent but framed differently in language.

This skill of transforming words into mathematical expressions helps solve real-world problems by bridging everyday language and mathematical concepts.

Basic Arithmetic

Basic arithmetic is the foundation of mathematics and includes four primary operations: addition, subtraction, multiplication, and division. In this exercise, we work with division, one of these key operations. It's essential for understanding not only individual mathematical tasks but also for progressing to more complex topics.
Division allows us to partition or distribute numbers evenly. For example, dividing sixty by twelve results in five, indicating that twelve fits into sixty exactly five times. This is crucial when you're distributing items equally among groups or determining how one quantity relates to another.
Additional arithmetic foundations:

• Addition: Combining quantities.
• Subtraction: Finding the difference between quantities.
• Multiplication: Finding the product of repeated addition.

Mastering these basic operations is vital for solving any mathematical problems efficiently.

Prealgebra Concepts

Prealgebra is an introductory mathematical field that prepares students for algebra by solidifying their understanding of basic arithmetic operations, including division. In prealgebra, the focus is on making sense of numbers and their relationships using fundamental operations and concepts. This exercise is an example of applying prealgebra concepts as it involves recognizing and correctly using division in the context of a numerical expression.
Key goals in prealgebra:

• Develop a familiarity with numerical symbols and expressions.
• Understand and manipulate expressions using basic arithmetic operations.
• Begin to solve simple equations and understand word problems through numerical expressions.

This foundational understanding aids in an easier transition to more advanced branches of mathematics, providing the skills needed for high school algebra and beyond.