How to Use a Number Line to Divide Fractions
Dividing fractions is an aspect of arithmetic that gives many students trouble. Although the procedure of multiplying the dividend by the reciprocal of the divisor to obtain the quotient seems simple enough from a computational standpoint, some people have difficulty visualizing this process. A technique of dividing fractions using a series of number lines enables you to picture the division procedure and may help you to understand the concept.
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Instructions
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Dividing Fractions Using a Number Line
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1
Write down your divisor and dividend, and make sure they are reduced to their most simplified form.
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2
Find the least common denominator by writing down multiples of each denominator and identifying the smallest multiple they have in common. For instance, taking the fractions 1/8 and 3/4 would yield a least common denominator of 8 because 8 is the smallest number that is a multiple of both 4 and 8.
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3
Draw a number line wherein the increments are in the form of the least common denominator. If the least common denominator you have found is 8, then you would create hash marks on the number line like 1/8, 2/8. 3/8, 4/8 until you are confident you have created a long enough number line to conduct your computation. The number line should be at least long enough to fit your largest fraction.
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4
Create a bar directly above your number that represents your dividend. For example, if your lowest common denominator is 8 and your dividend is 3/4, then draw a bar spanning from 0 to 6/8, which is equivalent to 3/4, on your number line.
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5
Construct another bar that represents your divisor directly above the bar depicting your dividend. Draw a bar representing the value of your divisor enough times side-by-side so that the bars at least span the length of your dividend bar. Make sure they are aligned with the hash marks of the number line below. Using the same numbers as in previous steps, if your divisor is 1/8, then you would draw bars with the value of 1/8 on the number line until you had at least reached the end of your dividend bar. This would result in drawing six divisor bars.
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6
Draw a vertical line from the end of your dividend bar up through your divisor bar. Count the number of divisor bars that were drawn without being intersected by the line. In our example, the line would not intersect any bar, so the quotient would simply be 6. If the line does intersect the final bar, determine the value of the fraction on the left side of the intersecting line by using the number line below. Add this fraction to the number of whole bars to get your quotient.
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Tips & Warnings
Using a straight-edge like a ruler to draw your number lines and bars on graph paper will help make the diagrams you draw more visually accurate and easy to understand.
References
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Comments
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this is actually going to help me on my test!, thank you!
