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Chapter 7: Problem 33

Multiply. $$15 \div 5$$

Short Answer

Expert verified
The result of \(15 \div 5\) is 3.

Step by step solution

01

Understand the Operation

In this problem, we are given a basic division operation: \(15 \div 5\). Division involves finding out how many times one number (the divisor) is contained in another number (the dividend). In this case, we need to determine how many times 5 is contained in 15.
02

Perform the Division

To divide 15 by 5, we can think about how many groups of 5 can be formed from 15. If we multiply 5 by 3, we get 15. Therefore, \(15 \div 5 = 3\). This means there are 3 groups of 5 in 15.
03

Check Your Answer

Multiply the quotient by the divisor to see if you get the dividend back: \(3 \times 5 = 15\). Since the product is equal to the original dividend, our answer is verified to be correct.

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Key Concepts

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

Divisor
In mathematics, understanding the concept of a **divisor** is fundamental when it comes to division. A divisor is the number by which another number is divided. If you consider the division problem \(15 \div 5\), the number 5 is the divisor. It is the number of equal parts that you are dividing the larger number \(15\) into.It's like having 15 pieces of candy that you want to distribute evenly among 5 friends. Each friend would get an equal amount of candy.- **Key Points:** - A divisor divides a dividend to create a quotient. - The divisor determines the size of each group when dividing.
Quotient
The outcome of dividing one number by another is called the **quotient**. In our initial problem, \(15 \div 5\), the answer is 3, which means 3 is the quotient. Essentially, the quotient tells us how many complete groups of the divisor fit within the dividend.Continuing with our candy example: if you have 15 candies and distribute them among 5 friends, each friend receives 3 candies. Here, 3 signifies the quotient.- **Important to Remember:** - The quotient is the result of the division. - It shows the count of times the divisor can iterate in the dividend without exceeding it.
Verified Answer
Once you arrive at the quotient, it is crucial to verify that your result is accurate, ensuring this by performing a multiplication check. For our original example, we take the quotient (3) and multiply it by the divisor (5):\[3 \times 5 = 15\]As this product equals the original dividend (15), the answer is validated. Verification solidifies our confidence in the calculation:- By cross-multiplying, you ensure there have been no errors.- A successful check means the quotient truly divides the original number correctly.This check benefits us by providing certainty and encouraging accuracy in arithmetic operations.

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Most popular questions from this chapter

Complete Exercises 86 and 87 without actually finding the percents. Does 0.055 represent a percent greater than \(1 \%\) or less than \(1 \% ?\)

Use a calculator to write each fraction as a decimal, and then change the decimal to a percent. Round all answers to the nearest tenth of a percent. $$\frac{236}{327}$$

Write as a percent. Round to the nearest tenth of a percent. $$\frac{7}{8}$$

Compensation Each of three employees earned an annual salary of \(545,000\) before Employee A was given a \(3 \%\) raise, Employee B was given a \(6 \%\) raise, and Employee C was given a \(4.5 \%\) raise. Which of the three employees now has the highest annual salary? Explain how you arrived at your answer.

Divide. Round the answers to the nearest thousandth, if necessary. $$\frac{25}{0.4}$$
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