Problem 449 - Prealgebra

Question

Explain how you use the multiplication facts to help with division.

Step-by-Step Solution

Answer

Use known multiplication facts to find the quotient in a division problem. For example, 15 divided by 3 is found by knowing that 3 times 5 is 15.

Step 1 - Understand the Relationship Between Multiplication and Division

Recognize that multiplication and division are inverse operations. This means that knowing one can help solve the other. For example, if you know that 3 multiplied by 4 equals 12, then you also know that 12 divided by 4 equals 3.

Step 2 - Identify the Multiplication Fact

Given a division problem, first identify the multiplication fact that relates to it. For instance, if the problem is 15 divided by 3, remember that the related multiplication fact is 3 times 5 equals 15.

Step 3 - Apply the Multiplication Fact

Use the multiplication fact to find the quotient. From the previous example, since 3 times 5 equals 15, then 15 divided by 3 must equal 5.

Step 4 - Check Your Work

Verify the result by multiplying the quotient by the divisor to see if you get the original dividend. In this case, multiply 5 by 3 to check that it indeed equals 15.

Key Concepts

Inverse Operations

Inverse operations are operations that reverse the effects of each other. Multiplication and division are great examples of this. If you multiply two numbers and then divide the result by one of those numbers, you end up back at the other number. For instance, if you multiply 4 by 3 to get 12, dividing 12 by 3 takes you back to 4. This interplay is very helpful in solving problems.
When you understand this relationship, it becomes easier to approach division problems using multiplication facts you already know. It simplifies the process and helps to confirm your results.

Multiplication Facts

Knowing your multiplication facts is like having a handy toolkit for solving division problems. When you're faced with a division problem, knowing the related multiplication facts can make it much simpler to solve.
For example, if you're asked to divide 20 by 4, recall that 4 multiplied by 5 equals 20. So, you instantly know that 20 divided by 4 is 5. This method can save you a lot of time.
Here are some steps to use multiplication facts for division:

• Identify the multiplication fact related to the division problem.
• Use this fact to find the quotient easily.
• For example, if you have 18 divided by 6, remember that 6 times 3 equals 18. So, 18 divided by 6 must be 3.

This approach makes division as straightforward as multiplication.

Division Verification

After solving a division problem, it's essential to verify your answer to ensure it's correct. This can be done using the multiplication facts you already know.
Verification adds an extra layer of confidence in your results.
Here’s how you can do it:

• Once you've found the quotient, multiply it by the divisor.
• Check if the product equals the original number (dividend).
• For example, if you divided 36 by 9 to get 4, multiply 4 by 9 to confirm it equals 36.

By doing this, you ensure your answer is accurate and your method was correct. This step helps strengthen your understanding and leaves no room for doubt.