Problem 388 - Prealgebra

Question

Divide. Then check by multiplying. $$57 \div 3$$

Step-by-Step Solution

Answer

19. Verified by multiplying 19 by 3.

Step 1 - Understand the Problem

The task requires dividing 57 by 3. This can be written as a fraction or a division expression: \[ \frac{57}{3} \]

Step 2 - Perform the Division

Divide 57 by 3. \[ 57 \div 3 = 19 \]

Step 3 - Check the Answer by Multiplying

To verify the result, multiply the quotient (19) by the divisor (3). \[ 19 \times 3 = 57 \] Since the product matches the original dividend, the answer is correct.

Key Concepts

Introduction to Division Problems

Division problems are a fundamental concept in mathematics and are used to determine how many times one number, called the divisor, is contained within another number, called the dividend. When you divide the dividend by the divisor, you get the quotient. In our example, we are dividing 57 by 3. This means we want to know how many times 3 fits into 57.

Division can be written in several ways: as a fraction, e.g., \( \frac{57}{3} \); using the division symbol \( \div \); or using a division expression. All these notations serve the same purpose of finding the quotient.

Understanding Multiplication Verification

To ensure our division result is accurate, we use multiplication verification. This step involves multiplying the quotient by the divisor to see if we get back to the original dividend.

In the given problem, after dividing 57 by 3 to get the quotient 19, we check our work by multiplying 19 (quotient) by 3 (divisor). This gives us: \( 19 \times 3 = 57 \).

Since the product (57) matches the original dividend, our division was correct. This verification step reassures us that no mistakes were made in the division process.

Exploring Arithmetic Operations

Arithmetic operations include addition, subtraction, multiplication, and division. Understanding how these operations interrelate is vital to mastering basic math skills.

For example, in division problems, multiplication is a helpful tool to verify the accuracy of your answer.

• Addition and subtraction help in breaking down and simplifying more complex division problems.
• Multiplication and division are inverse operations, meaning one operation can undo the other.

Practicing these operations together can improve your overall number sense and make solving problems easier and more intuitive.