As technology progresses, mankind ends up dealing with increasingly smaller materials, components and tools. In a world that demands precision, fractions are just a part of life. There's no limit to the amount of accuracy that fractions can express, and this presents challenges when trying to graph them. Your pencil sharpener isn't accurate enough to enable you to graph fractions to the same precision demanded in a machine shop, for instance, but neither is that kind of accuracy required.
Convert the fraction to an integer and a fraction by dividing the numerator by the denominator. The quotient is the integer part of your fraction, and the remainder is the new numerator. If the numerator is smaller than the denominator, the integer is zero. For example, given the fraction 7/3, 7 divided by 3 is 2 with a remainder of 1. Rewrite your fraction as 2 1/3.
Draw out a number line that will accommodate your number, with large spaces between integers. Locate the integer of your fraction on the number line. If your fraction is positive, the fraction will be graphed somewhere in between the integer and the next higher value. If it's negative, you will graph it between the integer and the next lower value. For example, 2 1/3 is positive, so it will be graphed between 2 and the next higher value, 3.
Multiply the numerator of your fraction by 10 and divide by the denominator. If the remainder is greater than half the denominator, round the quotient up by one. For example, with the fraction 1/3, calculate (1 x 10)/3 = 3 with a remainder of 1. The remainder is less than half of 3, so no rounding is necessary, and the resulting quotient is 3. This converts your fraction to an approximate number of 10ths, in this case 3/10.
Imagine 10 divisions between the two integers specified in Step 2. Mark light dots with your pencil to help you see all 10 divisions that fall between two integers. With practice, dividing a segment into 10 parts will come naturally.
Mark the appropriate division that you came up with in Step 3. In the example, that would be the third mark from the left for 3/10. Dividing a segment into 10 parts simplifies graphing fractions, especially when dealing with large denominators. For example, with the fraction 17/36, it would be hard to imagine 36 divisions, so converting it to 10ths makes it much easier. In this case it would be 5/10, which is halfway between the integers 0 and 1.
Choosing 10 divisions isn't essential. You can divide it into as many parts as you want. The smaller your divisions, the more accurate your graph will be, but there comes a point when more accuracy stops being practical. The number 10 works well for decimal values, but the number 16 is a good choice when working with inches, because most rulers divide inches into 16 parts. Multiply the numerator times 16 and divide by the denominator. Round off the result if necessary.