Problem 564 - Prealgebra

Question

Divide. Then check by multiplying. $$\frac{32}{8}$$

Step-by-Step Solution

Answer

The result of \(\frac{32}{8}\) is 4. Verification: 4 \(\times \) 8 = 32.

Step 1: Understand the Division

Interpret the problem as dividing 32 by 8. This is written as \(\frac{32}{8}\).

Step 2: Perform the Division

Calculate \(\frac{32}{8}\). Divide 32 by 8 to get the quotient. \(\frac{32}{8} = 4\).

Step 3: Check the Result by Multiplying

Multiply the quotient by the divisor to verify the result. The quotient is 4, and the divisor is 8. So, calculate 4 \( \times \) 8 which equals 32. Since 4 \(\times\) 8 = 32, the division is correct.

Key Concepts

Division in Prealgebra

Division is one of the basic operations in arithmetic. It involves splitting a number into equal parts. For example, when you divide 32 by 8, you are figuring out how many times 8 can fit into 32 evenly. Think of it like sharing 32 candies among 8 friends. Each friend would get 4 candies. In this exercise, we write the division as \(\frac{32}{8}\), which translates to dividing 32 by 8.

Multiplication Check

To ensure that our division is correct, we can use multiplication to check. Multiplication is the opposite of division. By multiplying the quotient and the divisor, we should get back to the original number we started with. In our case, the quotient is 4 and the divisor is 8. So we multiply 4 \(\times\) 8 and get 32. Since 4 \(\times\) 8 = 32, our division from earlier is verified as accurate.

Basic Arithmetic

Basic arithmetic includes operations like addition, subtraction, multiplication, and division. These are the foundational skills that you need to solve more complex math problems. Understanding these basics helps you move on to advanced topics like fractions, algebra, and geometry. In the exercise, we divided directly and then verified our solution using multiplication, both fundamental arithmetic operations.

Quotient and Divisor

In a division problem, the number you are dividing is called the dividend, and the number you are dividing by is the divisor. The result of the division is called the quotient. For example, in \(\frac{32}{8}\), 32 is the dividend and 8 is the divisor. The quotient we get from this division is 4. It's essential to know these terms for better understanding and communication in math problems.