Problem 31 - Prealgebra

Question

Write a numerical expression for each verbal phrase. twenty-four divided by six

Step-by-Step Solution

Answer

The numerical expression is \( \frac{24}{6} \).

Step 1: Identify the Operation

The phrase given is 'twenty-four divided by six'. The keyword to identify the mathematical operation here is 'divided by', which indicates division.

Step 2: Convert Verbal Phrase to Numbers

Replace the words 'twenty-four' and 'six' with their numerical values. This gives us 24 and 6, respectively.

Step 3: Formulate the Numerical Expression

Using the operation identified in Step 1, and the numbers from Step 2, construct the numerical expression. For division, we write: 24 ÷ 6, which can also be written as \( \frac{24}{6} \).

Key Concepts

Division

Division is a fundamental mathematical operation. It is used to split a number into equal parts or groups. Think of dividing a pizza into slices for friends. Each slice must be of equal size, showing how division works mathematically.

In any division problem, you have:

• The dividend: the number you are dividing. In our case, 24.
• The divisor: how many parts you divide the dividend into. Here, it is 6.
• The quotient: the result after dividing. For 24 ÷ 6, the quotient is 4.

Division can be presented in different ways:

• Using the division symbol, like 24 ÷ 6.
• As a fraction, written as \( \frac{24}{6} \).

Knowing how to express division correctly is essential for solving numerical expressions and helps in understanding how to manage quantities effectively in everyday life.

Verbal Phrases

Verbal phrases describe mathematical situations or operations using words. Translating these phrases into numerical expressions is a critical skill in solving math problems.

"Twenty-four divided by six" is the verbal phrase from the exercise. Each element of the phrase represents a part of a numerical expression. "Twenty-four" and "six" are the numbers involved, while "divided by" shows the operation needed. It's crucial to identify these components correctly:

• 'Twenty-four' indicates the number 24.
• 'Divided by' signals that you should perform division.
• 'Six' is the number 6, the divisor.

By understanding and identifying these components, you can readily convert words into math, which is a helpful skill for both school and everyday problem-solving.

Mathematical Operations

Mathematical operations, such as addition, subtraction, multiplication, and division, are the building blocks of math. Each operation tells you how to manipulate numbers to achieve a result. In our exercise, the focus is on division.

Operations have specific keywords linked to them in verbal phrases:

• "Plus" or "added to" for addition.
• "Minus" or "subtracted from" for subtraction.
• "Times" or "multiplied by" for multiplication.
• "Divided by" for division.

Recognizing these keywords is crucial in converting verbal expressions into numerical ones. This skill is vital because it allows students to interpret and solve real-world problems expressed in words. Mastering these operations facilitates better understanding and application of math in practical situations.