Question

Model -2/3+(-1 1/6) on a number line?

Answer 1

(-5/6)

Explanation:

Start by marking the point 0 on the number line.

To represent -2/3, you'll need to move 2/3 units to the left of 0, since this value is negative. One way to do this is to divide the space between 0 and -1 into three equal parts and move two of them to the left. This brings you to the point -2/3.

To represent (-1 1/6), you'll first need to represent -1, which is one unit to the left of 0. You'll then need to add 1/6 units to the left of -1. One way to do this is to divide the space between -1 and -2 into six equal parts and move one of them to the left. This brings you to the point (-1 1/6).

To find the sum of -2/3 and (-1 1/6), you'll need to add the distances we moved in steps 2 and 3. The total distance moved to the left is 2/3 + 1/6 = 5/6. Starting from 0, we move 5/6 units to the left to arrive at the final point, which is (-5/6).

Answer 2

To model -2/3 + (-1 1/6) on a number line, we first need to convert the mixed number (-1 1/6) into an improper fraction.

-1 1/6 = -7/6

Now we can add -2/3 and -7/6 by finding a common denominator. The smallest common multiple of 3 and 6 is 6, so we'll convert both fractions to have a denominator of 6.

-2/3 = -4/6

-7/6 = -7/6

Now we can add them:

-4/6 + (-7/6) = -11/6

So -2/3 + (-1 1/6) = -11/6.

To model this on a number line, we would start at zero and move to the left by 1 and 2/3 units (since -2/3 is less than 1 whole unit to the left of zero). Then, we would move an additional 1 and 1/6 units to the left (since -1 1/6 is one whole unit and 1/6 of another unit to the left of zero). This would bring us to the point represented by -11/6 on the number line.

Explanation: