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The number line has 0 as roughly a central point. To the right we have 3⅙ and to the left -6⅖.

We can mark off the whole number positions first from the zero➝1, 2, 3, 4 (to the right) and to zero←-1, -2, -3, -4, -5, -6, -7 (to the left). The gap between the whole numbers can be divided into 30 subdivisions. There’s no need to do this for every whole number, but on the right of zero subdivide between 3 and 4. On the left of zero subdivide between -7 and -6. On the right between 3 and 4 count off 5 subdivisions to represent 3⅙. On the left of -6, between -6 and -7, count off 12 subdivisions to represent -6⅖.

Now count how many whole numbers there are between -6 and 3. There are 9. So what we have left is 12 subdivisions on the left of -6 and 5 subdivisions on the right of 3. Add together these subdivisions and we get 12+5=17. We add because the subdivisions on the right are moving apart from the ones on the left. The subdivisions are 30ths so we have 9 wholes and 17/30. And that is the distance between the numbers: 9¹⁷⁄₃₀.

by Top Rated User (720k points)