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Chapter 1: Problem 431

Translate and simplify. The quotient of 45 and 15

Short Answer

Expert verified
The quotient is 3.

Step by step solution

01

Understand the Problem

The problem asks for the quotient of 45 and 15. Quotient means the result of division.
02

Set Up the Division

Write the division operation: \[ \frac{45}{15} \]
03

Perform the Division

Divide 45 by 15:\[ 45 \, \div \, 15 = 3 \]
04

Simplify

The result of the division \( \frac{45}{15} \) simplifies to 3.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Quotient
In mathematics, the term 'quotient' is used to describe the result of a division operation. When you divide one number by another, the outcome is called the quotient. For example, in the exercise you provided, the quotient of 45 and 15 is the result we get after performing the division of these two numbers.
In the given problem, the quotient is obtained as follows:
  • The dividend (the number to be divided) is 45
  • The divisor (the number by which we divide) is 15
When you perform the division \[ \frac{45}{15} \], the resulting quotient is 3.
This result means that 45 can be evenly divided by 15 exactly 3 times.
Simplification
Simplification in division is the process of reducing the expression to its simplest form. It involves performing the division operation and presenting the result in its lowest terms.
In our exercise:
  • We start with the quotient \[\frac{45}{15}\]
  • We then divide 45 by 15 to get 3
  • The quotient 3 is already in its simplest form
Simplifying the division ensures our answer is as clear and concise as possible.
Always remember, simplification makes it easier to understand and work with the result. In some cases, you might need to simplify further, but here, since 3 is already a whole number, no further simplification is required.
Division Operation
The division operation is one of the basic arithmetic operations. It involves splitting a number into equal parts and determining how many times one number fits into another. Here's how it works:
  • The number you want to divide is called the dividend
  • The number you divide by is called the divisor
  • The result of the division is the quotient
For example, in the problem provided, we divide 45 (the dividend) by 15 (the divisor). We set it up as follows: \[ \frac{45}{15} \].
Performing the division gives us the quotient, which is 3.
Division can be visualized in many contexts, such as spreading out items evenly or measuring segments. The key takeaway is that the division operation helps us determine how many times one number is contained within another.

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Most popular questions from this chapter

Divide. Then check by multiplying. $$\frac{97}{1}$$

Simplify. $$495 \div 45$$

The high temperature in Peoria one day was 86 degrees Fahrenheit and the low temperature was 28 degrees Fahrenheit. What was the difference between the high and low temperatures?

Translate from math notation to words. $$(10)(95)$$

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