Problem 389
Question
Divide. Then check by multiplying. $$\frac{96}{8}$$
Step-by-Step Solution
Verified Answer
12
1Step 1: Set up the division equation
Determine the operation needed to solve the problem. You need to divide 96 by 8. Write the equation as \(\frac{96}{8}\).
2Step 2: Perform the division
Divide the numerator (96) by the denominator (8). \(\frac{96}{8} = 12\).
3Step 3: Verify the result by multiplication
Multiply the quotient (12) by the denominator (8) to check the result. \(12 \times 8 = 96\). Since the original number is obtained, the division is correct.
Key Concepts
Understanding DivisionConnecting Division and MultiplicationVerification Techniques
Understanding Division
Division is one of the basic arithmetic operations. It is essentially the process of splitting a number into equal parts. In our exercise, we aim to divide 96 by 8. This can be written as \( \frac{96}{8} \). Here, 96 is known as the dividend, and 8 is the divisor.
When performing division, we are trying to find out how many times the divisor can be subtracted from the dividend until we reach zero. If the division is exact, we get a whole number called the quotient. If there's something left, it is called the remainder. In our problem, \( \frac{96}{8} \) gives us a quotient of 12:
\[ \frac{96}{8} = 12 \].
It's a simple process when you break it down into steps: Set up your division equation, perform the division, and write down the quotient. Always keep check to see if the operation is accurate.
When performing division, we are trying to find out how many times the divisor can be subtracted from the dividend until we reach zero. If the division is exact, we get a whole number called the quotient. If there's something left, it is called the remainder. In our problem, \( \frac{96}{8} \) gives us a quotient of 12:
\[ \frac{96}{8} = 12 \].
It's a simple process when you break it down into steps: Set up your division equation, perform the division, and write down the quotient. Always keep check to see if the operation is accurate.
Connecting Division and Multiplication
Multiplication and division are closely related. They are considered inverse operations, meaning that one can undo the other. When you divide 96 by 8 to get 12, you can think of it as finding how many times 8 fits into 96.
To verify, you can multiply the quotient (12) by your divisor (8) to check if you get back to the original dividend (96). In this scenario:
\[ 12 \times 8 = 96 \].
This simple multiplication confirms that our division was done correctly. So, always remember, after doing a division, you can check your result by multiplying the quotient back with the divisor. If it equals the original number, your division was correct.
To verify, you can multiply the quotient (12) by your divisor (8) to check if you get back to the original dividend (96). In this scenario:
\[ 12 \times 8 = 96 \].
This simple multiplication confirms that our division was done correctly. So, always remember, after doing a division, you can check your result by multiplying the quotient back with the divisor. If it equals the original number, your division was correct.
Verification Techniques
Verification is key to ensuring your calculations are correct. For division problems, this means using multiplication. Once we have our quotient, we should multiply it by the divisor to see if we get the dividend again.
Let's revisit our example to cement this: We divided 96 by 8 and got 12. Now we multiply 12 (quotient) by 8 (divisor):
\[ 12 \times 8 = 96 \].
This type of verification is straightforward and very effective. It ensures our results are accurate and also reinforces the inverse relationship between division and multiplication.
Always finish your division tasks with a verification step. You’ll find errors more easily and gain confidence in your math skills.
Let's revisit our example to cement this: We divided 96 by 8 and got 12. Now we multiply 12 (quotient) by 8 (divisor):
\[ 12 \times 8 = 96 \].
This type of verification is straightforward and very effective. It ensures our results are accurate and also reinforces the inverse relationship between division and multiplication.
Always finish your division tasks with a verification step. You’ll find errors more easily and gain confidence in your math skills.
Other exercises in this chapter
Problem 387
Divide. Then check by multiplying. $$72 \div 3$$
View solution Problem 388
Divide. Then check by multiplying. $$57 \div 3$$
View solution Problem 390
Divide. Then check by multiplying. $$\frac{78}{6}$$
View solution Problem 393
Divide. Then check by multiplying. $$924 \div 7$$
View solution