To multiply a fraction by a whole number on a number line, you represent the whole number as the number of "jumps," and the fraction as the size of each jump.
Here's a breakdown:
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Understand the Problem: Recognize that multiplying a fraction by a whole number is repeated addition of that fraction. For example, 2 * (3/12) means adding 3/12 to itself twice.
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Set up the Number Line: Draw a number line. You don't necessarily need to show all whole numbers; focus on the range needed to represent your answer. Divide the number line into segments representing the denominator of your fraction. For example, if you are working with twelfths (like in the example 3/12), divide the number line into equal segments, each representing 1/12.
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Make the Jumps: Starting at zero, make the number of "jumps" indicated by the whole number. The size of each jump corresponds to the fraction. So, if you're multiplying 2 * (3/12), you'll make two jumps, each covering 3/12 of the number line.
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Determine the Result: The point on the number line where you land after all the jumps is the answer. In the example of 2 * (3/12), you would land on 6/12.
Example:
Let's multiply 2 * (3/12):
- You need to make two jumps.
- Each jump covers 3/12 of the number line.
- The first jump lands you at 3/12.
- The second jump lands you at 6/12.
- Therefore, 2 * (3/12) = 6/12.
You can simplify the resulting fraction if needed (e.g., 6/12 = 1/2).
