Problem 606 - Prealgebra

Question

Translate each phrase to math notation and then simplify. The quotient of 63 and 21

Step-by-Step Solution

Answer

3

Step 1: Identify the Key Phrases

The given phrase is 'The quotient of 63 and 21'. The word 'quotient' indicates division.

Step 2: Translate to Math Notation

Express the phrase in mathematical notation. The quotient of 63 and 21 can be written as:

Step 3: Perform the Division

Divide 63 by 21: 63 ÷ 21 = 3

Step 4: Simplify the Expression

The simplified answer is 3.

Key Concepts

Division

Division is a basic arithmetic operation where you break down a number into equal parts. It is denoted by the symbol '÷' or a forward slash '/'.

When you divide one number by another, you determine how many times the divisor fits into the dividend.
Let's take an example:

• Suppose you have 20 candies, and you want to distribute them equally among 5 friends.
• You will perform the division 20 ÷ 5.

The result tells you that each friend will get 4 candies.

In the exercise provided, we are asked to find 'the quotient of 63 and 21'. Using division, we write it as:
\[ \frac{63}{21} \]

This way, division helps us solve problems where we need to share or distribute things equally.

Quotient

The term 'quotient' refers to the result of a division problem.
When you divide one number (the dividend) by another number (the divisor), the answer is called the quotient.

For example:

• In 20 ÷ 5, the quotient is 4.
• In 63 ÷ 21, the quotient is 3.

Finding the quotient is like answering the question, 'How many times does the divisor fit into the dividend?' In our exercise, the quotient of 63 and 21 is found by dividing them:
\[ \frac{63}{21} = 3 \]

Thus, the quotient helps us understand how many equal parts we have.

Simplification

Simplification means reducing a mathematical expression to its simplest form.
It makes it easier to understand and interpret the result.

In our given exercise, after dividing 63 by 21, we get a quotient of 3.
The number 3 is the simplest form of this particular division problem because it cannot be reduced any further.

Let's consider another example:

• If we have the fraction \( \frac{8}{4} \), we can simplify it by dividing the numerator (8) by the denominator (4), resulting in 2.

Simplification not only gives us a cleaner result but also helps in performing further calculations more efficiently.

In our original exercise, after performing the division, we simplify the quotient to the value 3, providing the simplest and most understandable answer.