Problem 367 - Prealgebra

Question

Divide. Then check by multiplying. $$72 / 8$$

Step-by-Step Solution

Answer

72 divided by 8 is 9. Checked by multiplying: 9 * 8 = 72.

Step 1 - Division

Divide 72 by 8. 72 divided by 8 equals 9. So, the solution to the division problem is 9.

Step 2 - Multiplication Check

To check the result, multiply 9 (the quotient) by 8 (the divisor). If the result is 72 (the dividend), the division is correct. 9 multiplied by 8 equals 72, which confirms our division result.

Key Concepts

Division

Division is the process of splitting a number into equal parts. When we divide, we determine how many times one number (the divisor) goes into another number (the dividend). In our example, we are dividing 72 by 8.

To solve 72 / 8:

• Start by checking how many times 8 fits into 72.
• Here, 8 goes into 72 exactly 9 times.

This means our quotient, or result of the division, is 9.

Multiplication

Multiplication is essentially repeated addition. If you multiply two numbers, you are adding one number to itself a certain number of times. In our example, to check our division result, we use multiplication:

• We multiply the quotient (9) by the divisor (8).
• So, 9 multiplied by 8 equals 72.

This step confirms the division was done correctly, as we get back to our original number (the dividend).

Quotient

The quotient is the result of dividing one number by another. In the division problem 72 / 8, the quotient is the answer we get after performing the division. Here, the quotient is 9.

To find the quotient:

• Divide the dividend (72) by the divisor (8).
• The answer, or quotient, is 9.

Remember, the quotient tells us how many times the divisor fits into the dividend.

Divisor

The divisor is the number by which we divide in a division problem. In 72 / 8, the divisor is 8. It shows how many parts we are dividing the dividend into.

To identify and use the divisor:

• Recognize the number by which you want to divide the dividend.
• In this problem, we are dividing 72 by 8.

The divisor helps us determine how many equal parts the dividend will be split into.

Dividend

The dividend is the number that you want to divide. In our division problem 72 / 8, 72 is the dividend. It is the number being split into smaller parts.

To work with the dividend:

• Identify the number that needs to be divided.
• In this case, 72 is the number we are dividing by 8.

Understanding the dividend helps us see the total amount that is being divided.