Problem 112 - Prealgebra

Question

Divide. $$207 \div 26$$

Step-by-Step Solution

Answer

207 divided by 26 equals 7 with a remainder of 25.

Step 1: Set Up the Division Problem

Place 207 inside the division bracket and 26 outside. You are dividing 207 by 26.

Step 2: Estimate the Quotient

Estimate how many times 26 can fit into the first two digits of 207, which is 20. As 26 is greater than 20, consider 207 directly. Estimate how many times 26 can fit in 207. Since 26*8 = 208, which slightly exceeds 207, consider 26*7.

Step 3: Calculate the Product

Multiply 7 by 26 to check your estimate: 7 * 26 = 182.

Step 4: Subtract and Bring Down

Subtract 182 from 207, leaving 25. Since 25 is less than 26, and there are no more numbers to bring down, the process is complete.

Step 5: Write the Answer with Remainder

Since 207 cannot be evenly divided by 26, write the result as 7 with a remainder of 25. Thus, 207 divided by 26 equals 7 R25.

Key Concepts

Division Problems

Division problems are a fundamental part of math that help us split a number into equal parts. It involves taking a dividend, the number you want to divide, and a divisor, the number you are dividing by. The result of a division is called the quotient. In the problem presented, 207 is the dividend and 26 is the divisor.

• The division symbol "÷" represents the division operation.
• The answer to a division problem can be a whole number or it might include a remainder.

For example, in our division problem, 26 does not perfectly divide 207 because multiplying 26 seven times makes 182, leaving a difference, known as the remainder. Understanding how to correctly interpret this difference is crucial in solving division problems efficiently.

Remainder in Division

In division, when the dividend is not evenly divisible by the divisor, we end up with a remainder. The remainder is what's left over after performing the division. In essence, it's the part of the dividend that is not completely divisible by the divisor.

• In our example, after dividing 207 by 26, the quotient is 7.
• Multiplying 7 by 26 gives us 182, which is less than 207.
• The remainder is the difference: 207 minus 182 leaves us with 25.

Therefore, when we express our final answer, it is written as 7 with a remainder of 25, often noted as 7 R25. Recognizing and calculating the remainder helps us understand the division process better and ensures accuracy in problem-solving.

Basic Arithmetic Operations

Understanding basic arithmetic operations is essential as they form the building blocks for more complex math problems. The four basic operations are addition, subtraction, multiplication, and division. These operations are interconnected, and division often involves both multiplication and subtraction.

• To solve a division, you may need to perform subtraction to find the remainder.
• Multiplication helps you estimate how many times the divisor fits into the dividend.

In our specific division example, estimating the quotient involved multiplication (7 times 26 equals 182), and computing the remainder required subtraction (207 minus 182 equals 25). Mastering these operations simplifies complex calculations and strengthens overall mathematical ability.