QQuestionMathematics
QuestionMathematics
Write a how-many-units-in 1 group word problem for 4 divided by 1 / 3 =? and use your problem and a math drawing, table, or double number line to explain why it makes sense to solve 4 divided by 1 / 3? by "inverting and multiplying" -in other words, by multiplying 4 by 3 / 1
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Step 1:I'll solve this problem step by step, following the specified formatting guidelines:
Problem: How many 1 / 3 -unit groups are in 4 whole units?
Step 2:: Understand the Division Problem
This is a division problem: $$4 \div \frac{1}{3}
The problem asks us to determine how many 1 / 3 -unit groups are contained within 4 whole units.
Step 3:: Visualization Using a Double Number Line
\begin{array}{c|c}
Let's create a conceptual double number line to help understand the division: \text{Whole Units} & \text{1 / 3 -Unit Groups} \ \hline 0 & 0 \ 1 & 3 \ 2 & 6 \ 3 & 9 \ 4 & 12 \end{array}
Step 4:: Explain the Division Strategy
- Multiply $$4 \times \frac{3}{1}
When dividing by a fraction, we can use the "invert and multiply" method. This means: - Change the division to multiplication
Step 5:: Perform the Calculation
4 \div \frac{1}{3} = 4 \times \frac{3}{1} = \frac{4 \times 3}{1} = \frac{12}{1} = 12
Step 6:: Conceptual Explanation
- Each 1 / 3 -unit group is 1 / 3 of a whole unit - To find how many 1 / 3 -unit groups are in 4 whole units, we multiply 4 by 3 - This gives us 12 total 1 / 3 -unit groups
Final Answer
Verification: - 12 \times \frac{1}{3} = 4 ✓ - The double number line shows 12 groups of 1 / 3 indeed equal 4 whole units ✓
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